Kannan Contraction Maps on the Space of Null Variable Exponent Second-Order Quantum Backward Difference Sequences of Soft Functions and Its Pre-Quasi Ideal

Abstract

In this article, we develop and study the space of null variable exponent second-order quantum backward difference sequences of soft functions, which are critical extensions to the concept of modular spaces. The mappings have been idealized through the use of extended s-soft functions and this soft function sequence space. The topological and geometric features of this new space are described, as well as the ideal mappings that correspond to them. We establish the existence of a Kannan contraction mapping fixed point acting on this space and its associated pre-quasi ideal. It's fascinating that we give various numerical experiments to show our findings. Additionally, several practical applications of the existence of solutions to nonlinear difference equations involving soft functions are discussed.