id	sid	eid	entity	type
ejpam-6699	1	1	european journal	ORG
ejpam-6699	1	2	2025	DATE
ejpam-6699	1	3	18	CARDINAL
ejpam-6699	1	4	4	CARDINAL
ejpam-6699	1	5	6699	CARDINAL
ejpam-6699	1	6	new york	GPE
ejpam-6699	1	7	non-archimedean	NORP
ejpam-6699	1	8	senthil gowri1	PERSON
ejpam-6699	1	9	siriluk donganont2,∗	PERSON
ejpam-6699	1	10	s. karthick3	PERSON
ejpam-6699	1	11	radhakrishnan balaanandhan4	PERSON
ejpam-6699	1	12	tamilvanan5 1	ORG
ejpam-6699	1	13	saveetha institute of medical	ORG
ejpam-6699	1	14	saveetha university	ORG
ejpam-6699	1	15	602105	DATE
ejpam-6699	1	16	tamil	NORP
ejpam-6699	1	17	india	GPE
ejpam-6699	1	18	2	CARDINAL
ejpam-6699	1	19	university of phayao	ORG
ejpam-6699	1	20	56000	CARDINAL
ejpam-6699	1	21	thailand 3	ORG
ejpam-6699	1	22	srm institute of science and technology	ORG
ejpam-6699	1	23	kattankulathur 603203	GPE
ejpam-6699	1	24	tamil nadu	LOC
ejpam-6699	1	25	india	GPE
ejpam-6699	1	26	4	CARDINAL
ejpam-6699	1	27	sri sankara	ORG
ejpam-6699	1	28	631561	DATE
ejpam-6699	1	29	kanchipuram	GPE
ejpam-6699	1	30	tamil	GPE
ejpam-6699	1	31	india	GPE
ejpam-6699	1	32	5	CARDINAL
ejpam-6699	2	1	kavaraipettai	PERSON
ejpam-6699	2	2	tamil	NORP
ejpam-6699	2	3	india	GPE
ejpam-6699	3	1	non-archimedean	NORP
ejpam-6699	3	2	non-archimedean	NORP
ejpam-6699	5	1	non-archimedean	NORP
ejpam-6699	7	1	2020	DATE
ejpam-6699	7	2	39b52	CARDINAL
ejpam-6699	7	3	39b72	DATE
ejpam-6699	7	4	46s40	CARDINAL
ejpam-6699	7	5	non-archimedean	NORP
ejpam-6699	7	6	1	CARDINAL
ejpam-6699	10	1	1	CARDINAL
ejpam-6699	10	2	1940	DATE
ejpam-6699	10	3	first	ORDINAL
ejpam-6699	12	1	https://doi.org/10.29020/nybg.ejpam.v18i4.6699	PERSON
ejpam-6699	12	2	s. gowri	PERSON
ejpam-6699	12	3	siriluk.pa@up.ac.th	PERSON
ejpam-6699	12	4	s. donganont	PERSON
ejpam-6699	12	5	s. karthick	PERSON
ejpam-6699	12	6	r.	NORP
ejpam-6699	12	7	k. tamilvanan	PERSON
ejpam-6699	13	1	1	CARDINAL
ejpam-6699	13	2	2025	CARDINAL
ejpam-6699	14	1	s. gowri et al	PERSON
ejpam-6699	15	1	j. pure	PERSON
ejpam-6699	15	2	18	CARDINAL
ejpam-6699	15	3	4	CARDINAL
ejpam-6699	15	4	2025	CARDINAL
ejpam-6699	15	5	6699 2	CARDINAL
ejpam-6699	15	6	14	CARDINAL
ejpam-6699	17	1	2	CARDINAL
ejpam-6699	17	2	1941	DATE
ejpam-6699	17	3	first	ORDINAL
ejpam-6699	19	1	fourth	ORDINAL
ejpam-6699	23	1	4[τ(t1	CARDINAL
ejpam-6699	27	1	normed	ORG
ejpam-6699	27	2	3–9	CARDINAL
ejpam-6699	28	1	non-archimedean	NORP
ejpam-6699	28	2	normed	ORG
ejpam-6699	29	1	algebraic properties	ORG
ejpam-6699	29	2	10	CARDINAL
ejpam-6699	31	1	normed	ORG
ejpam-6699	32	1	12–14]).these	NORP
ejpam-6699	32	2	1	CARDINAL
ejpam-6699	33	1	15–17	CARDINAL
ejpam-6699	34	1	non-archimedean	NORP
ejpam-6699	35	1	18–27	CARDINAL
ejpam-6699	36	1	non-archimedean	NORP
ejpam-6699	39	1	i=1 ti	PERSON
ejpam-6699	40	1	1≤i	CARDINAL
ejpam-6699	41	1	1≤i	CARDINAL
ejpam-6699	41	2	2	CARDINAL
ejpam-6699	41	3	1	CARDINAL
ejpam-6699	41	4	s. gowri et al	PERSON
ejpam-6699	42	1	j. pure	PERSON
ejpam-6699	42	2	18	CARDINAL
ejpam-6699	42	3	4	CARDINAL
ejpam-6699	42	4	2025	CARDINAL
ejpam-6699	42	5	6699 3	DATE
ejpam-6699	43	1	1	CARDINAL
ejpam-6699	43	2	4	CARDINAL
ejpam-6699	43	3	non-archimedean	NORP
