Search

Keeping in view the latest trends toward quantum calculus, due to its various applications in physics and applied mathematics, we introduce a new subclass of meromorphic multivalent functions in Janowski domain with the help of the q-differential operator. Furthermore, we investigate some useful geometric and algebraic properties of these functions. We discuss sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikeness, radius of convexity, inclusion property, and convex combinations via some examples and, for some particular cases of the parameters defined, show the credibility of these results. [ABSTRACT FROM AUTHOR]

In our present investigation, we obtain the improved third-order Hankel determinant for a class of starlike functions connected with modified sigmoid functions. Further, we investigate the fourth-order Hankel determinant, Zalcman conjecture, and also evaluate the fourth-order Hankel determinants for 2-fold, 3-fold, and 4-fold symmetric starlike functions. [ABSTRACT FROM AUTHOR]

In this paper, we define a new class of Sakaguchi type-meromorphic harmonic functions in the Janowski domain that are starlike with respect to symmetric point. Furthermore, we investigate some important geometric properties like sufficiency criteria, distortion bound, extreme point theorem, convex combination, and weighted means. [ABSTRACT FROM AUTHOR]

The main focus of this investigation is the applications of modified sigmoid functions. Due to its various uses in physics, engineering, and computer science, we discuss several geometric properties like necessary and sufficient conditions in the form of convolutions for functions to be in the special class S S G ∗ earlier introduced by Goel and Kumar and obtaining third-order Hankel determinant for this class using modified sigmoid functions. Also, the third-order Hankel determinant for 2- and 3-fold symmetric functions of this class is evaluated. [ABSTRACT FROM AUTHOR]

The main object of the present paper is to investigate a number of useful properties such as sufficiency criteria, distortion bounds, coefficient estimates, radius of starlikness and radius of convexity for a new subclass of meromorphic multivalent starlike functions, which are defined here by means of a newly defined q-linear differential operator. [ABSTRACT FROM AUTHOR]

In our present investigation, some coefficient functionals for a subclass relating to starlike functions connected with three-leaf mappings were considered. Sharp coefficient estimates for the first four initial coefficients of the functions of this class are addressed. Furthermore, we obtain the Fekete–Szegö inequality, sharp upper bounds for second and third Hankel determinants, bounds for logarithmic coefficients, and third-order Hankel determinants for two-fold and three-fold symmetric functions. [ABSTRACT FROM AUTHOR]

By making use of the concept of basic (or q-) calculus, many subclasses of analytic and symmetric q-starlike functions have been defined and studied from different viewpoints and perspectives. In this article, we introduce a new class of meromorphic multivalent close-to-convex functions with the help of a q-differential operator. Furthermore, we investigate some useful properties such as sufficiency criteria, coefficient estimates, distortion theorem, growth theorem, radius of starlikeness, and radius of convexity for this new subclass. [ABSTRACT FROM AUTHOR]

In this article, by utilizing the theory of quantum (or q-) calculus, we define a new subclass of analytic and multivalent (or p-valent) functions class A p , where class A p is invariant (or symmetric) under rotations. The well-known class of Janowski functions are used with the help of the principle of subordination between analytic functions in order to define this subclass of analytic and p-valent functions. This function class generalizes various other subclasses of analytic functions, not only in classical Geometric Function Theory setting, but also some q-analogue of analytic multivalent function classes. We study and investigate some interesting properties such as sufficiency criteria, coefficient bounds, distortion problem, growth theorem, radii of starlikeness and convexity for this newly-defined class. Other properties such as those involving convex combination are also discussed for these functions. In the concluding part of the article, we have finally given the well-demonstrated fact that the results presented in this article can be obtained for the (p , q) -variations, by making some straightforward simplification and will be an inconsequential exercise simply because the additional parameter p is obviously unnecessary. [ABSTRACT FROM AUTHOR]

The main purpose of this article is to examine the q-analog of starlike functions connected with a trigonometric sine function. Further, we discuss some interesting geometric properties, such as the well-known problems of Fekete-Szegö, the necessary and sufficient condition, the growth and distortion bound, closure theorem, convolution results, radii of starlikeness, extreme point theorem and the problem with partial sums for this class. [ABSTRACT FROM AUTHOR]