Year: 2025
Type: article
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.
Authors: Mayuri Nema, Dr. Abha Tenguria
Institution: Barkatullah University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W4411734326