In this paper, we present yet another new and novel variant of classical Banach contraction principle on a complete metric space endowed with a binary relation which, under universal relation, reduces to Banach contraction principle. In process, we observe that various kinds of binary relations, such as partial order, preorder, transitive relation, tolerance, strict order, symmetric closure, etc., utilized by earlier authors in several well-known metrical fixed point theorems can be weakened to the extent of an arbitrary binary relation.Mathematics Subject Classification. 47H10, 54H25.
In this article, we generalize some frequently used metrical notions such as: completeness, closedness, continuity, -continuity and compatibility to relation-theoretic setting and utilize these relatively weaker notions to prove our results on the existence and uniqueness of coincidence points involving a pair of mappings defined on a metric space endowed with an arbitrary binary relation. Particularly, under universal relation our results deduce the classical coincidence point theorems of Goebel, Jungck and others. Furthermore, our results generalize, modify, unify and extend several well-known results of the existing literature.
In this article, we prove some existence and uniqueness results on coincidence points for g-increasing mappings satisfying generalized ϕ-contractivity conditions in ordered metric spaces. As an application of one of our newly proved results, we indicate the formulation of a coupled coincidence theorem. Our results generalize, extend, modify, improve, sharpen, enrich, and complement several well-known results of the existing literature. Also, we point out that a recent coincidence point result proved in
Abstract. In this paper, we present a variant of Boyd-Wong fixed point theorem in a metric space equipped with a locally T -transitive binary relation, which under universal relation reduces to Boyd-Wong (Proc. Amer. Math. Soc. 20(1969), 458-464) and Jotic (Indian J. Pure Appl. Math. 26(1995), 947-952) fixed point theorems. Also, our results extend several other well-known fixed point theorems such as: Alam and Imdad (J. Fixed Point Theory Appl. 17(2015), no 4, 693-702) and Karapinar and Roldán-López-de-Hierro (J. Inequal. Appl. 2014Appl. :522(2014, 12 pages) besides some others.
In this article, we generalize some frequently used metrical notions such as: completeness, continuity, g-continuity, and compatibility to order-theoretic setting especially in ordered metric spaces besides introducing some new notions such as: the ICC property, DCC property, MCC property etc. and utilize these relatively weaker notions to prove some coincidence theorems for g-increasing Boyd-Wong type contractions which enrich some recent results due to Alam et al. (Fixed Point Theory Appl. 2014:216, 2014.
MSC: 47H10; 54H25
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