Proceedings of the American Mathematical Society, ISSN 0002-9939, 04/2008, Volume 136, Issue 4, pp. 1359 - 1373

We give some generalizations of the Banach Contraction Principle to mappings on a metric space endowed with a graph. This extends and subsumes many recent...

Sufficient conditions | Mathematical theorems | Business orders | Diagonal lemma | Linear transformations | Ordinary differential equations | Connectivity | Banach space | Vertices | MATHEMATICS | MATHEMATICS, APPLIED | Bernstein operator | FIXED-POINT THEOREMS | fixed point | PARTIALLY ORDERED SETS | Picard operator | connected graph | partial order

Sufficient conditions | Mathematical theorems | Business orders | Diagonal lemma | Linear transformations | Ordinary differential equations | Connectivity | Banach space | Vertices | MATHEMATICS | MATHEMATICS, APPLIED | Bernstein operator | FIXED-POINT THEOREMS | fixed point | PARTIALLY ORDERED SETS | Picard operator | connected graph | partial order

Journal Article

ISRN Applied Mathematics, ISSN 2090-5572, 2013, Volume 2013, pp. 1 - 4

We extend the application of nearly contraction mapping principle introduced by Sahu (2005) for existence of fixed points of demicontinuous mappings to certain...

Operators | Construction | Fixed points (mathematics) | Asymptotic properties | Mathematical analysis | Nonlinearity | Mapping | Banach space | Iterative methods

Operators | Construction | Fixed points (mathematics) | Asymptotic properties | Mathematical analysis | Nonlinearity | Mapping | Banach space | Iterative methods

Journal Article

Nonlinear Analysis: Modelling and Control, ISSN 1392-5113, 2018, Volume 23, Issue 1, pp. 31 - 39

In this paper, uniqueness results for boundary value problem of fractional differential equation are obtained. Both the Banach's contraction mapping principle...

Fractional differential equation | Banach’s contraction mapping principle | Uniqueness results | EXISTENCE | SYSTEM | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Banach's contraction mapping principle | POSITIVE SOLUTIONS | fractional differential equation | uniqueness results

Fractional differential equation | Banach’s contraction mapping principle | Uniqueness results | EXISTENCE | SYSTEM | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | Banach's contraction mapping principle | POSITIVE SOLUTIONS | fractional differential equation | uniqueness results

Journal Article

Numerical Functional Analysis and Optimization, ISSN 0163-0563, 08/2017, Volume 38, Issue 8, pp. 1060 - 1068

In this paper, we obtain an existence theorem for fixed points of contractive set-valued mappings on a metric space endowed with a graph. This theorem unifies...

Bernstein operators | metric space | 47H10 | set-valued mapping | fixed Point | graph | 47H04 | 54H25 | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | Operators | Theorems | Fixed points (mathematics) | Metric space | Existence theorems | Banach space | Linear operators

Bernstein operators | metric space | 47H10 | set-valued mapping | fixed Point | graph | 47H04 | 54H25 | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | Operators | Theorems | Fixed points (mathematics) | Metric space | Existence theorems | Banach space | Linear operators

Journal Article

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Full Text
Estimation of the complexity of a digital image from the viewpoint of fixed point theory

Applied Mathematics and Computation, ISSN 0096-3003, 04/2019, Volume 347, pp. 236 - 248

The present paper introduces and estimates the complexity of the fixed point property of a digital image ( ) for any -self-map of ( ), where a -self-map of ( )...

Closed k-surface | Banach contraction mapping principle | Uniformly k-connected | Digital topology | Complexity of a digital image | Iterations of a Banach contraction map | [formula omitted]-self-map | Strictly k-connected | Fixed point property | Complexity | k−DC-self-map | MATHEMATICS, APPLIED | PROPERTY | k - DC-self-map | CONTRACTION PRINCIPLE

Closed k-surface | Banach contraction mapping principle | Uniformly k-connected | Digital topology | Complexity of a digital image | Iterations of a Banach contraction map | [formula omitted]-self-map | Strictly k-connected | Fixed point property | Complexity | k−DC-self-map | MATHEMATICS, APPLIED | PROPERTY | k - DC-self-map | CONTRACTION PRINCIPLE

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2012, Volume 2012, Issue 1, pp. 1 - 7

We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However,...