ejpam-6699	44	1	2	CARDINAL
ejpam-6699	45	1	2 ≤	QUANTITY
ejpam-6699	45	2	1	CARDINAL
ejpam-6699	46	1	28	CARDINAL
ejpam-6699	47	1	∥β	PERSON
ejpam-6699	47	2	0	CARDINAL
ejpam-6699	48	1	νn∥β	ORG
ejpam-6699	48	2	νn∥β	ORG
ejpam-6699	48	3	νn−1	NORP
ejpam-6699	48	4	νn−1	PERSON
ejpam-6699	48	5	νn−1	PERSON
ejpam-6699	49	1	∥β	PERSON
ejpam-6699	50	1	1	CARDINAL
ejpam-6699	50	2	1	CARDINAL
ejpam-6699	51	1	2	CARDINAL
ejpam-6699	52	1	28	CARDINAL
ejpam-6699	54	1	n ∈ z+	ORG
ejpam-6699	55	1	∥β	PERSON
ejpam-6699	55	2	∈	ORG
ejpam-6699	55	3	0	CARDINAL
ejpam-6699	56	1	νn∥β	ORG
ejpam-6699	56	2	νn∥β	ORG
ejpam-6699	56	3	νn∥β ≤ max {	PERSON
ejpam-6699	56	4	νn∥β	ORG
ejpam-6699	57	1	∥β	PERSON
ejpam-6699	57	2	non-archimedean	NORP
ejpam-6699	58	1	1	CARDINAL
ejpam-6699	59	1	25	CARDINAL
ejpam-6699	61	1	∈ z.	PERSON
ejpam-6699	62	1	non-archimedean	NORP
ejpam-6699	66	1	3	CARDINAL
ejpam-6699	66	2	1	CARDINAL
ejpam-6699	66	3	n. s. gowri et al	PERSON
ejpam-6699	67	1	j. pure	PERSON
ejpam-6699	67	2	18	CARDINAL
ejpam-6699	67	3	4	CARDINAL
ejpam-6699	67	4	2025	CARDINAL
ejpam-6699	67	5	6699	CARDINAL
ejpam-6699	67	6	4	CARDINAL
ejpam-6699	67	7	14	CARDINAL
ejpam-6699	67	8	1	CARDINAL
ejpam-6699	68	1	28	CARDINAL
ejpam-6699	68	2	non-archimedean	NORP
ejpam-6699	68	3	zero	CARDINAL
ejpam-6699	69	1	1	CARDINAL
ejpam-6699	70	1	28	CARDINAL
ejpam-6699	70	2	lim	PERSON
ejpam-6699	70	3	e. lemma	PERSON
ejpam-6699	71	1	2	CARDINAL
ejpam-6699	72	1	28	CARDINAL
ejpam-6699	72	2	∥β	PERSON
ejpam-6699	72	3	0	CARDINAL
ejpam-6699	73	1	0	CARDINAL
ejpam-6699	73	2	1	CARDINAL
ejpam-6699	74	1	29	CARDINAL
ejpam-6699	74	2	1	CARDINAL
ejpam-6699	75	1	2.1	CARDINAL
ejpam-6699	76	1	non-archimedean	NORP
ejpam-6699	76	2	non-archimedean	NORP
ejpam-6699	77	1	normed vector	ORG
ejpam-6699	77	2	ultrametric constraints	ORG
ejpam-6699	79	1	2	CARDINAL
ejpam-6699	80	1	28	CARDINAL
ejpam-6699	80	2	30	DATE
ejpam-6699	80	3	k.	PERSON
ejpam-6699	82	1	∥β	PERSON
ejpam-6699	86	1	xn)|β	PERSON
ejpam-6699	88	1	non-archimedean	NORP
ejpam-6699	90	1	3	CARDINAL
ejpam-6699	91	1	28	CARDINAL
ejpam-6699	91	2	30	DATE
ejpam-6699	91	3	31	CARDINAL
ejpam-6699	91	4	zero	CARDINAL
ejpam-6699	91	5	non-archimedean	NORP
ejpam-6699	91	6	k.	PERSON
ejpam-6699	94	1	m∈n ∣∣∣det(x(m	PERSON
ejpam-6699	94	2	1	CARDINAL
ejpam-6699	94	3	2	CARDINAL
ejpam-6699	99	1	non-archimedean	NORP
ejpam-6699	101	1	∥β	PERSON
ejpam-6699	102	1	1	CARDINAL
ejpam-6699	103	1	28	CARDINAL
ejpam-6699	105	1	xn	ORG
ejpam-6699	105	2	non-archimedean	NORP
ejpam-6699	106	1	s. gowri et al	PERSON
ejpam-6699	107	1	j. pure	PERSON
ejpam-6699	107	2	18	CARDINAL
ejpam-6699	107	3	4	CARDINAL
ejpam-6699	107	4	2025	CARDINAL
ejpam-6699	107	5	6699 5	DATE
ejpam-6699	110	1	0	CARDINAL
ejpam-6699	112	1	0	CARDINAL
ejpam-6699	113	1	∈	ORG
ejpam-6699	113	2	x3	GPE
ejpam-6699	115	1	xn−1	GPE
ejpam-6699	116	1	x3	GPE
ejpam-6699	118	1	xn−1	GPE
ejpam-6699	118	2	xn∥β	ORG
ejpam-6699	119	1	x3	GPE
ejpam-6699	121	1	xn−1	GPE
ejpam-6699	121	2	x3	GPE
ejpam-6699	123	1	xn−1	GPE
ejpam-6699	123	2	∥y	PERSON
ejpam-6699	123	3	x3	GPE
ejpam-6699	125	1	xn−1	GPE
ejpam-6699	126	1	3	CARDINAL
ejpam-6699	128	1	∥β	PERSON
ejpam-6699	129	1	non-archimedean	NORP
