0000000000553866

AUTHOR

Poom Kumam

showing 7 related works from this author

Fixed Points for Weakα-ψ-Contractions in Partial Metric Spaces

2013

Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weakα-ψ-contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

Discrete mathematicsClass (set theory)Metric spacePure mathematicsApplied MathematicsInjective metric spaceMetric mapProduct metricFixed pointAnalysisMathematicsIntrinsic metricConvex metric spaceAbstract and Applied Analysis
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Best proximity point results for modified α-proximal C-contraction mappings

2014

First we introduce new concepts of contraction mappings, then we establish certain best proximity point theorems for such kind of mappings in metric spaces. Finally, as consequences of these results, we deduce best proximity point theorems in metric spaces endowed with a graph and in partially ordered metric spaces. Moreover, we present an example and some fixed point results to illustrate the usability of the obtained theorems. MSC:46N40, 46T99, 47H10, 54H25.

Pure mathematicsInjective metric spaceApplied Mathematicsmetric spacebest proximity pointFixed pointTopologyConvex metric spaceIntrinsic metricLeast fixed pointMetric spacefixed pointSettore MAT/05 - Analisi MatematicaMetric mapGeometry and TopologyCoincidence pointMathematicsFixed Point Theory and Applications
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Best proximity point theorems for rational proximal contractions

2013

Abstract We provide sufficient conditions which warrant the existence and uniqueness of the best proximity point for two new types of contractions in the setting of metric spaces. The presented results extend, generalize and improve some known results from best proximity point theory and fixed-point theory. We also give some examples to illustrate and validate our definitions and results. MSC:41A65, 46B20, 47H10.

Discrete mathematicsPure mathematicsMetric spaceDifferential geometrySettore MAT/05 - Analisi MatematicaApplied MathematicsProximity problemsUniquenessGeometry and TopologyFixed pointPoint theorybest proximity point contraction fixed point generalized proximal contraction optimal approximate solutionMathematicsFixed Point Theory and Applications
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Coincidence and fixed points for contractions and cyclical contractions in partial metric spaces

2012

Abstract We prove some coincidence and common fixed point results for three mappings satisfying a generalized weak contractive condition in ordered partial metric spaces. As application of the presented results, we give a unique fixed point result for a mapping satisfying a weak cyclical contractive condition. We also provide some illustrative examples. MSC:47H10, 54H25.

Discrete mathematicscyclic weak (ψϕ)-contractionApplied Mathematicspartial metric spacecommon fixed pointFixed pointcompatible mappingCoincidenceweakly increasing mappingsMetric spacecoincidence pointDifferential geometrySettore MAT/05 - Analisi MatematicaCommon fixed pointGeometry and TopologyCoincidence pointTopology (chemistry)MathematicsFixed Point Theory and Applications
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Fixed point theorems for fuzzy mappings and applications to ordinary fuzzy differential equations

2014

Abstract Ran and Reurings (Proc. Am. Math. Soc. 132(5):1435-1443, 2004) proved an analog of the Banach contraction principle in metric spaces endowed with a partial order and discussed some applications to matrix equations. The main novelty in the paper of Ran and Reurings involved combining the ideas in the contraction principle with those in the monotone iterative technique. Motivated by this, we present some common fixed point results for a pair of fuzzy mappings satisfying an almost generalized contractive condition in partially ordered complete metric spaces. Also we give some examples and an application to illustrate our results. MSC:46S40, 47H10, 34A70, 54E50.

Algebra and Number Theoryfuzzy mappingApplied MathematicsFixed-point theoremFuzzy logicComplete metric spaceAlgebraMetric spaceSettore MAT/05 - Analisi Matematicacomplete metric spaceordinary fuzzy differential equationaltering distance functionContraction principleC0-semigroupDifferential algebraic equationAnalysisNumerical partial differential equationsMathematicsAdvances in Difference Equations
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On modified α-ϕ-fuzzy contractive mappings and an application to integral equations

2016

Abstract We introduce the notion of a modified α-ϕ-fuzzy contractive mapping and prove some results in fuzzy metric spaces for such kind of mappings. The theorems presented provide a generalization of some interesting results in the literature. Two examples and an application to integral equations are given to illustrate the usability of our theory.

integral equationsGeneralization02 engineering and technologyFixed point01 natural sciencesFuzzy logicSettore MAT/05 - Analisi Matematica0202 electrical engineering electronic engineering information engineeringmodified α-ϕ-fuzzy contractive mappingDiscrete Mathematics and Combinatorics0101 mathematicsα-admissible mapping with respect to ηMathematicsDiscrete mathematicsbusiness.industryApplied Mathematicslcsh:MathematicsUsabilitylcsh:QA1-939Integral equationFuzzy metric space010101 applied mathematicsAlgebraintegral equationfixed point020201 artificial intelligence & image processing$alpha$-admissible mapping with respect to $eta$ fixed point modified $alpha$-$phi$-fuzzy contractive mapping integral equationsbusinessAnalysisJournal of Inequalities and Applications
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Fixed points for weak alpha-psi-contractions in partial metric spaces

2013

Recently, Samet et al. (2012) introduced the notion of $\alpha $ - $\psi $ -contractive mappings and established some fixed point results in the setting of complete metric spaces. In this paper, we introduce the notion of weak $\alpha $ - $\psi $ -contractive mappings and give fixed point results for this class of mappings in the setting of partial metric spaces. Also, we deduce fixed point results in ordered partial metric spaces. Our results extend and generalize the results of Samet et al.

Partial metric space fixed point alpha-psi-contractive mapping weak alpha-psi-contractive mapping.Settore MAT/03 - Geometria
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