Search
2 articles for “Complete metric space”
-
A Journey through Fixed Points and Non-expansive Mappings
Abstract: Fixed points in non-expansive mappings are elements that remain unchanged under the action of the mapping. Non-expansive mappings preserve or contract distances in a metric space. The rigorous proof of the Banach fixed-point theorem is presented at the outset of the paper, highlighting its fundamental significance. According to this theorem, every contraction mapping (a particular kind of non-expansive mapping that strictly reduces distances) has a single fixed point in a …
Published in Research & Reviews: Discrete Mathematical Structures · Vol. 11, Issue 1, 2024 Read article
-
A Study of Fixed-Point and Best Proximity Point
Abstract: Fixed-point theory plays a fundamental role in nonlinear analysis and has significant applications in optimization, differential equations, and applied mathematics. This study investigates the existence and properties of fixed points and best proximity points for various classes of mappings defined on metric and normed spaces. While fixed-point results guarantee the existence of a point that remains invariant under a given mapping, such points may not exist when the mapping is …
Published in Recent Trends in Mathematics · Vol. 3, Issue 1, 2026 · pp. 28–39 Read article