id sid eid entity type cana-4508 1 1 1074 CARDINAL cana-4508 1 2 32 CARDINAL cana-4508 2 1 9s CARDINAL cana-4508 2 2 2232 DATE cana-4508 3 1 vijayan 𝟏 PERSON cana-4508 5 1 m. sophia πŸ‘ PERSON cana-4508 5 2 πŸ’ 1department ORG cana-4508 5 3 omr ORG cana-4508 5 4 600 CARDINAL cana-4508 5 5 tamilnadu NORP cana-4508 5 6 india GPE cana-4508 7 1 2department TIME cana-4508 7 2 omr ORG cana-4508 7 3 600 CARDINAL cana-4508 7 4 tamilnadu NORP cana-4508 7 5 india GPE cana-4508 9 1 3department PERSON cana-4508 9 2 saveetha nagar PERSON cana-4508 9 3 thandalam GPE cana-4508 9 4 kanchipuram-chennai rd GPE cana-4508 9 5 602105 DATE cana-4508 9 6 tamil nadu LOC cana-4508 9 7 india GPE cana-4508 11 1 coimbatore-641021 DATE cana-4508 11 2 tamilnadu NORP cana-4508 11 3 india GPE cana-4508 12 1 12-01-2025 CARDINAL cana-4508 12 2 15-02-2025 CARDINAL cana-4508 12 3 01-03-2025 CARDINAL cana-4508 16 1 1 CARDINAL cana-4508 17 1 decades DATE cana-4508 18 1 1940 DATE cana-4508 18 2 1 CARDINAL cana-4508 19 1 1941 DATE cana-4508 19 2 donald hyers PERSON cana-4508 19 3 2 CARDINAL cana-4508 19 4 first ORDINAL cana-4508 20 1 3 CARDINAL cana-4508 20 2 4 DATE cana-4508 20 3 5 CARDINAL cana-4508 23 1 6 CARDINAL cana-4508 23 2 7 DATE cana-4508 23 3 8 CARDINAL cana-4508 24 1 1074 CARDINAL cana-4508 24 2 32 CARDINAL cana-4508 25 1 9s CARDINAL cana-4508 26 1 9 CARDINAL cana-4508 26 2 10 DATE cana-4508 26 3 11 DATE cana-4508 26 4 12 DATE cana-4508 26 5 13 CARDINAL cana-4508 28 1 linear ORG cana-4508 35 1 14 CARDINAL cana-4508 35 2 15 DATE cana-4508 35 3 16 DATE cana-4508 35 4 17 DATE cana-4508 35 5 18 DATE cana-4508 35 6 19 DATE cana-4508 35 7 20 DATE cana-4508 37 1 π’³π‘π‘œπ‘ π‘’π‘ β„’ ORG cana-4508 39 1 𝒴𝑠𝑒𝑐 β„’ ORG cana-4508 40 1 π’³π‘π‘œπ‘ π‘’π‘ β„’ ORG cana-4508 41 1 2 DATE cana-4508 42 1 3π‘π‘œπ‘ π‘’π‘2β„’ CARDINAL cana-4508 42 2 2 CARDINAL cana-4508 42 3 3𝑠𝑒𝑐 CARDINAL cana-4508 42 4 1 CARDINAL cana-4508 44 1 π’³π‘π‘œπ‘ π‘’π‘ β„’ ORG cana-4508 46 1 𝒴𝑠𝑒𝑐 β„’ ORG cana-4508 47 1 π’³π‘π‘œπ‘ π‘’π‘ β„’ ORG cana-4508 49 1 2 DATE cana-4508 50 1 2 CARDINAL cana-4508 53 1 3𝑠𝑒𝑐 CARDINAL cana-4508 55 1 1074 CARDINAL cana-4508 55 2 32 CARDINAL cana-4508 56 1 9s CARDINAL cana-4508 56 2 2234 CARDINAL cana-4508 56 3 2 CARDINAL cana-4508 56 4 2.1 CARDINAL cana-4508 57 1 0,∞ DATE cana-4508 58 1 β„› and lim ORG cana-4508 60 1 1 CARDINAL