In the present paper, we propose new generalized classes of (p,q)-starlike and (p,q)-convex functions. These classes are introduced by making use of a (p,q)-derivative operator. There are established Fekete–Szegö estimates $|a_3-\mu a_2^2|$ for functions belonging to the newly introduced subclasses. Certain subclasses of analytic univalent functions associated with quasi-subordination are defined.

Certain characteristics of univalent functions with negative coefficients of the form $f\left(z\right)=z-{\sum }_{n=1}^{\infty }{a}_{2n}{z}^{2n},a_{2n}>0$ have been studied by Silverman and Berman. Pokley, Patil and Shrigan have discovered some insights into the Hadamard product of $\mathcal{P}$-valent functions with negative coefficients. S. M. Khairnar and Meena More have obtained coefficient limits and convolution results for univalent functions lacking a alternating type coefficient. In this paper, using the $\mathfrak{q}$-Difference operator, we developed the a subclass of meromorphically $\mathcal{P}$-valent functions with alternating coefficients. Additionally, we obtained multivalent function convolution results and coefficient limits.

This work presents a novel investigation that utilizes the integral operator $I_{p,\lambda }^n$ in the field of geometric function theory, with a specific focus on sandwich theorems. We obtained findings about the differential subordination and superordination of a novel formula for a generalized integral operator. Additionally, certain sandwich theorems were discovered.

In this study, subordination, superordination, and sandwich theorems are established for a class of p-valent analytic functions involving a generalized integral operator that has as a special case p-valent Sălăgean integral operator. Relevant connections of the new results with several well-known ones are given as a conclusion for this investigation.

This article defines a new class of meromorphic parabolic starlike functions in the punctured unit disc $D^{*}=\{z\in \mathbb{C}:0<|z|<1\}$ that includes fixed second coefficients of class $\mathcal{A}{}_{s,c}^d\left(\psi ,\tau ,\nu ,\eta \right)$ and the q- hypergeometric functions. For the function belonging to the class $\mathcal{A}{}_{s,c}^d\left(\psi ,\tau ,\nu ,\eta \right),$ some properties are obtained, including the coefficient inequalities, closure theorems, and the radius of convexity.

In this article, we consider new subclasses of analytic and bi-univalent functions associated with the q-Srivastava-Attiya operator in the open unit disk. We obtain coefficient bounds for the Taylor-Maclaurin coefficients $ |a_2| $ and $ |a_3| $ of the functions of these new subclasses. Furthermore, we establish the Fekete-Szegö inequality for functions in the classes $ \mathcal{T}^{\epsilon}_{\tau, \mathfrak{q}, \alpha}(\psi), \; \mathcal{KH}^{\epsilon}_{\tau, \mathfrak{q}, \alpha}(\delta, \psi), \text{and}\; \mathcal{A}^{\epsilon}_{\tau, \mathfrak{q}, \alpha}(\delta, \psi) $.