In this work, applying Lemma due to Nunokawa et. al. cite{NCKS}, we obtain some sufficient inequalities for some certain subclasses of univalent functions.

It is shown that an analytic function taking circles to ellipses must be a Möbius transformation. It then follows that a harmonic mapping taking circles to ellipses is a harmonic Möbius transformation. Analytic Möbius transformations take circles to circles. This is their most basic, most celebrated geometric property. We add the adjective ‘analytic’ because in a previous paper [1] we introduce...

In this work, the subclass of the function class S of analytic and bi-univalent functions is defined and studied in the open unit disc. Estimates for initial coefficients of Taylor- Maclaurin series of bi-univalent functions belonging these class are obtained. By choosing the special values for parameters and functions it is shown that the class reduces to several earlier known classes of analy...

in this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk. upper bounds for the second and third coefficients of functions in this subclass are founded. our results, which are presented in this paper, generalize and improve those in related works of several earlier authors.

Given two univalent harmonic mappings f1 and f2 on D, which lift to minimal surfaces via the Weierstrass-Enneper representation theorem, we give necessary and sufficient conditions for f3 = (1−s)f1+sf2 to lift to a minimal surface for s ∈ [0, 1]. We then construct such mappings from Enneper’s surface to Scherk’s singularly periodic surface, Sckerk’s doubly periodic surface to the catenoid, and ...