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The aim of this study is to investigate a certain sufficiency criterion for uniform convexity, strong starlikeness, and strong convexity of Rabtonov fractional exponential functions. We also study the starlikeness and convexity of order  γ. Moreover, we find conditions so that the Rabotnov functions belong to the class of bounded analytic functions and Hardy spaces. Various consequences of these results are also presented. [ABSTRACT FROM AUTHOR]

This article extends the study of q-versions of analytic functions by introducing and studying the association of starlike functions with trigonometric cosine functions, both defined in their q-versions. Certain coefficient inequalities like coefficient bounds, Zalcman inequalities, and both Hankel and Toeplitz determinants for the new version of starlike functions are investigated. It is worth mentioning that most of the determined inequalities are sharp with the support of relevant extremal functions. [ABSTRACT FROM AUTHOR]

In this research, we define a few subclasses of analytic functions which are connected to sine functions and the cardioid domain in the unit disk. We investigate initial coefficient bounds, the Fekete–Szego problem and second and third Hankel determinants for the functions f belonging to these newly defined classes. We also define the class of m-fold symmetric functions related with the sine function and then investigate the bounds of the third Hankel determinant for twofold symmetric and threefold symmetric functions. [ABSTRACT FROM AUTHOR]

This paper presents a geometric approach to the problems in differential subordination theory. The necessary conditions for a function to be in various subfamilies of the class of starlike functions and the class of Carathéodory functions are studied, respectively. Further, several consequences of the findings are derived. [ABSTRACT FROM AUTHOR]

In this paper, we use the concept of quantum (or q -) calculus and define a q -analogous of a fractional differential operator and discuss some of its applications. We consider this operator to define new subclasses of uniformly q -starlike and q -convex functions associated with a new generalized conic domain, Λ β , q , γ . To begin establishing our key conclusions, we explore several novel lemmas. Furthermore, we employ these lemmas to explore some important features of these two classes, for example, inclusion relations, coefficient bounds, Fekete–Szego problem, and subordination results. We also highlight many known and brand-new specific corollaries of our findings. [ABSTRACT FROM AUTHOR]

The basic aspect of the research on coefficient problems for numerous families of univalent functions is to describe the coefficients of functions in a specific family by the coefficients of the Carathéodory functions. Thus, in utilizing the inequalities that are known for the class of Carathéodory functions, coefficient functionals may be examined. Several coefficient problems will be addressed in this study by utilizing the methodology for the abovementioned functions' family. The family of starlike functions with respect to symmetric points connected to a three-leaf-shaped image domain is the topic of our investigation. [ABSTRACT FROM AUTHOR]

This study introduces a subclass S q s * of starlike functions associated with the q-analogue of the sine function defined in symmetric unit disk. This article comprises the investigation of sharp coefficient bounds, and the upper bound of the third-order Hankel determinant for this class. It also includes the findings of Zalcman and generalized Zalcman conjectures for functions of this class. [ABSTRACT FROM AUTHOR]