In this paper, we define a generalized class of starlike functions which are based upon some convolution operators on Hilbert space involving the Fox-Wright generalization of the classical hypergeometric pFq function (with p numerator and q denominator parameters). The various results presented in this paper include (for example) normed coefficient inequalities and estimates, distortion theorem...

"In this paper, we consider the complex form of a new generalization Bernstein-Schurer operators. We obtain some quantitative upper estimates for approximation these operators attached to analytic functions. Moreover, prove that preserve properties original function such as univalence, starlikeness, convexity and spirallikeness."

The focus of this article is the introduction a new subclass analytic functions involving q-analogue Bessel function and obtained coefficient inequities, growth distortion properties, radii close-to-convexity, starlikeness, as well convex linear combination. Furthermore, we discussed partial sums, convolution, neighborhood properties for defined class.

An interesting criterion was given by Tuneski [N. Tuneski, On the quotient of the representations of convexity and starlikeness, Math. Nachr. 248–249 (2003) 200–203] for the analytic functions to be in the class S 1⁄21þAz 1þBz and its subclasses, where 1 6 B < A 6 1. This result is an extension of an earlier result of Silverman [H. Silverman, Convex and starlike criteria, Int. Math. Math. Sci. ...

The purpose of this paper is to introduce two novel subclasses Γλ n, α, β and Γλ n, α, β of meromorphic p-valent functions by using the linear operator D λ . Then we prove the necessary and sufficient conditions for a function f in order to be in the new classes. Further we study several important properties such as coefficients inequalities, inclusion properties, the growth and distortion theo...

It is known that the condition $mathfrak {Re} left{zf'(z)/f(z)right}>0$, $|z|

This article considers three types of analytic functions based on their infinite product representation. The radius the k-parabolic starlikeness these classes is studied. optimal parameter values for starlike are determined in unit disk. Several examples provided that include special such as Bessel, Struve, Lommel, and q-Bessel functions.