Modified Generalized Sequence of Functions

Uniform convergence is a more stringent type of convergence which preserves at least some shared properties of functions. In this sense, a unified method of generalized sequence of functions is more beneficial to study limiting operations. The purpose of this paper is to study the problem in a unifying approach using generalized sequence in order to obtain the basic result in general form and then indicate their application to concrete cases. It is quite observed that among various approaches, the abstract method is the simplest and most economical method for treating mathematical systems.