A Method for Establishing Unique Fixed Points in Modular Ultrametric Spaces Using Rational Contractions

Abstract

This invention presents a novel mathematical framework for solving fixed-point problems in modular ultrametric spaces. By employing rational-type contractions, it removes the restrictive assumption of spherical completeness and broadens the applicability of the theory to integral equations and well-posedness. The results significantly enhance the understanding and utilization of modular ultrametric spaces in mathematical analysis. This invention introduces a method for establishing unique fixed points in modular ultrametric spaces through rational-type contractive conditions, bypassing the traditional requirement for spherical completeness. The method enables broader application in mathematical fields by allowing fixed-point determination in a wider variety of spaces, particularly benefiting the study of integral equations and the analysis of well-posedness. By providing a framework for unique fixed points (UFPs) in self-mappings within these spaces, this invention offers novel approaches to formulating and solving fixed-point problems. The developed conditions and methods provide a robust alternative to existing fixed-point theorems, thus advancing the applicability of modular ultrametric space theory in non-Archimedean systems.

Specification

Description:This invention presents a novel mathematical framework for solving fixed-point problems in modular ultrametric spaces. By employing rational-type contractions, it removes the restrictive assumption of spherical completeness and broadens the applicability of the theory to integral equations and well-posedness. The results significantly enhance the understanding and utilization of modular ultrametric spaces in mathematical analysis. This invention introduces a method for establishing unique fixed points in modular ultrametric spaces through rational-type contractive conditions, bypassing the traditional requirement for spherical completeness. The method enables broader application in mathematical fields by allowing fixed-point determination in a wider variety of spaces, particularly benefiting the study of integral equations and the analysis of well-posedness. By providing a framework for unique fixed points (UFPs) in self-mappings within these spaces, this invention offers novel approaches to formulating and solving fixed-point problems. The developed conditions and methods provide a robust alternative to existing fixed-point theorems, thus advancing the applicability of modular ultrametric space theory in non-Archimedean systems. , C , Claims:1.Claim 1: A method for establishing a unique fixed point for self-mappings in modular ultrametric spaces using rational-type contractive conditions.
2.Claim 2: The method of Claim 1, wherein the rational-type contraction does not require the assumption of spherical completeness.
3.Claim 3: The method of Claim 2, wherein the fixed-point result is applied to integral equations to demonstrate well-posedness.
4.Claim 4: A system for formulating fixed-point problems accurately in modular ultrametric spaces using the method described in Claim 3.

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