In the present paper certain subclasses of strongly starlike and strongly convex functions defined by convolution with the generalized Hurwitz -Lerch Zeta function are investigated. Some inclusion relations are also mentioned as special cases of our main results.

In the present investigation we solve Fekete–Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions.

Keywords: Analytic functions Differential subordination Ma–Minda type starlike and convex functions Integral operators a b s t r a c t Two integral operators on the classes consisting of normalized p-valent Ma–Minda type starlike and convex functions are considered. Functions in these classes have the form zf ′ (z)/f (z) ≺ pϕ(z) and 1 + zf ′′ (z)/f ′ (z) ≺ pϕ(z) respectively, where ϕ is a conve...

For r > 0, let Dr := {z ∈ C : |z| < r} and D := D1 be the open unit disk in the complex plane C. Let A denote the family of all functions f that are analytic in D with the normalization f(0) = 0 = f ′(0) − 1. Let S denote the class of functions in A that are univalent in D. A domain D in C is called starlike (with respect to the origin) if every line segment joining the origin to any other poin...

Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the form f z zh z g z defined on the open unit disc U. The functions are in the class of the generalized Janowski starlike log-harmonic mapping, Slh A,B, α , with the functional zh z in the class of the generalized Janowski starlike functions, S∗ A,B, α . By means ...

We consider the class of analytic functions B(α) to investigate some properties for this class. The angular estimates of functions in the class B(α) are obtained. Finally, we derive some interesting conditions for the class of strongly starlike and strongly convex of order α in the open unit disk. 2000 Mathematics Subject Classification. Primary 30C45.

In this paper, we introduce some new subclasses of analytic functions related to starlike, convex, close-to-convex and quasi-convex functions defined by using a generalized operator and the differential subordination principle. Inclusion relationships for these subclasses are established. Moreover, we introduce some integral-preserving properties. Key-Words: Starlike function; Convex function; ...

In this paper, we introduce new general integral operators. New sufficient conditions for these operators to be p-valently starlike, p-valently close-to-convex, uniformly p-valent close-to-convex and strongly starlike of order γ (0 < γ ≤ 1) in the open unit disk are obtained.

By using the method of differential subordinations, we derive certain sufficient conditions for strongly starlike functions associated with an integral operator. All these results presented here are sharp. 2000 Mathematics Subject Classification. Primary 30C45; Secondary 30A10.