0-compact set | Mathematical and Computational Biology | fixed point | Analysis | Banach contraction principle | Mathematics, general | partial metric space | Mathematics | Applications of Mathematics | Topology | Differential Geometry | cyclic mapping | Partial metric space | Cyclic mapping | Fixed point | Fixed point theory | Usage | Metric spaces | Banach spaces | Contraction operators | Theorems | Mapping | Decomposition | Metric space

0-compact set | Mathematical and Computational Biology | fixed point | Analysis | Banach contraction principle | Mathematics, general | partial metric space | Mathematics | Applications of Mathematics | Topology | Differential Geometry | cyclic mapping | Partial metric space | Cyclic mapping | Fixed point | Fixed point theory | Usage | Metric spaces | Banach spaces | Contraction operators | Theorems | Mapping | Decomposition | Metric space

Journal Article

Fractals, ISSN 0218-348X, 06/2017, Volume 25, Issue 3, p. 1750033

This paper is devoted to the investigation of the Hadamard fractional calculus in three aspects. First, we study the semigroup and reciprocal properties of the...

Banach Contraction Mapping Principle | Semigroup | Perturbation | Well-Posedness | Hadamard-Type Fractional Operators | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | DIFFERENTIAL-EQUATIONS

Banach Contraction Mapping Principle | Semigroup | Perturbation | Well-Posedness | Hadamard-Type Fractional Operators | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MULTIDISCIPLINARY SCIENCES | DIFFERENTIAL-EQUATIONS

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 11/2012, Volume 64, Issue 10, pp. 3267 - 3275

In this paper, we study the solvability of a Caputo fractional differential equation model involving the -Laplacian operator with boundary value conditions. By...

[formula omitted]-Laplacian operator | Banach contraction mapping principle | Boundary value problem | Caputo fractional derivative | Existence and uniqueness | p-Laplacian operator | EXISTENCE | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | MULTIPLE POSITIVE SOLUTIONS | Analysis | Differential equations

[formula omitted]-Laplacian operator | Banach contraction mapping principle | Boundary value problem | Caputo fractional derivative | Existence and uniqueness | p-Laplacian operator | EXISTENCE | MATHEMATICS, APPLIED | BOUNDARY-VALUE-PROBLEMS | MULTIPLE POSITIVE SOLUTIONS | Analysis | Differential equations

Journal Article

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Banach's Contraction Principle for Nonlinear Contraction Mappings in Modular Metric Spaces

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, ISSN 0126-6705, 01/2017, Volume 40, Issue 1, pp. 335 - 344

The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces,...

MATHEMATICS | FIXED-POINT THEOREMS | Banach theorem | Modular metric space | Edelstein theorem | Fixed point

MATHEMATICS | FIXED-POINT THEOREMS | Banach theorem | Modular metric space | Edelstein theorem | Fixed point

Journal Article

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Banach’s Contraction Principle for Nonlinear Contraction Mappings in Modular Metric Spaces

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 1/2017, Volume 40, Issue 1, pp. 335 - 344

The notion of a modular metric on an arbitrary set and the corresponding modular spaces, generalizing classical modulars over linear spaces like Orlicz spaces,...

47H10 | Banach theorem | 47H09 | Mathematics, general | Modular metric space | Mathematics | Edelstein theorem | Applications of Mathematics | Fixed point | Fixed points (mathematics) | Vector spaces

47H10 | Banach theorem | 47H09 | Mathematics, general | Modular metric space | Mathematics | Edelstein theorem | Applications of Mathematics | Fixed point | Fixed points (mathematics) | Vector spaces

Journal Article

IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, ISSN 0265-0754, 09/2019, Volume 36, Issue 3, pp. 869 - 899

In this article, we study the controllability of finite-dimensional dynamical control systems modelled by semilinear impulsive ordinary differential equations...

