Common fixed point results for four mappings satisfying almost generalized (S, T)-contractive condition in partially ordered metric spaces
Section snippets
Introduction and preliminaries
Kannan [16] proved a fixed point theorem for a map satisfying a contractive condition that did not require continuity at each point. Afterward Sessa [18] introduced the notion of weakly commuting maps, which generalized the concept of commuting maps. Then Jungck generalized this idea, first to compatible mappings [14] and then to weakly compatible mappings [15].
The concept of almost contraction property was extended to a pair of self maps as follows. Definition 1.1 Let (X, d) be a metric space. A map f : X → X is[13]
Main results
Theorem 2.1 Let (X, ⪯, d) be an ordered complete metric space. Let f, g, S and T be self maps on X, with f(X) ⊆ T(X) and g(X) ⊆ S(X) and dominating maps f and g are weak annihilators of T and S, respectively. Suppose that f and g satisfy almost generalized (S, T)-contractive condition (2) for every two comparable elements x, y ∈ X. If for a nondecreasing sequence {xn} with xn ⪯ yn for all n and yn → u implies that xn ⪯ u and furthermore (a) {f, S} and {g, T} are weakly compatible; (b) one of f(X), g(X),S(X) and T(X) is a
Acknowledgments
The authors are indebted to the anonymous referee for his/her careful reading of the text and for suggestions for improvement in several places. Second author is thankful to the Ministry of Science and Technological Development of Serbia.
References (19)
- et al.
Common fixed points of four maps in partially ordered metric spaces
Appl. Math. Lett.
(2011) - et al.
Common fixed points of almost generalized contractive mappings in ordered metric spaces
Appl. Math. Comput.
(2011) - et al.
Common fixed points of generalized almost nonexpansive mappings
Filomat
(2010) - et al.
On fixed points of Berinde’s contractive mappings in cone metric spaces
Carpathian J. Math.
(2010) - et al.
A note on a fixed point theorem of Berinde on weak contraction
Carpathian J. Math.
(2008) Approximating common fixed points of noncommuting discontinuous weakly contractive mappings in metric spaces
Carpathian J. Math.
(2009)Some remarks on a fixed point theorem for Ćirić-type almost contractions
Carpathian J. Math.
(2009)Common fixed points of noncommuting almost contractions in cone metric spaces
Math. Commun.
(2010)Approximating common fixed points of noncommuting almost contractions in metric spaces
Fixed Point Theory
(2010)