Common Fixed Point Theorems and Non-Expansive Mapping In Banach Space
Abstract
First, we derive several properties of a fundamentally nonexpansive self-mapping defined on a nonempty subset of a Banach space. Then, we demonstrate that if the Banach space satisfies the Opial condition, the fixed point set of such a mapping with a convex range is nonempty. In particular, we prove that when the reflexive Banach space is uniformly convex and the range of the mapping is bounded, closed, and convex, its fixed point set is also nonempty, closed, and convex.
How to Cite This Article
Mayuri Nema, Dr. Abha Tenguria (2025). Common Fixed Point Theorems and Non-Expansive Mapping In Banach Space . International Journal of Multidisciplinary Research and Growth Evaluation (IJMRGE), 6(3), 1953-1958 . DOI: https://doi.org/10.54660/IJMRGE.2025.6.3.1953-1958