In this paper, the concepts of symmetric q-calculus and conic regions are used to define a new domain $\widetilde{{\mathsf{\Omega }}_{k,q,\alpha }},$ which generalizes the symmetric conic domains. By using the domain $\widetilde{{\mathsf{\Omega }}_{k,q,\alpha }}$, we define a new subclass of analytic and q-starlike functions in the open unit disk U and establish some new results for functions of this class. We also investigate a number of useful properties and characteristics of this subclass, such as coefficients estimates, structural formulas, distortion inequalities, necessary and sufficient conditions, closure and subordination results. The proposed approach is also compared with some existing methods to show the reliability and effectiveness of the proposed methods.

In this article, we study the Fekete-Szegö functional associated with a new class of analytic functions related to the class of bounded turning by using the principle of quasi-subordination. We derived the coefficient estimates including the classical Fekete-Szegö inequality for functions belonging to this class. We also improved some existing results.

In our current study, we apply differential subordination and quantum calculus to introduce and investigate a new class of analytic functions associated with the q-differential operator and the symmetric balloon-shaped domain. We obtain sharp results concerning the Maclaurin coefficients the second and third-order Hankel determinants, the Zalcman conjecture, and its generalized conjecture for this newly defined class of q-starlike functions with respect to symmetric points.

In the current article, we utilize the concept of subordination to establish a new subclass of analytic functions associated with a bounded domain that is symmetric about the real axis. By applying the convolution technique, we derive the necessary and sufficient condition, the radius of convexity for this recently introduced class. Furthermore, we prove the sharp upper bounds for the second-order Hankel determinants $|{\mathcal{H}}_{2,1}\xi |,|{\mathcal{H}}_{2,2}\xi |$ and third-order Hankel determinant $|{\mathcal{H}}_{3,1}\xi |$ for the functions $\xi$ belonging to the newly defined class.

In this article, our objective is to define and study a new subclass of analytic functions associated with the q-analogue of the sine function, operating in conjunction with a convolution operator. By manipulating the parameter q, we observe that the image of the unit disc under the q-sine function exhibits a visually appealing resemblance to a figure-eight shape that is symmetric about the real axis. Additionally, we investigate some important geometrical problems like necessary and sufficient conditions, coefficient bounds, Fekete-Szegö inequality, and partial sum results for the functions belonging to this newly defined subclass.

In the present paper, we introduce and explore certain new classes of meromorphic functions related with closed-to-convexity and q-calculus. Such results as coefficient estimates, grow the property and partial sums are derived. It is important to mentioned that our results are generalization of number of existing results in literature.