id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
cana-5236	Rashmi B T., Dileep L.	On Class of Analytic Function Defined by Generalized Ruscheweyh Derivative	2025	10	.pdf	application/pdf	3476	209	86	(𝐷𝜆 𝑚𝑓(𝑧))′ ) ≥ 𝑅𝑒 𝑝(𝑧) {𝑎 + 2(1 − 𝑎)(1 − 𝐵2𝑟2) 2 + (𝐴 − 𝐵)𝑘𝑟 − 2𝐴𝐵𝑟2 − 2𝑎𝑟{(𝐴 − 𝐵)𝑘 − 4𝐵(𝐴 − 𝐵)𝑟 + 𝐵2(𝐴 − 𝐵)𝑘𝑟2} (2 + (𝐴 − 𝐵)𝑘𝑟 − 2𝐴𝐵𝑟2)𝜉 } = 𝑅𝑒 𝑝(𝑧) { 𝑎1𝑟4 + 𝑎2𝑟3 + 𝑎3𝑟2 + 𝑎4𝑟 + 4(2𝑎 − 1) (2 + (𝐴 − 𝐵)𝑘𝑟 − 2𝐴𝐵𝑟2)𝜉 } > 0, provided 𝑇(𝑟) = 𝑎1𝑟4 + 𝑎2𝑟3 + 𝑎3𝑟2 + 𝑎4𝑟 + 4(2𝑎 − 1) > 0, where 𝑎1 = 4𝑎2𝐴2𝐵2 − 4(𝑎 − 1)2𝐵4 𝑎2 = 2a(2a − 1)(B − A)𝐵2𝑘 𝑎3 = 8𝑎2(𝑎 − 2) + 8𝑎(1 − 𝑎)𝐴𝐵 − 𝑎2(𝐴 − 𝐵)2𝑘2 𝑎4 = 2𝑎(2𝑎 − 3)(𝐴 − 𝐵)𝑘 and 𝜉 = 2(2𝑎 − 1) − 𝑎(𝐴 − 𝐵)𝑘𝑟 + 2(𝐵2 − 𝑎(𝐴 + 𝐵)𝐵)𝑟2. [1, −1, 𝛽, 𝑏 + 1], z 𝜖 𝒰, where β (0 ≤ β < 1) is one of the roots of (3.3) 𝜂1𝜂2𝑏2(𝑚 + 2)2(1 − 𝛼)2 − 𝑏(𝑚 + 2)(1 − 𝛼)[𝜂1(𝐵 + 1) + 𝜂2(𝐵 − 1)] + (𝐵2 − 1)	cache/cana-5236.pdf	txt/cana-5236.txt