Harmonic functions with missing coefficients

On Meromorphic Harmonic Starlike Functions with Missing Coefficients

Subclass of Multivalent Harmonic Functions with Missing Coefficients

A continuous function f u iv is a complex-valued harmonic function in a simply connected complex domain D ⊂ C if both u and v are real harmonic in D. It was shown by Clunie and Sheil-Small 1 that such harmonic function can be represented by f h g, where h and g are analytic in D. Also, a necessary and sufficient condition for f to be locally univalent and sense preserving in D is that |h′ z | >...

On a class of analytic functions with missing coefficients

and Applied Analysis 3 2. The bounds on Ref ′ z , Re f z /z , and |f z | in Tn A,B, γ, α In this section, we let λm ( A,B, γ ) ⎧ ⎪ ⎪⎨ ⎪ ⎪⎩ m ∑ j 0 ⎛ ⎝ γ j ⎞ ⎠ ⎛ ⎝ −γ m − j ⎞ ⎠AjBm−j , ( A ≤ 1; 0 < γ < 1, A − B −B m−1, γ 1, 2.1

Sakaguchi - Type Harmonic Univalent Functions with Negative Coefficients

A subclass of harmonic univalent functions with negative coefficients

Abstract In this paper we introduce a new family Ā(α, β, γ) of harmonic univalent functions with negative coefficients using fractional calculus operator Ωλwhich contains various well known classes of harmonic univalent functions as well as many new ones. We obtain coefficient estimate, distortion theorem and various other properties for functions belonging to the class Ā(α, β, γ) in the unit d...