Metrical Fixed Point Theorems Research Articles

Fixed point results of \((\phi,\psi)\)-weak contractions in ordered \(b\)-metric spaces

The purpose of this paper is to prove some results on fixed point, coincidence point, coupled coincidence point and coupled common fixed point for the mappings satisfying generalized \((\phi, \psi)\)-contraction conditions in complete partially ordered \(b\)-metric spaces. Our results generalize, extend and unify most of the fundamental metrical fixed point theorems in the existing literature. A few examples are illustrated to support our findings.

Perov-fixed point theorems on a metric space equipped with ordered theoretic relation

<abstract><p>In this paper, we introduce a few new generalizations of the classical Perov-fixed point theorem for single-valued and multi-valued mappings in a complete generalized metric space endowed with a binary relation. We have furnished our work with examples to show that several metrical-fixed point theorems can be obtained from an arbitrary binary relation.</p></abstract>

Relation-theoretic metrical fixed point theorems under nonlinear contractions

Relation-theoretic metrical fixed point theorems under nonlinear contractions

Metrical fixed point theorems via locally finitely T-transitive binary relations under certain control functions

Metrical fixed point theorems via locally finitely T-transitive binary relations under certain control functions

Wardowski type fixed point theorems in complete metric spaces

AbstractIn this paper, we state and prove Wardowski type fixed point theorems in metric space by using a modified generalized F-contraction maps. These theorems extend other well-known fundamental metrical fixed point theorems in the literature (Dung and Hang in Vietnam J. Math. 43:743-753, 2015 and Piri and Kumam in Fixed Point Theory Appl. 2014:210, 2014, etc.). Examples are provided to support the usability of our results.

Unified relation-theoretic metrical fixed point theorems under an implicit contractive condition with an application

AbstractThe main purpose of this article is to establish relation-theoretic metrical fixed point theorems via an implicit contractive condition which is general enough to yield a multitude of corollaries corresponding to several well known contraction conditions (e.g. Banach (Fundam. Math. 3:133-181, 1922), Kannan (Am. Math. Mon. 76:405-408, 1969), Reich (Can. Math. Bull. 14:121-124, 1971), Bianchini (Boll. Unione Mat. Ital. 5:103-108, 1972), Chatterjea (C. R. Acad. Bulg. Sci. 25:727-730, 1972), Hardy and Rogers (Can. Math. Bull. 16:201-206, 1973), Ćirić (Proc. Am. Math. Soc. 45:267-273, 1974) and several others) wherein even such corollaries are new results on their own. As an example we utilize our main results, to prove a theorem on the existence and uniqueness of the solution of an integral equation besides providing an illustrative example.

Sharpening some core theorems of Nieto and Rodríguez-López with application to boundary value problem

AbstractIn this paper, we prove sharpened versions of some classical order-theoretic metrical fixed point theorems due to Nieto and Rodríguez-López (Order 22(3):223-239, 2005) using order-theoretic variants of completeness and continuity besides some another notions such as: the ICC property, the DCC property, and the MCC property. In this continuation, we further extend our results for Boyd-Wong type nonlinear contractions. Finally, as an application of our certain newly proved results, we establish the existence and uniqueness of solution of a first order periodic boundary value problem.

Relation-theoretic contraction principle

In this paper, we present yet another new and novel variant of classical Banach contraction principle on a complete metric space en- dowed 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.

Fixed point theorems for a generalized almost "Equation missing"-contraction with respect to S in ordered metric spaces

AbstractIn this paper, the existence theorems of fixed points and common fixed points for two weakly increasing mappings satisfying a new condition in ordered metric spaces are proved. Our results extend, generalize and unify most of the fundamental metrical fixed point theorems in the literature.MSC:47H09, 47H10.