A New Approach of Some Contractive Mappings on Metric Spaces

Ion Marian Olaru and Nicolae Adrian Secelean
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Ion Marian Olaru: Department of Mathematics and Computer Science, Lucian Blaga University of Sibiu, Dr. I. Raţiu Street, No. 5–7, 550012 Sibiu, Romania
Nicolae Adrian Secelean: Department of Mathematics and Computer Science, Lucian Blaga University of Sibiu, Dr. I. Raţiu Street, No. 5–7, 550012 Sibiu, Romania

Mathematics, 2021, vol. 9, issue 12, 1-12

Abstract: In this paper, we introduce a new contraction-type mapping and provide a fixed-point theorem which generalizes and improves some existing results in the literature. Thus, we prove that the Boyd and Wong theorem (1969) and, more recently, the fixed-point results due to Wardowski (2012), Turinici (2012), Piri and Kumam (2016), Secelean (2016), Proinov (2020), and others are consequences of our main result. An application in integral equations and some illustrative examples are indicated.

Keywords: fixed point; Picard operator; contractive mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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