The aim of present investigation is to study a new class analytic function related with the Sokol-Nunokawa class. We derived relationships this strongly starlike functions and obtained many interesting results.

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 the present paper, we introduce and investigate some properties of two subclasses $ Lambda_{n}( lambda , beta ) $ and $ Lambda_{n}^{+}( lambda , beta ) $;  meromorphic and starlike  functions of order $ beta $. In particular, several inclusion relations, coefficient estimates, distortion theorems and covering theorems are proven here for each of these function classes.

In this paper, we introduce and investigate two new subclasses of the functions class $ Sigma $ of bi-univalent functions defined in the open unit disk, which are associated with the Aghalary-Ebadian-Wang operator. We  estimate the coefficients $|a_{2} |$ and  $|a_{3} |$ for functions in these new subclasses. Several  consequences of the result are also pointed out.

and Applied Analysis 3 where we refer to 1.4 for the am’s and we follow the convention ∏m−1 j m · · · 1. We can easily check that cm’s satisfy the following relation: m 2 m 1 cm 2 − ( m2 − n2 ) cm am 2.2 for any m ∈ {0, 1, 2, . . .}. Theorem 2.1. Assume that n is a positive integer and the radius of convergence of the power series ∑∞ m 0 amx m is ρ > 0. Let ρ0 min{1, ρ}. Then, every solution y ...

We survey the recent results concerning the applications of power series method to the study of Hyers–Ulam stability of differential equations.

The purpose of this present paper is to derive some subordination and superordination results for certain analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.

In this paper‎, ‎we introduce a new class$T_{k}^{s,a}[A,B,alpha‎ ,‎beta ]$ of analytic functions by using a‎ ‎newly defined convolution operator‎. ‎This class contains many known classes of‎ ‎analytic and univalent functions as special cases‎. ‎We derived some‎ ‎interesting results including inclusion relationships‎, ‎a radius problem and‎ ‎sharp coefficient bound for this class‎.