A Note on Extended Z -Contraction

Maryam A. Alghamdi, Selma Gulyaz-Ozyurt and Erdal Karapınar
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Maryam A. Alghamdi: Department of Mathematics, College of Science, University of Jeddah, Jeddah 21589, Saudi Arabia
Selma Gulyaz-Ozyurt: Department of Mathematics, Sivas Cumhuriyet University, 58140 Sivas, Turkey
Erdal Karapınar: Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan

Mathematics, 2020, vol. 8, issue 2, 1-14

Abstract: In this article, we aim to evaluate and merge the as-scattered-as-possible results in fixed point theory from a general framework. In particular, we considered a common fixed point theorem via extended Z -contraction with respect to ψ -simulation function over an auxiliary function ξ in the setting of b -metric space. We investigated both the existence and uniqueness of common fixed points of such mappings. We used an example to illustrate the main result observed. Our main results cover several existing results in the corresponding literature.

Keywords: Z-contraction; simulation functions; b-metric (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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