LINEAR-SYSTEMS | MATHEMATICS, APPLIED | Banach contraction mapping principle | CONSTRAINED CONTROLLABILITY | time delays | Schauder fixed-point theorem | controllability | NONLINEAR-SYSTEMS | RELATIVE-CONTROLLABILITY | impulsive systems | OBSERVABILITY | VARIABLE DELAYS | AUTOMATION & CONTROL SYSTEMS

LINEAR-SYSTEMS | MATHEMATICS, APPLIED | Banach contraction mapping principle | CONSTRAINED CONTROLLABILITY | time delays | Schauder fixed-point theorem | controllability | NONLINEAR-SYSTEMS | RELATIVE-CONTROLLABILITY | impulsive systems | OBSERVABILITY | VARIABLE DELAYS | AUTOMATION & CONTROL SYSTEMS

Journal Article

Journal of Theoretical and Applied Information Technology, ISSN 1992-8645, 06/2016, Volume 88, Issue 2, pp. 367 - 374

Journal Article

Electronic Journal of Differential Equations, ISSN 1072-6691, 09/2014, Volume 2014, Issue 191, pp. 1 - 17

In this article, we introduced and explore the properties of two sets of functions: weighted pseudo periodic functions of class r, and weighted Stepanov-like...

Banach contraction mapping principle | Neutral functional differential equation | Weighted pseudo periodicity | Weighted Stepanov-like pseudo periodic | weighted Stepanov-like pseudo periodic | neutral functional differential equation

Banach contraction mapping principle | Neutral functional differential equation | Weighted pseudo periodicity | Weighted Stepanov-like pseudo periodic | weighted Stepanov-like pseudo periodic | neutral functional differential equation

Journal Article

Mathematical Communications, ISSN 1331-0623, 2018, Volume 23, Issue 2, pp. 259 - 277

In this paper, we introduce the concept of a pseudo affine-periodic function via measure theory, that is, a measure pseudo (Q, T)-affine-periodic function. The...

Leray-Schauder alternative theorem | Measure theory | Measure pseudo affine-periodic function | Banach contraction mapping principle | Exponential dichotomy | MATHEMATICS | MATHEMATICS, APPLIED | exponential dichotomy | WEIGHTED PSEUDO | DYNAMICAL-SYSTEMS | measure theory | AUTOMORPHIC-FUNCTIONS

Leray-Schauder alternative theorem | Measure theory | Measure pseudo affine-periodic function | Banach contraction mapping principle | Exponential dichotomy | MATHEMATICS | MATHEMATICS, APPLIED | exponential dichotomy | WEIGHTED PSEUDO | DYNAMICAL-SYSTEMS | measure theory | AUTOMORPHIC-FUNCTIONS

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 2010, Volume 411, Issue 16, pp. 1742 - 1749

The Banach fixed-point theorem states that a contraction mapping on a complete metric space has a unique fixed point. Given an oracle access to a finite metric...

Banach fixed-point theorem | Query complexity | Caristi–Kirk fixed-point theorem | Contraction mapping principle | Caristi-Kirk fixed-point theorem | THEOREMS | PRINCIPLE | COMPUTER SCIENCE, THEORY & METHODS

Banach fixed-point theorem | Query complexity | Caristi–Kirk fixed-point theorem | Contraction mapping principle | Caristi-Kirk fixed-point theorem | THEOREMS | PRINCIPLE | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

SIAM Journal on Control and Optimization, ISSN 0363-0129, 2003, Volume 42, Issue 5, pp. 1604 - 1622

Various sufficient conditions for approximate controllability of linear evolution systems in abstract spaces have been obtained, but approximate...

Semilinear evolution equations | Controllability | Stochastic evolution equations | The contraction mapping principle | The schauder fixed point theorem | Symmetric operators | MATHEMATICS, APPLIED | semilinear evolution equations | TERMS | symmetric operators | the contraction mapping principle | controllability | the Schauder. fixed point theorem | stochastic evolution equations | HEAT-EQUATION | SYSTEMS | OBSERVABILITY | AUTOMATION & CONTROL SYSTEMS | BANACH-SPACE

Semilinear evolution equations | Controllability | Stochastic evolution equations | The contraction mapping principle | The schauder fixed point theorem | Symmetric operators | MATHEMATICS, APPLIED | semilinear evolution equations | TERMS | symmetric operators | the contraction mapping principle | controllability | the Schauder. fixed point theorem | stochastic evolution equations | HEAT-EQUATION | SYSTEMS | OBSERVABILITY | AUTOMATION & CONTROL SYSTEMS | BANACH-SPACE

Journal Article

Journal of Nonlinear and Convex Analysis, ISSN 1345-4773, 2015, Volume 16, Issue 9, pp. 1925 - 1936

Let K be a non-empty closed subset of a Banach space X endowed with a graph G and let T : K -> X be a G-contraction that satisfies Rothe's boundary condition,...