ejpam-6699	129	2	n ≥ 2	ORG
ejpam-6699	130	1	1	CARDINAL
ejpam-6699	133	1	i=1 ti	PERSON
ejpam-6699	134	1	1≤i	CARDINAL
ejpam-6699	135	1	1≤i	CARDINAL
ejpam-6699	137	1	26r + 120 6	DATE
ejpam-6699	139	1	2	CARDINAL
ejpam-6699	140	1	4	CARDINAL
ejpam-6699	140	2	2	CARDINAL
ejpam-6699	140	3	0,∞	DATE
ejpam-6699	140	4	0,∞	DATE
ejpam-6699	140	5	0,∞	DATE
ejpam-6699	147	1	νn−1	PERSON
ejpam-6699	147	2	2	CARDINAL
ejpam-6699	149	1	∈	ORG
ejpam-6699	150	1	νn−1 ∈	PERSON
ejpam-6699	154	1	νn−1	PERSON
ejpam-6699	154	2	3	CARDINAL
ejpam-6699	156	1	νn−1 ∈	PERSON
ejpam-6699	157	1	s. gowri et al	PERSON
ejpam-6699	158	1	j. pure	PERSON
ejpam-6699	158	2	18	CARDINAL
ejpam-6699	158	3	4	CARDINAL
ejpam-6699	158	4	2025	CARDINAL
ejpam-6699	158	5	6699 6	CARDINAL
ejpam-6699	158	6	14	CARDINAL
ejpam-6699	160	1	0	DATE
ejpam-6699	162	1	0	CARDINAL
ejpam-6699	162	2	2	CARDINAL
ejpam-6699	162	3	obtain∥∥ϕ(2t)− 24ϕ(t	DATE
ejpam-6699	163	1	νn−1	PRODUCT
ejpam-6699	165	1	νn−1	PERSON
ejpam-6699	166	1	4	CARDINAL
ejpam-6699	166	2	4	CARDINAL
ejpam-6699	166	3	gives∥∥∥∥ϕ(2t)24 − ϕ(t	PERSON
ejpam-6699	168	1	νn−1	NORP
ejpam-6699	170	1	νn−1	PERSON
ejpam-6699	171	1	5	CARDINAL
ejpam-6699	171	2	2pt	ORG
ejpam-6699	171	3	5	CARDINAL
ejpam-6699	172	1	24p	CARDINAL
ejpam-6699	174	1	νn−1	NORP
ejpam-6699	176	1	νn−1	PERSON
ejpam-6699	176	2	∣∣∣p µ∥t∥sβ1 ϖ(ν1	PERSON
ejpam-6699	178	1	νn−1	PERSON
ejpam-6699	179	1	6	CARDINAL
ejpam-6699	179	2	|2|	ORG
ejpam-6699	179	3	1	CARDINAL
ejpam-6699	180	1	6	CARDINAL
ejpam-6699	180	2	zero	CARDINAL
ejpam-6699	180	3	24p	CARDINAL
ejpam-6699	182	1	24p	CARDINAL
ejpam-6699	182	2	∈	ORG
ejpam-6699	182	3	q4	PERSON
ejpam-6699	182	4	2	CARDINAL
ejpam-6699	182	5	1	CARDINAL
ejpam-6699	185	1	νn−1∥β = lim	PERSON
ejpam-6699	187	1	2ptr	DATE
ejpam-6699	188	1	∣∣∣p	PERSON
ejpam-6699	190	1	νn−1	PERSON
ejpam-6699	191	1	0	CARDINAL
ejpam-6699	192	1	lemma 2	ORG
ejpam-6699	192	2	q4	PERSON
ejpam-6699	192	3	q4	PERSON
ejpam-6699	193	1	5	CARDINAL
ejpam-6699	193	2	∥∥∥∥ϕ(t)−	ORG
ejpam-6699	193	3	24p	CARDINAL
ejpam-6699	195	1	νn−1	NORP
ejpam-6699	197	1	νn−1	PERSON
ejpam-6699	198	1	q4	PERSON
ejpam-6699	198	2	3	CARDINAL
ejpam-6699	200	1	4	CARDINAL
ejpam-6699	200	2	3	CARDINAL
ejpam-6699	203	1	νn−1	PRODUCT
ejpam-6699	203	2	∣∣∣	CARDINAL
ejpam-6699	203	3	4(2	CARDINAL
ejpam-6699	205	1	νn−1	PRODUCT
ejpam-6699	205	2	max	PERSON
ejpam-6699	207	1	4(2	CARDINAL
ejpam-6699	209	1	νn−1	PRODUCT
ejpam-6699	209	2	∣∣∣p ∥t∥sβ1 ϖ(ν1	PERSON
ejpam-6699	211	1	νn−1	PERSON
ejpam-6699	212	1	q′	PERSON
ejpam-6699	212	2	4(t	DATE
ejpam-6699	212	3	q4	PERSON
ejpam-6699	212	4	one	CARDINAL
ejpam-6699	212	5	3	CARDINAL
ejpam-6699	213	1	s. gowri et al	PERSON
ejpam-6699	214	1	j. pure	PERSON
ejpam-6699	214	2	18	CARDINAL
ejpam-6699	214	3	4	CARDINAL
ejpam-6699	214	4	2025	CARDINAL
ejpam-6699	214	5	6699 7	DATE
ejpam-6699	214	6	14	CARDINAL
ejpam-6699	214	7	3	CARDINAL
ejpam-6699	215	1	0,∞	DATE
ejpam-6699	215	2	0,∞	DATE
ejpam-6699	216	1	0,∞	DATE
ejpam-6699	222	1	νn−1	PERSON
ejpam-6699	222	2	9	CARDINAL
ejpam-6699	226	1	νn−1 ∈	PERSON
ejpam-6699	230	1	νn−1	PERSON
ejpam-6699	230	2	10	CARDINAL
ejpam-6699	232	1	νn−1 ∈	PERSON
ejpam-6699	235	1	0	DATE
