On a generalization of uniformly convex and related functions

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Abstract

In this paper, we define and study some subclasses of analytic functions by using the concept of k-uniformly convexity. Several interesting properties, coefficients and radius problems are investigated. The behaviour of these classes under a certain integral operator is also studied. We indicate the relevant connections of our results with various known ones.

Keywords

Conic domains
Univalent
k-uniformly convex
Bounded boundary rotation
Subordination
Integral operator
Caratheodory functions
Elliptic integral

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