cana-4508 60 2 2 CARDINAL cana-4508 63 1 3 CARDINAL cana-4508 63 2 𝐴(𝒳 GPE cana-4508 63 3 𝐴(𝒳 GPE cana-4508 64 1 π’°β†’βˆž DATE cana-4508 67 1 4 CARDINAL cana-4508 68 1 2 CARDINAL cana-4508 69 1 ≀ 1 CARDINAL cana-4508 69 2 0 DATE cana-4508 69 3 5 CARDINAL cana-4508 69 4 ∈ β„‹. PERSON cana-4508 69 5 5 CARDINAL cana-4508 70 1 2 CARDINAL cana-4508 70 2 2 CARDINAL cana-4508 70 3 2 CARDINAL cana-4508 70 4 6 CARDINAL cana-4508 70 5 5 CARDINAL cana-4508 70 6 6 CARDINAL cana-4508 71 1 2 CARDINAL cana-4508 71 2 2 CARDINAL cana-4508 72 1 7 CARDINAL cana-4508 73 1 2 CARDINAL cana-4508 73 2 2 CARDINAL cana-4508 73 3 ≀ 1 CARDINAL cana-4508 79 1 1074 CARDINAL cana-4508 79 2 32 CARDINAL cana-4508 80 1 9s CARDINAL cana-4508 80 2 2025 CARDINAL cana-4508 80 3 2235 CARDINAL cana-4508 83 1 9 CARDINAL cana-4508 83 2 ∈ ORG cana-4508 85 1 1 CARDINAL cana-4508 85 2 0 CARDINAL cana-4508 87 1 1 CARDINAL cana-4508 98 1 𝐴(𝒳 GPE cana-4508 99 1 π’°β†’βˆž DATE cana-4508 101 1 1 CARDINAL cana-4508 101 2 3 CARDINAL cana-4508 101 3 𝐴 ORG cana-4508 101 4 1 CARDINAL cana-4508 104 1 2 CARDINAL cana-4508 104 2 1 CARDINAL cana-4508 109 1 𝐴(𝒳 GPE cana-4508 110 1 0 CARDINAL cana-4508 111 1 𝐴 ORG cana-4508 111 2 1 CARDINAL cana-4508 111 3 𝐴 ORG cana-4508 111 4 1 CARDINAL cana-4508 111 5 3 CARDINAL cana-4508 111 6 1074 CARDINAL cana-4508 111 7 32 CARDINAL cana-4508 113 1 9s CARDINAL cana-4508 113 2 2236 CARDINAL cana-4508 113 3 1 CARDINAL cana-4508 113 4 𝑁‖𝐴((π‘π‘œπ‘ π‘’π‘ β„’ PERSON cana-4508 121 1 𝐴 ORG cana-4508 122 1 2.2 CARDINAL cana-4508 124 1 1 CARDINAL cana-4508 124 2 𝒯{||𝒳||p||𝒴||p GPE cana-4508 124 3 ||𝒳||2p + ||𝒴||2p DATE cana-4508 124 4 1 2 CARDINAL cana-4508 124 5 10 CARDINAL cana-4508 125 1 βˆ’1 DATE cana-4508 128 1 𝒯||𝒳||2p DATE cana-4508 129 1 2p CARDINAL cana-4508 130 1 11 CARDINAL cana-4508 130 2 3.1 CARDINAL cana-4508 131 1 0,∞ DATE cana-4508 131 2 4 CARDINAL cana-4508 132 1 2n CARDINAL cana-4508 132 2 β„› and lim ORG cana-4508 133 1 2n CARDINAL cana-4508 134 1 0 CARDINAL cana-4508 134 2 12 CARDINAL cana-4508 134 3 13 CARDINAL cana-4508 134 4 1074 CARDINAL cana-4508 134 5 32 CARDINAL cana-4508 135 1 9s CARDINAL cana-4508 135 2 2025 CARDINAL cana-4508 135 3 2237 CARDINAL cana-4508 135 4 𝑄(𝒳)β€– DATE cana-4508 135 5 1 3(π‘π‘œπ‘ π‘’π‘β„’ CARDINAL cana-4508 136 1 2 CARDINAL cana-4508 137 1 2β„‹ CARDINAL