ejpam-6699	237	1	0	CARDINAL
ejpam-6699	237	2	9	CARDINAL
ejpam-6699	237	3	have∥∥ϕ(2t)−	PRODUCT
ejpam-6699	239	1	νn−1	PRODUCT
ejpam-6699	241	1	νn−1	PERSON
ejpam-6699	242	1	11	CARDINAL
ejpam-6699	242	2	11	CARDINAL
ejpam-6699	242	3	24ϕ	CARDINAL
ejpam-6699	244	1	νn−1	NORP
ejpam-6699	246	1	νn−1	PERSON
ejpam-6699	247	1	12	CARDINAL
ejpam-6699	247	2	12	CARDINAL
ejpam-6699	247	3	2p	CARDINAL
ejpam-6699	248	1	24(p+1)ϕ	CARDINAL
ejpam-6699	249	1	νn−1	NORP
ejpam-6699	249	2	∣∣∣p ∥t∥sβ1 ϖ(ν1	PERSON
ejpam-6699	251	1	νn−1	PERSON
ejpam-6699	252	1	13	CARDINAL
ejpam-6699	252	2	|2|	ORG
ejpam-6699	252	3	1	CARDINAL
ejpam-6699	253	1	13	CARDINAL
ejpam-6699	253	2	zero	CARDINAL
ejpam-6699	255	1	p→∞ 24pϕ	DATE
ejpam-6699	255	2	2p	CARDINAL
ejpam-6699	255	3	14	CARDINAL
ejpam-6699	256	1	q4	PERSON
ejpam-6699	257	1	9	CARDINAL
ejpam-6699	257	2	1	CARDINAL
ejpam-6699	257	3	∥∆q4(t1	DATE
ejpam-6699	260	1	νn−1∥β = lim	PERSON
ejpam-6699	260	2	∣∣∣24pβ∣∣∣	DATE
ejpam-6699	260	3	2p	CARDINAL
ejpam-6699	262	1	2p	CARDINAL
ejpam-6699	264	1	νn−1	NORP
ejpam-6699	264	2	∥tj∥sβ1 ϖ(ν1	PERSON
ejpam-6699	266	1	νn−1	PERSON
ejpam-6699	267	1	0	CARDINAL
ejpam-6699	268	1	lemma 2	ORG
ejpam-6699	269	1	10	CARDINAL
ejpam-6699	269	2	12	CARDINAL
ejpam-6699	270	1	2p	CARDINAL
ejpam-6699	272	1	νn−1	NORP
ejpam-6699	274	1	νn−1	PERSON
ejpam-6699	275	1	15	CARDINAL
ejpam-6699	275	2	s. gowri et al	PERSON
ejpam-6699	276	1	j. pure	PERSON
ejpam-6699	276	2	18	CARDINAL
ejpam-6699	276	3	4	CARDINAL
ejpam-6699	276	4	2025	CARDINAL
ejpam-6699	276	5	6699 8	DATE
ejpam-6699	276	6	14	CARDINAL
ejpam-6699	276	7	15	CARDINAL
ejpam-6699	276	8	q4	PERSON
ejpam-6699	276	9	14	CARDINAL
ejpam-6699	276	10	10	CARDINAL
ejpam-6699	277	1	4	CARDINAL
ejpam-6699	277	2	10	CARDINAL
ejpam-6699	280	1	νn−1	PRODUCT
ejpam-6699	280	2	∣∣∣24pβ∣∣∣	CARDINAL
ejpam-6699	280	3	2p	CARDINAL
ejpam-6699	281	1	4	CARDINAL
ejpam-6699	281	2	2p	CARDINAL
ejpam-6699	283	1	νn−1	NORP
ejpam-6699	283	2	2p	CARDINAL
ejpam-6699	284	1	2p	CARDINAL
ejpam-6699	284	2	2p	CARDINAL
ejpam-6699	284	3	4	CARDINAL
ejpam-6699	284	4	2p	CARDINAL
ejpam-6699	284	5	∣∣∣p ∥t∥sβ1 ϖ(ν1	PERSON
ejpam-6699	285	1	νn−1	PERSON
ejpam-6699	286	1	zero	CARDINAL
ejpam-6699	290	1	νn−1	PRODUCT
ejpam-6699	290	2	0	CARDINAL
ejpam-6699	290	3	lemma 2	ORG
ejpam-6699	290	4	q4 = q′ 4.	PERSON
ejpam-6699	291	1	q4	PERSON
ejpam-6699	292	1	4	CARDINAL
ejpam-6699	293	1	0,∞	DATE
ejpam-6699	293	2	lim	ORG
ejpam-6699	293	3	2pt1	ORG
ejpam-6699	295	1	2	CARDINAL
ejpam-6699	296	1	0	CARDINAL
ejpam-6699	297	1	16	CARDINAL
ejpam-6699	298	1	0,∞	DATE
ejpam-6699	299	1	∥∆ϕ(t1	ORG
ejpam-6699	305	1	tr)ϖ(ν1	GPE
ejpam-6699	307	1	νn−1	PERSON
ejpam-6699	307	2	17	CARDINAL
ejpam-6699	309	1	∈	ORG
ejpam-6699	310	1	νn−1 ∈	PERSON
ejpam-6699	314	1	νn−1	PERSON
ejpam-6699	314	2	18	CARDINAL
ejpam-6699	315	1	max	PERSON
ejpam-6699	315	2	∣∣∣2−4iβ	GPE
ejpam-6699	315	3	2i−1	CARDINAL
ejpam-6699	315	4	0	DATE
ejpam-6699	315	5	0	DATE
ejpam-6699	317	1	1 ≤	QUANTITY
ejpam-6699	317	2	19	CARDINAL
ejpam-6699	318	1	lim t→∞ lim	PERSON
ejpam-6699	318	2	max	PERSON
ejpam-6699	318	3	∣∣∣2−4iβ	GPE
ejpam-6699	318	4	2i−1	CARDINAL
ejpam-6699	318	5	0	DATE
