A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type

By A. Aliouche. 2006

165 citations recorded by the source corpus.

Abstract In this paper, we proved a common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type and a property (E.A) introduced in [M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181–188]. Our theorem generalizes Theorem 2.2 of [M. Aamri, D. El Moutawakil, Common fixed points under contractive conditions in symmetric spaces, Appl. Math. E-Notes 3 (2003) 156–162] and Theorem 2 of [M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181–188].

Subfields: Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/569c7ee34fe2346944addfc7c85cf063a4d7011d

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In Geometry and Topology

Citations in the corpus

A common fixed point theorem using implicit relation and property (E.A) in metric spaces (2007, background): “For a related problem, see Theorem 1 and Corollary 3 in [2].”
QUASI-CONTRACTIONS ON SYMMETRIC AND CONE SYMMETRIC SPACES (2011, background): “In the case of arbitrary symmetric spaces additional assumptions are needed [2, 3, 10, 22].”
Altering Distance and Common Fixed Points under Implicit Relations (2009, background): “Some fixed point theorems in symmetric spaces for compatible and weakly compatible mappings are proved in [1], [11], [20], [17] and other papers.”
SOME FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS SATISFYING AN IMPLICIT RELATION (2009, background): “Again in [2], Aliouche proved a fixed point theorem using a general contractive condition of integral type on symmetric spaces.”
Fixed Points of Weakly Compatible Maps Satisfying a General Contractive Condition of Integral Type (2007, background): “The authors in [2–6] proved some fixed point theorems involving more general contractive conditions.”
Common Fixed Point Theorems for Hybrid Pairs of Occasionally Weakly Compatible Mappings Satisfying Generalized Contractive Condition of Integral Type (2007, background): “Rhoades [6] proved two fixed point theorems involving more general contractive conditions (see also [7–9]).”
Fixed point theorems for mappings satisfying contractive conditions of integral type and applications (2011, methodology): “The authors [2,3,9-11,28,30] and others continued the study of Branciari.”