Combining Orlicz Space and Lagrange's Theorem for Accurate Gap Estimation in Functions

Abstract

This paper investigates the integration of Orlicz space with Lagrange's theorem to

enhance the precision of gap estimations in functions. We review fundamental

concepts and theorems related to Orlicz spaces and Lagrange's theorem,

culminating in the development of a novel theorem that unifies these tools. We

provide proofs for this new theorem and illustrate its applications with practical

examples. These findings are pertinent to fields such as numerical analysis,

nonlinear analysis, and complex system modeling.