cana-4508 137 2 14 CARDINAL cana-4508 137 3 𝐴(𝒳 GPE cana-4508 138 1 2𝑁 CARDINAL cana-4508 138 2 15 CARDINAL cana-4508 139 1 13 CARDINAL cana-4508 140 1 2 CARDINAL cana-4508 140 2 1 3(π‘π‘œπ‘ π‘’π‘β„’ CARDINAL cana-4508 140 3 2𝒯(𝒳 CARDINAL cana-4508 140 4 0 CARDINAL cana-4508 140 5 16 CARDINAL cana-4508 140 6 ∈ β„‹. PERSON cana-4508 140 7 2 CARDINAL cana-4508 140 8 16 CARDINAL cana-4508 141 1 2 CARDINAL cana-4508 141 2 2 CARDINAL cana-4508 141 3 4 β€– ≀ QUANTITY cana-4508 141 4 3(π‘π‘œπ‘ π‘’π‘β„’ CARDINAL cana-4508 141 5 4 CARDINAL cana-4508 141 6 17 CARDINAL cana-4508 141 7 16 CARDINAL cana-4508 141 8 17 CARDINAL cana-4508 141 9 2 CARDINAL cana-4508 142 1 4 CARDINAL cana-4508 143 1 2 CARDINAL cana-4508 143 2 2 CARDINAL cana-4508 143 3 2 CARDINAL cana-4508 143 4 4 CARDINAL cana-4508 143 5 1 3(π‘π‘œπ‘ π‘’π‘β„’ CARDINAL cana-4508 143 6 2 CARDINAL cana-4508 144 1 2 CARDINAL cana-4508 144 2 18 CARDINAL cana-4508 144 3 ∈ ORG cana-4508 146 1 1 3(π‘π‘œπ‘ π‘’π‘β„’ CARDINAL cana-4508 150 1 2β„‹ CARDINAL cana-4508 150 2 1 3(π‘π‘œπ‘ π‘’π‘β„’ CARDINAL cana-4508 154 1 2β„‹ CARDINAL cana-4508 154 2 19 CARDINAL cana-4508 154 3 ∈ ORG cana-4508 154 4 1074 CARDINAL cana-4508 154 5 32 CARDINAL cana-4508 155 1 9s CARDINAL cana-4508 155 2 2238 DATE cana-4508 157 1 2𝑁 DATE cana-4508 157 2 2𝑀 CARDINAL cana-4508 157 3 1 CARDINAL cana-4508 157 4 0 CARDINAL cana-4508 158 1 2𝑀 CARDINAL cana-4508 160 1 2(𝑁+𝑀 CARDINAL cana-4508 160 2 1 CARDINAL cana-4508 164 1 1 3(π‘π‘œπ‘ π‘’π‘β„’ CARDINAL cana-4508 166 1 2(β„‹+𝑀 CARDINAL cana-4508 166 2 1 3(π‘π‘œπ‘ π‘’π‘β„’ CARDINAL cana-4508 169 1 2(β„‹+𝑀 CARDINAL cana-4508 170 1 2𝑁 DATE cana-4508 172 1 1 CARDINAL cana-4508 172 2 14 CARDINAL cana-4508 172 3 1 CARDINAL cana-4508 174 1 2𝑁 CARDINAL cana-4508 174 2 13 CARDINAL cana-4508 174 3 1 CARDINAL cana-4508 178 1 π’¬π‘ž(𝒳,𝒴 PERSON cana-4508 179 1 0 CARDINAL cana-4508 179 2 1074 CARDINAL cana-4508 179 3 32 CARDINAL cana-4508 180 1 9s CARDINAL cana-4508 180 2 2239 CARDINAL cana-4508 180 3 1 CARDINAL cana-4508 180 4 1 CARDINAL cana-4508 180 5 14 CARDINAL cana-4508 180 6 ‖𝐴(𝒳 GPE cana-4508 181 1 1 CARDINAL cana-4508 181 2 2𝑁‖𝐴((π‘π‘œπ‘ π‘’π‘ CARDINAL cana-4508 187 1 2 3(π‘π‘œπ‘ π‘’π‘β„’ CARDINAL cana-4508 190 1 2(β„‹+𝑁 CARDINAL cana-4508 191 1 3.2 CARDINAL cana-4508 193 1 β‰  2 PERSON cana-4508 193 2 𝒯{||𝒳||p||𝒴||p GPE cana-4508 