A subclass of bi-univalent functions related to shell-like curves connected with Fibonacci numbers associated with (p, q)-derivative

In this paper, we define a new subclass of bi-univalent functions related to shell-like curves connected with Fibonacci numbers by using (p, q)-derivative and the coefficient estimates, Fekete-Szego inequalities are discussed for the functions belonging to this class.Publisher's Versio

Some new applications of the quantum-difference operator on subclasses of multivalent q-starlike and q-convex functions associated with the Cardioid domain

In this study, we consider the quantum difference operator to define new subclasses of multivalent $q$-starlike and $q$-convex functions associated with the cardioid domain. We investigate a number of interesting problems for functions that belong to these newly defined classes, such as bounds for the first two Taylor-Maclaurin coefficients, estimates for the Fekete-Szeg ö type functional, and coefficient inequalities. The important point of this article is that all the bounds that we have investigated are sharp. Many well-known corollaries are also presented to demonstrate the relationship between prior studies and the results of this article

Starlike Functions of Complex Order with Respect to Symmetric Points Defined Using Higher Order Derivatives

In this paper, we introduce and study a new subclass of multivalent functions with respect to symmetric points involving higher order derivatives. In order to unify and extend various well-known results, we have defined the class subordinate to a conic region impacted by Janowski functions. We focused on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of our results which are extensions of those given in earlier works are presented here as corollaries

Geometric inequalities via a symmetric differential operator defined by quantum calculus in the open unit disk

The present investigation covenants with the concept of quantum calculus besides the convolution operation to impose a comprehensive symmetric q-differential operator defining new classes of analytic functions. We study the geometric representations with applications. The applications deliberated to indicate the certainty of resolutions of a category of symmetric differential equations type Briot-Bouquet

ZALCMAN CONJECTURE AND HANKEL DETERMINANT OF ORDER THREE FOR STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH SHELL-LIKE CURVES

The aim of this article is to estimate an upper bound of |_3(1)|, the Zalcman coefficient functional for = 3 and = 4, and also to investigate the fifth, sixth, seventh coefficients of starlike and convex functions associated with shell-like curves. Similar type of outcomes are estimated for the functions ^(−1) and /()

A certain class of starlike functions

AbstractThis paper presents a new class of functions analytic in the open unit disc, and closely related to the class of starlike functions. Besides being an introduction to this field, it provides an interesting connections defined class with well known classes. The paper deals with several ideas and techniques used in geometric function theory. The order of starlikeness in the class of convex functions of negative order is also considered here