Abstract
In this paper, the fixed-point theorem for monotone contraction mappings in the setting of a uniformly convex smooth Banach space is studied. This paper provides a version of the Banach fixed-point theorem in a complete metric space.
Highlights
Fixed-point problems of contraction mappings always exist, and it is unique due to eorem 1. is is a very useful result, and it has been applied in the determination of the existence and uniqueness of many results in analysis and economics
Let X be a smooth Banach space and let X∗ be the dual space of X. e generalised projection functional φ(·, ·): X × X ⟶ R is defined by φ(y, x) ‖y‖2 − 2R〈y, Jx〉 +‖x‖2, (5)
Main Result e proof of the main result of this paper is given which is accomplished in eorem 2. e following lemma and proposition shall aid in arriving at the conclusion of the main result
Summary
E following theorem due to Banach and Steinhaus [1] is the first and simplest of the metric fixed-point theory of Lipschitz maps. Fixed-point problems of contraction mappings always exist, and it is unique due to eorem 1. A version of eorem 1 in the setting of a smooth Banach spaces for monotone contraction mappings is provided.
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