In this paper, various features of a new class normalized multivalent harmonic functions in the open unit disk are analyzed, including bounds on coefficients, growth estimations, starlikeness and convexity radii. It is further demonstrated that closed when its members convoluted. can also be seen previously introduced investigated classes appear as special cases for class.

Abstract The aim of this paper is to prove the theorem which generates many examples functions belonging a geometrically defined class uniformly starlike introduced by Goodman in 1991. Only very few explicit were known until now. Next we obtain inclusion relations between some subclasses convex and functions.

Motivated by the recent work on symmetric domains, this article investigates certain features of domain which are caused secant hyperbolic functions. Geometric characteristics analytic functions associated with discussed, include inclusion results, structural formula, sharp radii results such as radius starlikeness and convexity order α. It also finds a for ratios Euler numbers.

In this paper, our main focus is to define a new subfamily of q-analogue analytic functions associated with the q-cosine function. Furthermore, we investigate some useful results such as necessary and sufficient condition based on convolution idea, growth distortion bounds, closure theorem, convex combination, radii starlikeness, extreme point theorem partial sums for newly-defined class.