Search results for "Periodic point"

showing 3 items of 3 documents

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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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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Coupled fixed-point results for T-contractions on cone metric spaces with applications

2015

The notion of coupled fixed point was introduced in 2006 by Bhaskar and Lakshmikantham. On the other hand, Filipovićet al. [M. Filipovićet al., “Remarks on “Cone metric spaces and fixed-point theorems of T-Kannan and T-Chatterjea contractive mappings”,” Math. Comput. Modelling 54, 1467–1472 (2011)] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper we prove some coupled fixed-point theorems for certain T-contractions and study the existence of solutions of a system of nonlinear integral equations using the results of our work. The results of this paper extend and generalize well-known comparable results in the literature.

coupled fixed pointPure mathematicscone metric spaceGeneral MathematicsInjective metric spaceMathematical analysisPeriodic pointFixed pointNonlinear integral equationConvex metric spaceT-contractionMetric spaceCone (topology)Settore MAT/05 - Analisi Matematicasubsequentially convergentsequentially convergentMathematicsMathematical Notes
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