Nonlinear contractions involving simulation functions in a metric space with a partial order
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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.
Share and Cite
ISRP Style
Hajer Argoubi, Bessem Samet, Calogero Vetro, Nonlinear contractions involving simulation functions in a metric space with a partial order, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 6, 1082--1094
AMA Style
Argoubi Hajer, Samet Bessem, Vetro Calogero, Nonlinear contractions involving simulation functions in a metric space with a partial order. J. Nonlinear Sci. Appl. (2015); 8(6):1082--1094
Chicago/Turabian Style
Argoubi, Hajer, Samet, Bessem, Vetro, Calogero. "Nonlinear contractions involving simulation functions in a metric space with a partial order." Journal of Nonlinear Sciences and Applications, 8, no. 6 (2015): 1082--1094
Keywords
- Partial order
- nonlinear contraction
- coincidence point
- common fixed point
- simulation function.
MSC
References
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