193 3 + { DATE cana-4508 193 4 ||𝒳||2p + ||𝒴||2p DATE cana-4508 193 5 1 CARDINAL cana-4508 193 6 20 CARDINAL cana-4508 194 1 3((cosecβ„’ CARDINAL cana-4508 194 2 4 CARDINAL cana-4508 194 3 2 CARDINAL cana-4508 194 4 3|(cosecβ„’ DATE cana-4508 194 5 4 CARDINAL cana-4508 195 1 2 CARDINAL cana-4508 197 1 3|(cosecβ„’ DATE cana-4508 197 2 4 CARDINAL cana-4508 198 1 2 CARDINAL cana-4508 198 2 2p CARDINAL cana-4508 199 1 21 CARDINAL cana-4508 199 2 4 CARDINAL cana-4508 199 3 4.1 CARDINAL cana-4508 200 1 0,∞ DATE cana-4508 200 2 2.1 CARDINAL cana-4508 200 3 3.1 CARDINAL cana-4508 200 4 22 CARDINAL cana-4508 200 5 1074 CARDINAL cana-4508 200 6 32 CARDINAL cana-4508 201 1 9s CARDINAL cana-4508 201 2 2240 CARDINAL cana-4508 201 3 1 2 CARDINAL cana-4508 201 4 1 CARDINAL cana-4508 208 1 2β„‹ + DATE cana-4508 209 1 2β„‹ CARDINAL cana-4508 209 2 23 CARDINAL cana-4508 209 3 4 CARDINAL cana-4508 209 4 15 CARDINAL cana-4508 210 1 2 CARDINAL cana-4508 211 1 2 CARDINAL cana-4508 212 1 2 CARDINAL cana-4508 212 2 24 CARDINAL cana-4508 212 3 2.1 CARDINAL cana-4508 214 1 1 2(π‘π‘œπ‘ π‘’π‘β„’ CARDINAL cana-4508 219 1 25 CARDINAL cana-4508 219 2 2 CARDINAL cana-4508 219 3 𝒬𝑒(0 PERSON cana-4508 220 1 0 CARDINAL cana-4508 220 2 ∈ β„‹. hence ‖𝒬𝑒(𝒳,𝒴)β€– PERSON cana-4508 220 3 2 + 𝒯(βˆ’π’³,βˆ’π’΄ DATE cana-4508 220 4 2 CARDINAL cana-4508 220 5 26 CARDINAL cana-4508 220 6 3.1 CARDINAL cana-4508 220 7 1 6(π‘π‘œπ‘ π‘’π‘β„’ CARDINAL cana-4508 223 1 2β„‹ + DATE cana-4508 224 1 2β„‹ CARDINAL cana-4508 224 2 27 CARDINAL cana-4508 224 3 28 CARDINAL cana-4508 224 4 28 CARDINAL cana-4508 226 1 𝑄(𝒳)β€– PRODUCT cana-4508 227 1 1 2(π‘π‘œπ‘ π‘’π‘β„’ CARDINAL cana-4508 231 1 1074 CARDINAL cana-4508 231 2 32 CARDINAL cana-4508 232 1 9s CARDINAL cana-4508 232 2 2241 CARDINAL cana-4508 236 1 2β„‹ + DATE cana-4508 237 1 2β„‹ CARDINAL cana-4508 237 2 4.2 CARDINAL cana-4508 238 1 1,2 CARDINAL cana-4508 238 2 𝒯{||𝒳||p||𝒴||p GPE cana-4508 238 3 + { DATE cana-4508 238 4 ||𝒳||2p + ||𝒴||2p DATE cana-4508 238 5 1 2 CARDINAL cana-4508 238 6 1 CARDINAL cana-4508 238 7 29 CARDINAL cana-4508 239 1 βˆ’1 DATE cana-4508 240 1 2 CARDINAL cana-4508 240 2 1 CARDINAL cana-4508 242 1 2 CARDINAL cana-4508 243 1 1 CARDINAL cana-4508 243 2 2𝑃 CARDINAL cana-4508 245 1 2 CARDINAL cana-4508 245 2 2𝑃 CARDINAL cana-4508 246 1 30 CARDINAL cana-4508 246 2 1 