Harmonic univalent functions defined by post quantum calculus operators

Certain subclass of $p$-valent meromorphic Bazilevi'{c} functions defined by fractional $q$-calculus operators

The aim of the present paper is to introduce and investigate a new subclass of Bazilevi'{c} functions in the punctured unit disk $mathcal{U}^*$ which have been described through using of the well-known fractional $q$-calculus operators, Hadamard product and a linear operator. In addition, we obtain some sufficient conditions for the func...

On a New Subclass of Harmonic Univalent Functions Defined by Fractional Calculus Operator

The purpose of the present paper is to establish some results involving coefficient conditions, distortion bounds, extreme points, convolution, convex combinations and neighborhoods for a new class of harmonic univalent functions in the open unit disc. We also discuss a class preserving integral operator. Relevant connections of the results presented here with various known results are briefly ...

A Class of Univalent Harmonic Functions Defined by Multiplier Transformation

A continuous function f(x+ iy) = u(x, y) + iv(x, y) defined in a domain D ⊂ C (Complex plane) is harmonic in D if u and v are real harmonic in D. Clunie and Shiel-Small [3] showed that in a simply connected domain such functions can be written in the form f = h+g, where both h and g are analytic. We call h the analytic part and g, the co-analytic part of f . Let w(z) = g ′(z) h′(z) be the dilat...

On Some Subclasses of Harmonic Functions Defined by Fractional Calculus

On Univalent Harmonic Functions

Two classes of univalent harmonic functions on unit disc satisfying the conditions ∑∞ n=2(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) and ∑∞ n=2 n(n−α)(|an|+|bn|) ≤ (1−α)(1−|b1|) are given. That the ranges of the functions belonging to these two classes are starlike and convex, respectively. Sharp coefficient relations and distortion theorems are given for these functions. Furthermore results concerning th...