Nonlinear contractions involving simulation functions in a metric space with a partial order

Volume 8, Issue 6, pp 1082--1094 http://dx.doi.org/10.22436/jnsa.008.06.18

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Authors

Hajer Argoubi - FST Campus Universitaire, 2092-El Manar, Tunis, Tunisia. Bessem Samet - Department of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia. Calogero Vetro - Dipartimento di Matematica e Informatica, Universita degli Studi di Palermo, via Archirafi 34, 90123 Palermo, Italy.

Abstract

Very recently, Khojasteh, Shukla and Radenović [F. Khojasteh, S. Shukla, S. Radenović, Filomat, 29 (2015), 1189-1194] introduced the notion of \(\mathcal{Z}\)-contraction, that is, a nonlinear contraction involving a new class of mappings namely simulation functions. This kind of contractions generalizes the Banach contraction and unifies several known types of nonlinear contractions. In this paper, we consider a pair of nonlinear operators satisfying a nonlinear contraction involving a simulation function in a metric space endowed with a partial order. For this pair of operators, we establish coincidence and common fixed point results. As applications, several related results in fixed point theory in a metric space with a partial order are deduced.

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Keywords

• Partial order
• nonlinear contraction
• coincidence point
• common fixed point
• simulation function.

MSC

•  54H25
•  47H10
•  54C30

References

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