CARDINAL cana-4508 246 3 wiley, newyork, 1964 ( ORG cana-4508 246 4 chapter vi PERSON cana-4508 246 5 1 CARDINAL cana-4508 247 1 2 CARDINAL cana-4508 247 2 proc.nat GPE cana-4508 248 1 222 CARDINAL cana-4508 249 1 3 CARDINAL cana-4508 249 2 j. math ORG cana-4508 251 1 japan GPE cana-4508 251 2 2 CARDINAL cana-4508 251 3 1950 DATE cana-4508 251 4 64 CARDINAL cana-4508 252 1 4 CARDINAL cana-4508 253 1 1999 DATE cana-4508 253 2 67 CARDINAL cana-4508 254 1 5 CARDINAL cana-4508 254 2 g. isac PERSON cana-4508 255 1 m. rassias PERSON cana-4508 255 2 j. math PERSON cana-4508 258 1 261 CARDINAL cana-4508 258 2 2001 DATE cana-4508 258 3 543 CARDINAL cana-4508 259 1 6 CARDINAL cana-4508 259 2 approximately of approximately linear DATE cana-4508 259 3 linear ORG cana-4508 259 4 j. funct PERSON cana-4508 261 1 46 DATE cana-4508 261 2 1982 DATE cana-4508 261 3 126 CARDINAL cana-4508 262 1 1074 CARDINAL cana-4508 262 2 32 CARDINAL cana-4508 263 1 9s CARDINAL cana-4508 263 2 2242 CARDINAL cana-4508 264 1 7 CARDINAL cana-4508 264 2 approximately of approximately linear DATE cana-4508 264 3 linear ORG cana-4508 265 1 sc GPE cana-4508 265 2 108 CARDINAL cana-4508 265 3 1984 DATE cana-4508 265 4 445 CARDINAL cana-4508 266 1 8 CARDINAL cana-4508 266 2 k.w. jun PERSON cana-4508 266 3 h.m. kim PERSON cana-4508 266 4 acta mathematica sinica PERSON cana-4508 266 5 english LANGUAGE cana-4508 266 6 27 CARDINAL cana-4508 266 7 10 CARDINAL cana-4508 266 8 2011 DATE cana-4508 266 9 1907-1922 DATE cana-4508 267 1 9 CARDINAL cana-4508 267 2 ioan a. PERSON cana-4508 268 1 babesbolyai GPE cana-4508 268 2 mathematica 4 PERSON cana-4508 268 3 2009 DATE cana-4508 269 1 10 CARDINAL cana-4508 269 2 amjad ali PERSON cana-4508 269 3 kamal shah PERSON cana-4508 269 4 ali khan PERSON cana-4508 271 1 j. nonlinear sci. PERSON cana-4508 271 2 10 CARDINAL cana-4508 271 3 6 (2017 CARDINAL cana-4508 271 4 2986-2997 DATE cana-4508 272 1 11 CARDINAL cana-4508 272 2 snezhana GPE cana-4508 272 3 hristova GPE cana-4508 272 4 donal o’regan PERSON cana-4508 274 1 12 DATE cana-4508 274 2 11 CARDINAL cana-4508 274 3 2024): 1626 DATE cana-4508 275 1 12 CARDINAL cana-4508 275 2 alina ramona PERSON cana-4508 275 3 dorian popa PERSON cana-4508 276 1 malaysian NORP cana-4508 276 2 mathematical sciences ORG cana-4508 276 3 2 CARDINAL cana-4508 276 