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One of the fundamental parts of Geometric Function Theory is the study of analytic functions in different domains with critical geometrical interpretations. This article defines a new generalized domain obtained based on the quotient of two analytic functions. We derive various properties of the new class of normalized analytic functions X defined in the new domain, including the sharp estimates for the coefficients a 2 , a 3 , and a 4 , and for three second-order and third-order Hankel determinants, H 2 , 1 X , H 2 , 2 X , and H 3 , 1 X . The optimality of each obtained estimate is given as well. [ABSTRACT FROM AUTHOR]

Many researchers have defined the q-analogous of differential and integral operators for analytic functions using the concept of quantum calculus in the geometric function theory. In this study, we conduct a comprehensive investigation to identify the uses of the Sălăgean q-differential operator for meromorphic multivalent functions. Many features of functions that belong to geometrically defined classes have been extensively studied using differential operators based on q-calculus operator theory. In this research, we extended the idea of the q-analogous of the Sălăgean differential operator for meromorphic multivalent functions using the fundamental ideas of q-calculus. With the help of this operator, we extend the family of Janowski functions by adding two new subclasses of meromorphic q-starlike and meromorphic multivalent q-starlike functions. We discover significant findings for these new classes, including the radius of starlikeness, partial sums, distortion theorems, and coefficient estimates. [ABSTRACT FROM AUTHOR]

This article defines a new operator called the q-Babalola convolution operator by using quantum calculus and the convolution of normalized analytic functions in the open unit disk. We then study a new class of analytic and bi-univalent functions defined in the open unit disk associated with the q-Babalola convolution operator. The main results of the investigation include some upper bounds for the initial Taylor–Maclaurin coefficients and Fekete–Szego inequalities for the functions in the new class. Many applications of the finds are highlighted in the corollaries based on the various unique choices of the parameters, improving the existing results in Geometric Function Theory. [ABSTRACT FROM AUTHOR]