On Classes of Functions Related to Starlike Functions with Respect to Symmetric Conjugate Points Defined by a Fractional Differential Operator |
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| Authors: | F. M. Al-Oboudi |
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| Affiliation: | 1. Department of Mathematical Sciences, Faculty of Science, Princess Nora Bint Abdul Rahman University, Riyadh, Saudi Arabia
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| Abstract: | Let A denote the class of analytic functions f, in the open unit disk E = {z : |z| < 1}, normalized by f(0) = f′(0) − 1 = 0. In this paper, we introduce and study the class STn,al,m(h){ST^{n,alpha}_{lambda,m}(h)} of functions f ? A{fin A}, with fracDn,al fm(z)z 1 0{frac{D^{n,alpha}_lambda f_m(z)}{z}neq 0}, satisfying | fracz(Dn,al f(z))￠Dn,al fm(z)prec h(z), z ? E,frac{zleft(D^{n,alpha}_lambda f(z)right)'}{D^{n,alpha}_lambda f_m(z)}prec h(z),quad zin E, |
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