Metrical fixed point theorems via locally finitely T-transitive binary relations under certain control functions
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In this article, a relation-theoretic contraction principle due to Alam and Imdad was extended to a nonlinear contraction using a relatively weaker class of continuous control functions employing a locally finitely T -transitive binary relation.Abstract:
In this paper, we extend relation-theoretic contraction principle due to Alam and Imdad to a nonlinear contraction using a relatively weaker class of continuous control functions employing a locally finitely T -transitive binary relation, which improves the corresponding fixed point theorems especially due to: Alam and Imdad (J. Fixed Point Theory Appl. 17 (2015) 693702), Agarwal et al: (Applicable Analysis, 87 (1) (2008) 109-116), Berzig and Karapinar (Fixed Point Theory Appl. 2013:205 (2013) 18 pp), Berzig et al: (Abstr. Appl. Anal. 2014:259768 (2014) 12 pp) and Turinici (The Sci. World J. 2014:169358 (2014) 10 pp). 2010 Mathematics Subject Classification: 47H10; 54H25read more
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References
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Journal ArticleDOI
Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales
Journal ArticleDOI
A lattice-theoretical fixpoint theorem and its applications
TL;DR: In this paper, the authors formulate and prove an elementary fixpoint theorem which holds in arbitrary complete lattices, and give various applications (and extensions) of this result in the theories of simply ordered sets, real functions, Boolean algebras, as well as in general set theory and topology.
Journal ArticleDOI
A fixed point theorem in partially ordered sets and some applications to matrix equations
TL;DR: In this paper, an analogue of Banach's fixed point theorem in partially ordered sets is proved, and several applications to linear and nonlinear matrix equations are discussed, including the application of the Banach theorem to the Partially ordered Set (POPS) problem.
Journal ArticleDOI
Contractive Mapping Theorems in Partially Ordered Sets and Applications to Ordinary Differential Equations
TL;DR: It is proved the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions admitting only the existence of a lower solution.
Journal ArticleDOI
On nonlinear contractions
D. W. Boyd,J. S. W. Wong +1 more
TL;DR: In this article, it was shown that for a metrically convex space, the conclusion of Banach's theorem still holds, and that one need only assume that ip(t) 0, together with a semicontinuity condition on \[/.