A New Subclass of Salagean‐Type Harmonic Univalent Functions

Abstract

We define and investigate a new subclass of Salagean-type harmonic univalent functions. We obtain coefficient conditions, extreme points, distortion bounds, convolution, and convex combination for the above subclass of harmonic functions.which are analytic in the open unit disk Í {z ∈ : |z| < 1}.We denote the subclass of A consisting of analytic and univalent functions f z in the unit disk Í by S.The following classes of functions and many others are well known and have been studied repeatedly by many authors, namely, Sȃlȃgean 1 , Abdul Halim 2 , and Darus 3 to mention but a few.2 Abstract and Applied Analysis iii δ α {f z ∈ A : Re{f z } > α, 0 ≤ α < 1, z ∈ Í}.

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“…Note that this problem has yet to be solved for certain classes introduced in various studies (see for examples [5], [21], [22] and [23]). Note that Hankel problems have also been solved successfully for fractional operator which can be seen in [20].…”

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“…Note that this problem has yet to be solved for certain classes introduced in various studies (see for examples [5], [21], [22] and [23]). Note that Hankel problems have also been solved successfully for fractional operator which can be seen in [20].…”