Abstract
AbstractIn this work, partial answers to Reich, Mizoguchi and Takahashi’s and Amini-Harandi’s conjectures are presented via a light version of Caristi’s fixed point theorem. Moreover, we introduce the idea that many of known fixed point theorems can easily be derived from the Caristi theorem. Finally, the existence of bounded solutions of a functional equation is studied.
Highlights
1 Introduction and preliminaries In the literature, the Caristi fixed point theorem is known as one of the very interesting and useful generalizations of the Banach fixed point theorem for self-mappings on a complete metric space
The Caristi fixed point theorem is a modification of the ε-variational principle of Ekeland ([, ]), which is a crucial tool in nonlinear analysis, in particular, optimization, variational inequalities, differential equations, and control theory
We show that many of the known Banach contraction generalizations can be deduced and generalized by Caristi’s fixed point theorem and its consequences
Summary
Introduction and preliminariesIn the literature, the Caristi fixed point theorem is known as one of the very interesting and useful generalizations of the Banach fixed point theorem for self-mappings on a complete metric space. Let (X, d) be a complete metric space and T : X → X a map.
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