Convex sum of univalent functions

Convex and Starlike Univalent Functions

Generating Starlike and Convex Univalent Functions

Alexander [1] was the first to introduce certain subclasses of univalent functions examining the geometric properties of the image f(D) of D under f . The convex functions are those that map D onto a convex set. A function w = f(z) is said to be starlike if, together with any of its points w, the image f(D) contains the entire segment {tw : 0 ≤ t ≤ 1}. Thus we introduce the denotations S = {f ∈...

Subclasses of Univalent Functions Subordinate to Convex Functions

In this paper, we define a new subclass Ao(A, B) of univalent functions and investigate several interesting characterization theorems involving a general class S" [A, B] of starlike functions

On a Subclass of Quasi-Convex Univalent Functions

Abstract: The aim of this paper is to introduce and study a new class [ ] * C A,B, δ α of Janowski QuasiConvex univalent functions of order alpha associated with Ruscheweyh derivative. Sharp coefficient bound, distortion result and some inclusion results are discussed. Invariance of [ ] * C A,B, δ α under convolution with convex functions has also been examined and some of its applications are ...

Distributed Optimization of Convex Sum of Non-Convex Functions

We present a distributed solution to optimizing a convex function composed of several nonconvex functions. Each non-convex function is privately stored with an agent while the agents communicate with neighbors to form a network. We show that coupled consensus and projected gradient descent algorithm proposed in [1] can optimize convex sum of non-convex functions under an additional assumption o...