Certain subclasses of analytic functions: Fekete-Szegö inequalities involving $q$-Bessel functions and Carlson-Shaffer operator

In this paper, we introduce a new linear operator involving the $q$-analogue of generalized Bessel functions and the $q$-analogue of the Carlson-Shaffer operator. By using this operator, we define and investigate certain subclasses of analytic functions in the open unit disk. We obtain coefficient estimates and establish Fekete-Szegö-type inequalities for the newly introduced function classes. Moreover, by employing the Hadamard product, we study several geometric properties and derive necessary as well as sufficient conditions for these classes. The results obtained in this work generalize and extend a number of earlier results in the existing literature.