ejpam-6699	318	6	0	DATE
ejpam-6699	320	1	1 + t ≤	QUANTITY
ejpam-6699	320	2	0	CARDINAL
ejpam-6699	320	3	20	CARDINAL
ejpam-6699	323	1	0	DATE
ejpam-6699	325	1	0	CARDINAL
ejpam-6699	325	2	17	CARDINAL
ejpam-6699	325	3	− ϕ(t	PERSON
ejpam-6699	327	1	νn−1	NORP
ejpam-6699	327	2	0	DATE
ejpam-6699	329	1	0)ϖ(ν1	CARDINAL
ejpam-6699	331	1	νn−1	PERSON
ejpam-6699	332	1	21	CARDINAL
ejpam-6699	332	2	s. gowri et al	PERSON
ejpam-6699	333	1	j. pure	PERSON
ejpam-6699	333	2	18	CARDINAL
ejpam-6699	333	3	4	CARDINAL
ejpam-6699	333	4	2025	CARDINAL
ejpam-6699	333	5	6699 9	DATE
ejpam-6699	333	6	14	CARDINAL
ejpam-6699	333	7	2it	ORG
ejpam-6699	333	8	get∥∥∥∥ϕ(2i+1	ORG
ejpam-6699	333	9	24(i+1	CARDINAL
ejpam-6699	333	10	24i	DATE
ejpam-6699	335	1	νn−1	NORP
ejpam-6699	335	2	2it	ORDINAL
ejpam-6699	335	3	0	DATE
ejpam-6699	337	1	0	DATE
ejpam-6699	338	1	νn−1	PERSON
ejpam-6699	339	1	22	CARDINAL
ejpam-6699	339	2	16	CARDINAL
ejpam-6699	339	3	zero	CARDINAL
ejpam-6699	339	4	24	CARDINAL
ejpam-6699	341	1	m→∞	CARDINAL
ejpam-6699	341	2	24	CARDINAL
ejpam-6699	343	1	17	CARDINAL
ejpam-6699	343	2	1	CARDINAL
ejpam-6699	343	3	q4	PERSON
ejpam-6699	346	1	νn−1∥β = lim	PERSON
ejpam-6699	346	2	1 24p ∆ϕ	QUANTITY
ejpam-6699	346	3	2pt1	ORG
ejpam-6699	348	1	2	CARDINAL
ejpam-6699	349	1	νn−1	NORP
ejpam-6699	349	2	2pt1	ORG
ejpam-6699	351	1	2	CARDINAL
ejpam-6699	352	1	νn−1	PERSON
ejpam-6699	353	1	0	CARDINAL
ejpam-6699	354	1	lemma 2,	ORG
ejpam-6699	354	2	q4	PERSON
ejpam-6699	355	1	21	CARDINAL
ejpam-6699	355	2	obtain:∥∥∥∥ϕ(t)−	ORG
ejpam-6699	355	3	28	DATE
ejpam-6699	356	1	νn−1	NORP
ejpam-6699	356	2	0	DATE
ejpam-6699	357	1	0	DATE
ejpam-6699	357	2	0	DATE
ejpam-6699	359	1	0	DATE
ejpam-6699	361	1	νn−1	PERSON
ejpam-6699	362	1	get:∥∥∥∥ϕ(t)−	NORP
ejpam-6699	362	2	24p	CARDINAL
ejpam-6699	363	1	νn−1	NORP
ejpam-6699	363	2	∣∣∣	MONEY
ejpam-6699	363	3	2t−1	CARDINAL
ejpam-6699	363	4	0	DATE
ejpam-6699	365	1	1 ≤	MONEY
ejpam-6699	367	1	νn−1	PERSON
ejpam-6699	368	1	23	CARDINAL
ejpam-6699	368	2	23	CARDINAL
ejpam-6699	368	3	18	CARDINAL
ejpam-6699	368	4	19	CARDINAL
ejpam-6699	369	1	4	CARDINAL
ejpam-6699	369	2	18	CARDINAL
ejpam-6699	372	1	νn−1	PRODUCT
ejpam-6699	372	2	∣∣∣	CARDINAL
ejpam-6699	372	3	∥∥q4(2	GPE
ejpam-6699	372	4	4(2 tt	PERCENT
ejpam-6699	374	1	νn−1	PRODUCT
ejpam-6699	374	2	∥∥q4(2	GPE
ejpam-6699	375	1	4(2 tt	QUANTITY
ejpam-6699	376	1	νn−1	PERSON
ejpam-6699	377	1	20	CARDINAL
ejpam-6699	377	2	zero	CARDINAL
ejpam-6699	379	1	νn−1	PRODUCT
ejpam-6699	379	2	0	CARDINAL
ejpam-6699	379	3	lemma 2	ORG
ejpam-6699	379	4	q4	DATE
ejpam-6699	379	5	4	CARDINAL
ejpam-6699	380	1	q4	PERSON
ejpam-6699	381	1	s. gowri et al	PERSON
ejpam-6699	382	1	j. pure	PERSON
ejpam-6699	382	2	18	CARDINAL
ejpam-6699	382	3	4	CARDINAL
ejpam-6699	382	4	2025	CARDINAL
ejpam-6699	382	5	6699 10	DATE
ejpam-6699	382	6	14	CARDINAL
ejpam-6699	383	1	0,∞	DATE
ejpam-6699	383	2	lim	ORG
ejpam-6699	383	3	2p	CARDINAL
ejpam-6699	383	4	2p	CARDINAL
ejpam-6699	385	1	2p	CARDINAL
ejpam-6699	386	1	24	CARDINAL
ejpam-6699	387	1	0,∞	DATE
ejpam-6699	388	1	∥∆ϕ(t1	ORG
ejpam-6699	394	1	tr)ϖ(ν1	GPE
ejpam-6699	396	1	νn−1	PERSON
ejpam-6699	396	2	25	CARDINAL
ejpam-6699	398	1	∈	ORG
