0000000000234203

AUTHOR

Deepesh Kumar Patel

showing 2 related works from this author

Fixed points of α-type F-contractive mappings with an application to nonlinear fractional differential equation

2016

Abstract In this paper, we introduce new concepts of α-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from α-GF-contractions given in [8]. Then, sufficient conditions for the existence and uniqueness of fixed point are established for these new types of contractive mappings, in the setting of complete metric space. Consequently, the obtained results encompass various generalizations of the Banach contraction principle. Moreover, some examples and an application to nonlinear fractional differential equation are given to illustrate the usability of the new theory.

Pure mathematicsClass (set theory)General Mathematics010102 general mathematicsMathematical analysisGeneral Physics and AstronomyFixed pointType (model theory)Fixed point01 natural sciencesComplete metric space010101 applied mathematicsNonlinear fractional differential equationsNonlinear fractional differential equationPeriodic pointsSettore MAT/05 - Analisi MatematicaUniqueness0101 mathematicsContraction principleMathematics
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Some coincidence and periodic points results in a metric space endowed with a graph and applications

2015

The purpose of this paper is to obtain some coincidence and periodic points results for generalized $F$-type contractions in a metric space endowed with a graph. Some examples are given to illustrate the new theory. Then, we apply our results to establishing the existence of solution for a certain type of nonlinear integral equation.

Pure mathematicsAlgebra and Number TheoryPeriodic sequencePeriodic pointCoincidence point nonlinear integral equation periodic point.Type (model theory)TopologyNonlinear integral equationnonlinear integral equationCoincidenceCoincidence pointMetric spaceperiodic point54H25Settore MAT/05 - Analisi MatematicaGraph (abstract data type)05C40Coincidence pointAnalysis47H10Mathematics
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