On P-equi-statistical relative convergence in sequences of fuzzy-valued functions with applications to Korovkin-type approximation

In this study, we introduce and investigate new forms of convergence, namely, P-statistical relative pointwise, uniform, and P-equi-statistical relative convergence, for sequences of functions whose values lie in the space of fuzzy numbers. These notions, motivated by a synthesis of statistical and relative convergence frameworks, are explored both in terms of their structural characteristics and mutual interrelationships. Furthermore, we examine the behavior of their corresponding r-level sets to provide deeper insight into their convergence dynamics. As a principal application, we apply approximation theorems of Korovkin-type for sequences of functions with fuzzy values under the newly proposed modes of convergence, and we compute the rate of convergence.