On a new class of analytic functions associated with conic domain

AbstractThe aim of this paper is to generalize the conic domain defined by Kanas and Wisniowska, and define the class of functions which map the open unit disk E onto this generalized conic domain. A brief comparison between these conic domains is the main motivation of this paper. A correction is made in selecting the range interval of order of conic domain

Study of quantum calculus for a new subclass of q-starlike bi-univalent functions connected with vertical strip domain

In this study, using the ideas of subordination and the quantum-difference operator, we established a new subclass $\mathcal{S} ^{\ast }\left(\delta, \sigma, q\right)$ of $q$-starlike functions and the subclass $\mathcal{S}_{\Sigma }^{\ast }\left(\delta, \sigma, q\right)$ of $q$-starlike bi-univalent functions associated with the vertical strip domain. We examined sharp bounds for the first two Taylor-Maclaurin coefficients, sharp Fekete-Szegö type problems, and coefficient inequalities for the function $h$ that belong to $\mathcal{S}^{\ast }\left(\delta, \sigma, q\right)$, as well as sharp bounds for the inverse function $h$ that belong to $\mathcal{S}^{\ast }\left(\delta, \sigma, q\right)$. We also investigated some results for the class of bi-univalent functions $\mathcal{S}_{\Sigma }^{\ast }\left(\delta, \sigma, q\right)$ and well-known corollaries were also highlighted to show connections between previous results and the findings of this paper

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