id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-5356	Debasmita Dash, Saumya Singh	A New Subclass of Meromorphic Functions Associated with Sălăgean Operator 	2025	10	.pdf	application/pdf	3967	176	70	For the series 𝑆1 and 𝑆2,the terms of 𝑧𝑗+𝑝. Since 𝑧𝑗+𝑝 terms are independent of the constant parts, we can combine the inequalities to solve for the coefficients 𝑎𝑗 , given the following condition must hold: (𝑘 + 1)|2 − 𝛾 − 𝑛(1 − 𝛼)| {(1 − 𝜆) (1 + 𝑗 𝑝 )} 𝑛 (1 + 𝑗)𝑎𝑗 ≤ (1 − 𝛽)(𝛼𝑗 + 1 − 𝑟) {(1 − 𝜆) (1 + 𝑗 𝑝 )} 𝑛 𝑎𝑗 Then dividing both sides by {(1 − 𝜆) (1 + 𝑗 𝑝 )} 𝑛 , we get (𝑘 + 1)|2 − 𝛾 − 𝑛(1 − 𝛼)|(1 + 𝑗)𝑎𝑗 ≤ (1 − 𝛽)(𝛼𝑗 + 1 − 𝑟)𝑎𝑗 For non- zero 𝑎𝑗 , divide through by 𝑎𝑗 (𝑘 + 1)|2 1074-133X Vol 32 No. 10s (2025) 1877 https://internationalpubls.com Then expand and simplify (𝑘 + 1)|2 − 𝛾 − 𝑛(1 − 𝛼)| ≤ (1 − 𝛽) (𝛼𝑗 + 1 − 𝑟) (1 + 𝑗) This gives a bound for the coefficients 𝑎𝑗 Then the solution depends on analysing the coefficients 𝑎𝑗 satisfying: 𝑎𝑗 ≤ (1 − 𝛽)(𝛼𝑗 + 1 − 𝑟) (𝑘 + 1)|2 − 𝛾 − 𝑛(1 − 𝛼)|(1 + 𝑗)	cache/cana-5356.pdf	txt/cana-5356.txt