A Generalization of Fixed-Point Theorems for Mappings with a Contractive Iterate

Valentin Georgiev and Boyan Zlatanov ()
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Valentin Georgiev: Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 “Tzar Assen” Str., 4000 Plovdiv, Bulgaria
Boyan Zlatanov: Department of Mathematical Analysis, Faculty of Mathematics and Informatics, University of Plovdiv Paisii Hilendarski, 24 “Tzar Assen” Str., 4000 Plovdiv, Bulgaria

Mathematics, 2024, vol. 12, issue 23, 1-11

Abstract: In this paper, a generalization of fixed-point mappings with an iterate at a point in complete metric spaces is shown, using the notions of T-closed sets and i-P-regularity/d-P-regularity, proving conditions for the existence and uniqueness of the fixed point. Examples are provided to illustrate the results and an application to coupled fixed points is shown.

Keywords: fixed point; contractive iterate at a point; coupled fixed point; T-closed set (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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