4 2020): 13571371 DATE cana-4508 277 1 13 CARDINAL cana-4508 277 2 a.k. GPE cana-4508 277 3 2021 CARDINAL cana-4508 280 1 14 CARDINAL cana-4508 280 2 konsalraj ORG cana-4508 280 3 j. PERSON cana-4508 280 4 fatima PERSON cana-4508 280 5 n. PERSON cana-4508 280 6 mlaiki PERSON cana-4508 280 7 normed ORG cana-4508 281 1 2022 CARDINAL cana-4508 281 2 14 DATE cana-4508 281 3 1700 DATE cana-4508 282 1 15 CARDINAL cana-4508 282 2 k. PERSON cana-4508 282 3 mlaiki PERSON cana-4508 282 4 n. PERSON cana-4508 282 5 mukheimer DATE cana-4508 282 6 a. intuitionistic PERSON cana-4508 282 7 euler PERSON cana-4508 282 8 lagrange GPE cana-4508 283 1 2022 CARDINAL cana-4508 283 2 14 DATE cana-4508 283 3 2454 DATE cana-4508 284 1 16 CARDINAL cana-4508 284 2 k.; alsinai, PERSON cana-4508 284 3 normed ORG cana-4508 285 1 2023 CARDINAL cana-4508 285 2 11 DATE cana-4508 285 3 681 CARDINAL cana-4508 286 1 17 CARDINAL cana-4508 286 2 k almazah ORG cana-4508 287 1 2023 CARDINAL cana-4508 287 2 11 DATE cana-4508 287 3 887 CARDINAL cana-4508 288 1 18 CARDINAL cana-4508 288 2 ahmad PERSON cana-4508 288 3 p. agilan PERSON cana-4508 288 4 k. julietraja PERSON cana-4508 288 5 s. annadurai PERSON cana-4508 288 6 nabil mlaiki PERSON cana-4508 289 1 neutrosophic normed ORG cana-4508 290 1 2024 DATE cana-4508 290 2 1 CARDINAL cana-4508 290 3 2024 CARDINAL cana-4508 290 4 47 DATE cana-4508 291 1 19 CARDINAL cana-4508 291 2 k. PERSON cana-4508 291 3 kanimozhi PERSON cana-4508 291 4 b. PERSON cana-4508 291 5 a. PERSON cana-4508 292 1 2024, 31 DATE cana-4508 292 2 63 CARDINAL cana-4508 293 1 20 CARDINAL cana-4508 293 2 k, ORG cana-4508 293 3 sarah aljohani PERSON cana-4508 293 4 nabil mlaiki PERSON cana-4508 295 1 j. anal PERSON cana-4508 296 1 22 2024 CARDINAL cana-4508 296 2 201 CARDINAL cana-4508 297 1 1074 CARDINAL cana-4508 297 2 32 CARDINAL cana-4508 298 1 9s CARDINAL cana-4508 298 2 2243 CARDINAL cana-4508 299 1 21 CARDINAL cana-4508 299 2 vijayan.v, sophia.m, ganapathy.g ORG cana-4508 299 3 neutrosophic normed ORG cana-4508 300 1 2025 DATE cana-4508 300 2 32 CARDINAL cana-4508 301 1 7s CARDINAL cana-4508 301 2 2025 DATE cana-4508 301 3 806 CARDINAL cana-4508 302 1 vijayan.v ORG cana-4508 302 2 sophia PERSON cana-4508 303 1 normed ORG cana-4508 303 2 2025 DATE cana-4508 303 3 32 CARDINAL cana-4508 305 1 9s CARDINAL