Multiparametric Contractions and Related Hardy-Roger Type Fixed Point Theorems

Antonio Francisco Roldán López de Hierro, Erdal Karapınar and Andreea Fulga
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Antonio Francisco Roldán López de Hierro: Department of Statistics and Operations Research, University of Granada, 18010 Granada, Spain
Erdal Karapınar: Department of Medical Research, China Medical University, Taichung 40402, Taiwan
Andreea Fulga: Department of Mathematics and Computer Sciences, Universitatea Transilvania Brasov, 500036 Brasov, Romania

Mathematics, 2020, vol. 8, issue 6, 1-18

Abstract: In this paper we present some novel fixed point theorems for a family of contractions depending on two functions (that are not defined on t = 0 ) and on some parameters that we have called multiparametric contractions. We develop our study in the setting of b -metric spaces because they allow to consider some families of functions endowed with b -metrics deriving from similarity measures that are more general than norms. Taking into account that the contractivity condition we will employ is very general (of Hardy-Rogers type), we will discuss the validation and usage of this novel condition. After that, we introduce the main results of this paper and, finally, we deduce some consequences of them which illustrates the wide applicability of the main results.

Keywords: b-metric space; multiparametric contraction; fixed point; contractivity condition; Hardy-Rogers contractivity condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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