Nonlinear contractions involving simulation functions in a metric space with a partial order
By Hajer Argoubi, Bessem Samet, Calogero Vetro. 2015
150 citations recorded by the source corpus.
Very recently, Khojasteh, Shukla and Radenović [F. Khojasteh, S. Shukla, S. Radenović, Filomat, 29 (2015), 1189–1194] introduced the notion of 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. c ©2015 All rights reserved.
Subfields: Numerical Analysis, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/c0503d08d40b831a347606101621118d492afc1e
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In Numerical Analysis
In Statistical and Nonlinear Physics
Citations in the corpus
- Interpolative Rus-Reich-Ćirić Type Contractions via Simulation Functions (2019, unknown): “[1], that is, ζ satisfies only (ζ2) and (ζ3).”
- On the Power of Simulation and Admissible Functions in Metric Fixed Point Theory (2017, background): “[2] relaxed the conditions of the notion of simulation function a little bit to guarantee that the considered set is nonempty.”