Convergence and Fixed Points of Self-Mappings in MR-Metric Spaces: Theory and Applications

In this paper, we present some important results for self-mappings in $MR-metric$ spaces, ensuring the existence and uniqueness of fixed points in contraction mappings. The study reveals the important role of contraction properties in achieving convergence. The paper continues to develop these concepts by providing concrete examples that demonstrate their importance in measurable spaces. Finally, these results lay the foundation for future investigations into the stability of fixed points and their applications via mathematical frameworks applicable to real life.