On Wijsman f?-Statistical Convergence of Order ? of Modulus Functions

Abstract

In the present paper, we introduce and investigate the concepts of Wijsman f rho-statistical convergence of order alpha and Wijsman strong f rho-convergence of order alpha. These notions are defined as natural generalizations of classical statistical convergence and Wijsman convergence, incorporating the tools of modulus functions and natural density through the function f. We provide a detailed analysis of their structural properties, including inclusion relations, basic characterizations, and illustrative examples. Furthermore, we establish the inclusion relations between Wijsman f rho-statistical convergence and Wijsman strong f rho-convergence of order alpha, showing conditions under which one implies the other. These notions are different in general, while coinciding under certain restrictions on the function f, the parameter alpha, and the sequence rho. The results obtained not only extend some well-known findings in the literature but also open up new directions for further study in the theory of statistical convergence and its applications to analysis and approximation theory.