Applications on a subclass of β-uniformly starlike functions connected with q-Borel distribution

The aim of this paper is to define the operator of [Formula: see text]-derivative based upon the Borel distribution and by using this operator, we familiarize a new subclass of [Formula: see text]-uniformly starlike functions [Formula: see text]-[Formula: see text] Further, we obtain coefficient estimates, distortion theorems, convex linear combinations and radii of close-to-convexity, starlikeness and convexity for functions [Formula: see text]-[Formula: see text] We also determine the second Hankel inequality for functions belonging to this subclass.

Certain Properties of Komatu Integral Transform with Negative Coefficients with Reference to Uniform Starlike and Uniform Convex Functions

The authors obtained a new subclass about strongly starlike and strongly convex functions with respect to Komatu integral transforms and the inclusion properties of these classes such as 𝓢𝒑𝑻(𝝀, 𝑰𝝂 𝝆 ) and 𝓤𝓒𝓥𝓣(𝝀, 𝑰𝝂 𝝆 ) were discussed . Furthermore, a new subclass about uniformly starlike functions along uniformly convex functions including negative coefficients defined by the Komatu integral transforms are introduced. The various properties about these classes are obtained here including (for instance) coefficient estimates, extreme points, distortion and covering theorems. Mathematics Subject Classification: Primary 30C45

A Subclass of Analytic Functions Related tok-Uniformly Convex and Starlike Functions

We investigate some subclasses ofk-uniformly convex andk-uniformly starlike functions in open unit disc, which is generalization of class of convex and starlike functions. Some coefficient inequalities, a distortion theorem, the radii of close-to-convexity, and starlikeness and convexity for these classes of functions are studied. The behavior of these classes under a certain modified convolution operator is also discussed.