ejpam-6699	399	1	νn−1 ∈	PERSON
ejpam-6699	403	1	νn−1	PERSON
ejpam-6699	403	2	26	CARDINAL
ejpam-6699	405	1	max	PERSON
ejpam-6699	405	2	0	DATE
ejpam-6699	405	3	0	DATE
ejpam-6699	407	1	1 ≤	QUANTITY
ejpam-6699	408	1	27	CARDINAL
ejpam-6699	408	2	lim t→∞ lim	PERSON
ejpam-6699	408	3	max	PERSON
ejpam-6699	408	4	0	DATE
ejpam-6699	408	5	0	DATE
ejpam-6699	410	1	1 + t ≤	QUANTITY
ejpam-6699	410	2	0	CARDINAL
ejpam-6699	410	3	28	CARDINAL
ejpam-6699	410	4	q4	PERSON
ejpam-6699	413	1	0	DATE
ejpam-6699	415	1	0	CARDINAL
ejpam-6699	415	2	25	CARDINAL
ejpam-6699	415	3	obtain∥∥ϕ(2t)− 24ϕ(t	DATE
ejpam-6699	417	1	νn−1	PRODUCT
ejpam-6699	417	2	0	DATE
ejpam-6699	419	1	0)ϖ(ν1	CARDINAL
ejpam-6699	421	1	νn−1	PERSON
ejpam-6699	422	1	29	CARDINAL
ejpam-6699	422	2	24pϕ	ORDINAL
ejpam-6699	422	3	2p	CARDINAL
ejpam-6699	423	1	30	CARDINAL
ejpam-6699	423	2	24	CARDINAL
ejpam-6699	423	3	4	CARDINAL
ejpam-6699	425	1	p→∞ 24pϕ	DATE
ejpam-6699	425	2	2p	CARDINAL
ejpam-6699	425	3	30	CARDINAL
ejpam-6699	425	4	ϕ(t	PERSON
ejpam-6699	428	1	νn−1	PERSON
ejpam-6699	428	2	26	CARDINAL
ejpam-6699	429	1	q4	PERSON
ejpam-6699	433	1	νn−1∥β = lim	PERSON
ejpam-6699	433	2	∣∣∣24pβ∣∣∣	DATE
ejpam-6699	433	3	2p	CARDINAL
ejpam-6699	435	1	2p	CARDINAL
ejpam-6699	437	1	νn−1	NORP
ejpam-6699	437	2	s. gowri et al	PERSON
ejpam-6699	438	1	j. pure	PERSON
ejpam-6699	438	2	18	CARDINAL
ejpam-6699	438	3	4	CARDINAL
ejpam-6699	438	4	2025	CARDINAL
ejpam-6699	438	5	6699 11	DATE
ejpam-6699	438	6	14	CARDINAL
ejpam-6699	438	7	zero	CARDINAL
ejpam-6699	438	8	24	CARDINAL
ejpam-6699	438	9	q4	PERSON
ejpam-6699	439	1	4	CARDINAL
ejpam-6699	439	2	26	CARDINAL
ejpam-6699	442	1	νn−1	PRODUCT
ejpam-6699	442	2	2	CARDINAL
ejpam-6699	443	1	4	CARDINAL
ejpam-6699	443	2	2	CARDINAL
ejpam-6699	445	1	νn−1	NORP
ejpam-6699	445	2	2	CARDINAL
ejpam-6699	446	1	νn−1	PERSON
ejpam-6699	446	2	0	CARDINAL
ejpam-6699	447	1	28	CARDINAL
ejpam-6699	449	1	q4 = q′ 4	PERSON
ejpam-6699	449	2	lemma 2.	ORG
ejpam-6699	449	3	4	CARDINAL
ejpam-6699	449	4	4.1	CARDINAL
ejpam-6699	449	5	non-archimedean	NORP
ejpam-6699	449	6	non-archimedean	NORP
ejpam-6699	449	7	normed	ORG
ejpam-6699	450	1	1	CARDINAL
ejpam-6699	450	2	∥∆ϕ(t1	ORG
ejpam-6699	452	1	∥tj∥s	PERSON
ejpam-6699	452	2	0	CARDINAL
ejpam-6699	452	3	1	CARDINAL
ejpam-6699	454	1	∥ϕ(t)−q4(t)∥ ≤ µ|2−4|∥t∥s	FAC
ejpam-6699	454	2	∈	ORG
ejpam-6699	454	3	4.2	CARDINAL
ejpam-6699	454	4	non-archimedean	NORP
ejpam-6699	454	5	0	CARDINAL
ejpam-6699	454	6	1	CARDINAL
ejpam-6699	455	1	∥∆ϕ(t1	ORG
ejpam-6699	458	1	∈	ORG
ejpam-6699	458	2	∈	ORG
ejpam-6699	460	1	4.3	CARDINAL
ejpam-6699	460	2	3	CARDINAL
ejpam-6699	461	1	ϕ(t	PERSON
ejpam-6699	462	1	t4	PERSON
ejpam-6699	462	2	4	CARDINAL
ejpam-6699	463	1	2	CARDINAL
ejpam-6699	463	2	only one	CARDINAL
ejpam-6699	464	1	t4	PERSON
ejpam-6699	465	1	s. gowri et al	PERSON
ejpam-6699	466	1	j. pure	PERSON
ejpam-6699	466	2	18	CARDINAL
ejpam-6699	466	3	4	CARDINAL
ejpam-6699	466	4	2025	CARDINAL
ejpam-6699	466	5	6699 12	DATE
ejpam-6699	466	6	14 5	DATE
ejpam-6699	467	1	non-archimedean	NORP
ejpam-6699	468	1	normed	ORG
ejpam-6699	468	2	ultrametric structures	ORG
ejpam-6699	469	1	2	CARDINAL
