Work

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

Year: 2015

Type: article

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.

Source: The Journal of Nonlinear Sciences and Applications

DOI: 10.22436/jnsa.008.06.18

Authors: Hajer Argoubi, Bessem Samet, Calogero Vetro

Institutions: Tunis El Manar University, King Saud University, University of Palermo

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: King Saud University

Award: G3014190477