Using the derivative operators’ q-analogs values, a wide variety of holomorphic function subclasses, q-starlike, and q-convex functions have been researched examined. With aid fundamental ideas from theory q-calculus operators, we describe new q-operators harmonic Hϱ,χ;qγF(ϖ) in this work. We also define subclass related to Janowski q-analog Le Roy-type Mittag–Leffler functions. Several importa...

The general classes of multivalent starlike, convex, close-to-convex and quasiconvex functions are introduced. These classes provide a unified treatment to various known subclasses. Inclusion and convolution properties are derived using the methods of convex hull and differential subordination. 1. Motivation and Preliminaries Let U = {z : |z| < 1} be the unit disk and H(U) be the class of all a...

Let denote the functions' class that is normalized, analytic, as well univalent in unit disc given by src=image/13426735_01.gif>. Convex, starlike, close-to-convex functions resemble main subclasses of src=image/13426735_02.gif>, expressed src=image/13426735_03.gif>, src=image/13426735_04.gif>, accordingly. Many mathematicians have recently studied radius problem...

In this lecture, we aim at presenting a certain linear operator which is defined by means of the Hadamard product (or convolution) with a generalized hypergeometric function and then investigating its various mapping as well as inclusion properties involving such subclasses of analytic and univalent functions as (for example) k-uniformly convex functions and k-starlike functions. Relevant conne...

In this paper, we investigate the sharp bounds of second Hankel determinant Logarithmic coefficients for starlike and convex functions with respect to symmetric points in open unit disk.

A set of vertices $S$ a graph $G$ is $monophonically \ convex$ if every induced path joining two contained in $S$. The $monophonic convex hull$ $S$, $\langle S \rangle$, the smallest monophonically containing convexly independent$ $v \not\in \langle - \{v\} \rangle$ for \in S$. rank$ size largest monophonic independent $G$. We present characterization sets. Using this result, we show how to det...

the rational cubic function with three parameters has been extended to rational bi-cubic function to visualize the shape of regular convex surface data. the rational bi-cubic function involves six parameters in each rectangular patch. data dependent constraints are derived on four of these parameters to visualize the shape of convex surface data while other two are free to refine the shape of s...

We will give the relation between the class of Janowski starlike functions of complex order and the class of Janowski convex functions of complex order. As a corollary of this relation, we obtain the radius of starlikeness for the class of Janowski convex functions of complex order. 1. Introduction. Let F be the class of analytic functions in D = {z | |z| < 1}, and let S denote those functions ...

We prove sharp bounds on eigenvalues of the Laplacian that complement the Faber–Krahn and Luttinger inequalities. In particular, we prove that the ball maximizes the first eigenvalue and minimizes the spectral zeta function and heat trace. The normalization on the domain incorporates volume and a computable geometric factor that measures the deviation of the domain from roundness, in terms of m...