ejpam-6699	469	2	3	CARDINAL
ejpam-6699	469	3	non-archimedean	NORP
ejpam-6699	469	4	non-archimedean	NORP
ejpam-6699	470	1	4	CARDINAL
ejpam-6699	470	2	5	CARDINAL
ejpam-6699	471	1	non-archimedean	NORP
ejpam-6699	472	1	6	CARDINAL
ejpam-6699	474	1	university of phayao	ORG
ejpam-6699	474	2	thailand science	ORG
ejpam-6699	474	3	2026	CARDINAL
ejpam-6699	476	1	1	CARDINAL
ejpam-6699	476	2	s. m. ulam	PERSON
ejpam-6699	478	1	interscience	ORG
ejpam-6699	478	2	new york	GPE
ejpam-6699	478	3	ny, usa, 1960	ORG
ejpam-6699	479	1	2	CARDINAL
ejpam-6699	479	2	d. h. hyers	PERSON
ejpam-6699	481	1	the national academy of sciences of the usa	ORG
ejpam-6699	481	2	27:222–224	CARDINAL
ejpam-6699	481	3	1941	DATE
ejpam-6699	482	1	3	CARDINAL
ejpam-6699	482	2	s. czerwik	PERSON
ejpam-6699	484	1	singapore	GPE
ejpam-6699	484	2	2002	DATE
ejpam-6699	485	1	s. gowri et al	PERSON
ejpam-6699	486	1	j. pure	PERSON
ejpam-6699	486	2	18	CARDINAL
ejpam-6699	486	3	4	CARDINAL
ejpam-6699	486	4	2025	CARDINAL
ejpam-6699	486	5	6699 13	DATE
ejpam-6699	486	6	4	CARDINAL
ejpam-6699	486	7	s. m. jung	PERSON
ejpam-6699	488	1	new york	GPE
ejpam-6699	488	2	ny, usa, 2011	ORG
ejpam-6699	489	1	5	CARDINAL
ejpam-6699	489	2	h. azadi kenary	PERSON
ejpam-6699	489	3	h. rezaei	PERSON
ejpam-6699	489	4	m. sharifzadeh	PERSON
ejpam-6699	489	5	d. y. shin	PERSON
ejpam-6699	489	6	j. r. lee	PERSON
ejpam-6699	491	1	1–17	CARDINAL
ejpam-6699	491	2	2012	DATE
ejpam-6699	492	1	6	CARDINAL
ejpam-6699	492	2	y. s. lee	PERSON
ejpam-6699	492	3	s. y. chung	PERSON
ejpam-6699	494	1	2009	DATE
ejpam-6699	495	1	7	CARDINAL
ejpam-6699	497	1	4:91–96, 2003	DATE
ejpam-6699	498	1	8	CARDINAL
ejpam-6699	498	2	m. rassias	PERSON
ejpam-6699	500	1	american	NORP
ejpam-6699	500	2	72:297–300	CARDINAL
ejpam-6699	500	3	1978	DATE
ejpam-6699	501	1	9	CARDINAL
ejpam-6699	501	2	k. tamilvanan	PERSON
ejpam-6699	501	3	h. k. nashine	PERSON
ejpam-6699	501	4	r. george	PERSON
ejpam-6699	502	1	1:1–9	CARDINAL
ejpam-6699	502	2	2022	CARDINAL
ejpam-6699	503	1	10	CARDINAL
ejpam-6699	503	2	n. koblitz	PERSON
ejpam-6699	505	1	new york	GPE
ejpam-6699	505	2	ny, usa, 1984	ORG
ejpam-6699	506	1	11	CARDINAL
ejpam-6699	506	2	w. h. schikhof	PERSON
ejpam-6699	507	1	ultrametric	PERSON
ejpam-6699	508	1	cambridge university press	ORG
ejpam-6699	508	2	cambridge	GPE
ejpam-6699	508	3	uk	GPE
ejpam-6699	508	4	1984	DATE
ejpam-6699	509	1	12	CARDINAL
ejpam-6699	509	2	s. bosch	PERSON
ejpam-6699	509	3	r. remmert	PERSON
ejpam-6699	510	1	non-archimedean	NORP
ejpam-6699	511	1	berlin/heidelberg	ORG
ejpam-6699	511	2	germany	GPE
ejpam-6699	511	3	1984	DATE
ejpam-6699	512	1	13	CARDINAL
ejpam-6699	512	2	f. q. gouvêa	PERSON
ejpam-6699	514	1	berlin/heidelberg	ORG
ejpam-6699	514	2	germany	GPE
ejpam-6699	514	3	2nd	ORDINAL
ejpam-6699	514	4	1997	DATE
ejpam-6699	515	1	14	CARDINAL
ejpam-6699	515	2	a. f. monna	PERSON
ejpam-6699	516	1	dirichlet	PERSON
ejpam-6699	517	1	reidel	NORP
ejpam-6699	517	2	dordrecht	ORG
ejpam-6699	517	3	netherlands	GPE
ejpam-6699	517	4	1975	DATE
ejpam-6699	518	1	15	CARDINAL
ejpam-6699	518	2	n. alessa	PERSON
ejpam-6699	518	3	k. tamilvanan	PERSON
ejpam-6699	518	4	k. loganathan	PERSON
ejpam-6699	518	5	k. k. selvi	PERSON
ejpam-6699	519	1	non-archimedean	NORP
ejpam-6699	520	1	2021:9953214	DATE
ejpam-6699	520	2	2021	DATE
ejpam-6699	521	1	16	CARDINAL
ejpam-6699	521	2	j. konsalraj	PERSON
ejpam-6699	521	3	n. fatima	PERSON
ejpam-6699	521	4	n. mlaiki	PERSON
ejpam-6699	521	5	n. souayah	PERSON
ejpam-6699	522	1	normed	ORG
ejpam-6699	522	2	8:1700	DATE
ejpam-6699	522	3	2022	CARDINAL
ejpam-6699	523	1	17	CARDINAL
ejpam-6699	523	2	r. k. sharma	PERSON
ejpam-6699	523	3	s. chandok	PERSON
ejpam-6699	524	1	non-archimedean	NORP
ejpam-6699	525	1	2022	CARDINAL
ejpam-6699	526	1	18	CARDINAL
ejpam-6699	526	2	j. aczél	PERSON
ejpam-6699	528	1	new york	GPE
ejpam-6699	528	2	ny, usa, 1966	ORG
ejpam-6699	529	1	19	CARDINAL
ejpam-6699	529	2	b. radhakrishnan	PERSON
ejpam-6699	529	3	k. tamilvanan	PERSON
ejpam-6699	531	1	11(19):1–18	DATE
ejpam-6699	531	2	2023	CARDINAL
ejpam-6699	532	1	20	CARDINAL
ejpam-6699	532	2	j. c. bae	PERSON
ejpam-6699	532	3	c. g. park	PERSON
ejpam-6699	534	1	9:103–110, 2004	DATE
ejpam-6699	535	1	21	CARDINAL
ejpam-6699	535	2	e. castillo	PERSON
ejpam-6699	537	1	springer, cham	ORG
ejpam-6699	537	2	switzerland	GPE
ejpam-6699	537	3	2021	DATE
ejpam-6699	538	1	22	CARDINAL
ejpam-6699	538	2	s. s. dragomir	PERSON
ejpam-6699	540	1	s. gowri et al	PERSON
ejpam-6699	541	1	j. pure	PERSON
ejpam-6699	541	2	18	CARDINAL
ejpam-6699	541	3	4	CARDINAL
ejpam-6699	541	4	2025	CARDINAL
ejpam-6699	541	5	6699 14	DATE
ejpam-6699	541	6	14	CARDINAL
ejpam-6699	541	7	tamkang journal of mathematics, 31:223–234, 2000	ORG
ejpam-6699	542	1	23	CARDINAL
ejpam-6699	542	2	m. s. khan	PERSON
ejpam-6699	542	3	m. imdad	PERSON
ejpam-6699	543	1	kannan	GPE
ejpam-6699	543	2	non-archimedean	NORP
ejpam-6699	544	1	23:1–12	CARDINAL
ejpam-6699	544	2	2021	CARDINAL
ejpam-6699	545	1	24	CARDINAL
ejpam-6699	545	2	d. miheţ.	PERSON
ejpam-6699	545	3	normed	ORG
ejpam-6699	546	1	9:1–6, 2008	DATE
ejpam-6699	547	1	25	CARDINAL
ejpam-6699	547	2	b. radhakrishnan	PERSON
ejpam-6699	549	1	iaeng international journal of applied mathematics	ORG
ejpam-6699	549	2	53(3):1–7	CARDINAL
ejpam-6699	549	3	2022	CARDINAL
ejpam-6699	550	1	26	CARDINAL
ejpam-6699	550	2	b. radhakrishnan	PERSON
ejpam-6699	550	3	s. o. hilali	PERSON
ejpam-6699	550	4	m. kameswari	PERSON
ejpam-6699	550	5	m. alhagyan	PERSON
ejpam-6699	550	6	k. tamilvanan	PERSON
ejpam-6699	550	7	a. gargouri	PERSON
ejpam-6699	551	1	ultrametric spaces	ORG
ejpam-6699	552	1	2024	DATE
ejpam-6699	553	1	27	CARDINAL
ejpam-6699	555	1	24:23–34	CARDINAL
ejpam-6699	555	2	2022	CARDINAL
ejpam-6699	556	1	28	CARDINAL
ejpam-6699	556	2	l. chang	PERSON
ejpam-6699	556	3	g. liu	PERSON
ejpam-6699	556	4	g. shen	PERSON
ejpam-6699	558	1	2015	DATE
ejpam-6699	559	1	29	CARDINAL
ejpam-6699	559	2	s. pinelas	ORG
ejpam-6699	559	3	v. govindan	PERSON
ejpam-6699	559	4	k. tamilvanan	PERSON
ejpam-6699	561	1	2018(20):1–10	CARDINAL
ejpam-6699	561	2	2018	DATE
ejpam-6699	562	1	30	CARDINAL
ejpam-6699	562	2	l. i. cădariu	PERSON
ejpam-6699	562	3	radu	PERSON
ejpam-6699	563	1	41:25–48, 2003	DATE
ejpam-6699	564	1	31	CARDINAL
ejpam-6699	564	2	jung	PERSON
ejpam-6699	566	1	2003	DATE