Property (L) | Property (M) | Orbitally G-continuity | Non self mapping | Picard operator | Rothe's boundary condition | Banach space | Directed graph | Fixed point | G-contraction | MATHEMATICS, APPLIED | GENERALIZED CONTRACTIONS | ADMISSIBLE PERTURBATIONS | METRIC-SPACES | APPROXIMATION | PARTIALLY ORDERED SETS | MATHEMATICS | FIXED-POINT THEOREMS | orbitally G-continuity | fixed point | directed graph | property (M) | non self mapping | property (L) | OPERATORS | ORDINARY DIFFERENTIAL-EQUATIONS

Property (L) | Property (M) | Orbitally G-continuity | Non self mapping | Picard operator | Rothe's boundary condition | Banach space | Directed graph | Fixed point | G-contraction | MATHEMATICS, APPLIED | GENERALIZED CONTRACTIONS | ADMISSIBLE PERTURBATIONS | METRIC-SPACES | APPROXIMATION | PARTIALLY ORDERED SETS | MATHEMATICS | FIXED-POINT THEOREMS | orbitally G-continuity | fixed point | directed graph | property (M) | non self mapping | property (L) | OPERATORS | ORDINARY DIFFERENTIAL-EQUATIONS

Journal Article

Advances in Difference Equations, ISSN 1687-1839, 12/2018, Volume 2018, Issue 1, pp. 1 - 7

In this paper, the existence and uniqueness of solutions for a class of nonlinear integro-differential equations on unbounded domains in Banach spaces are...

Banach contraction mapping principle | 34G20 | Fixed points of operator | Mathematics | 47H10 | Ordinary Differential Equations | Functional Analysis | 47G20 | Analysis | Difference and Functional Equations | Mathematics, general | 47H07 | Integro-differential equation | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | VOLTERRA TYPE | MIXED-TYPE | DIFFERENTIAL-EQUATIONS | INTEGRAL-EQUATIONS | GLOBAL-SOLUTIONS | INITIAL-VALUE PROBLEMS | Nonlinear equations | Error analysis | Mathematical analysis | Differential equations | Uniqueness | Banach spaces | Banach space

Banach contraction mapping principle | 34G20 | Fixed points of operator | Mathematics | 47H10 | Ordinary Differential Equations | Functional Analysis | 47G20 | Analysis | Difference and Functional Equations | Mathematics, general | 47H07 | Integro-differential equation | Partial Differential Equations | MATHEMATICS | MATHEMATICS, APPLIED | VOLTERRA TYPE | MIXED-TYPE | DIFFERENTIAL-EQUATIONS | INTEGRAL-EQUATIONS | GLOBAL-SOLUTIONS | INITIAL-VALUE PROBLEMS | Nonlinear equations | Error analysis | Mathematical analysis | Differential equations | Uniqueness | Banach spaces | Banach space

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 8/2018, Volume 15, Issue 4, pp. 1 - 16

In this paper, we study the existence and uniqueness of Stepanov-almost periodic mild solution to the non-autonomous neutral functional differential equation...

34C27 | almost periodic function | 47D06 | contraction mapping principle | neutral functional differential equation | evolution family | 43A60 | Mathematics, general | Mathematics | 34K14 | Stepanov-almost periodic function | MATHEMATICS | MATHEMATICS, APPLIED | Differential equations

34C27 | almost periodic function | 47D06 | contraction mapping principle | neutral functional differential equation | evolution family | 43A60 | Mathematics, general | Mathematics | 34K14 | Stepanov-almost periodic function | MATHEMATICS | MATHEMATICS, APPLIED | Differential equations

Journal Article

MISKOLC MATHEMATICAL NOTES, ISSN 1787-2405, 2018, Volume 19, Issue 2, pp. 847 - 863

The existence and uniqueness of solutions for a multi-point boundary value problem (BVP) of impulsive fractional differential equations are investigated by...

Schaefer's fixed point theorem | EXISTENCE | MATHEMATICS | Banach contraction mapping principle | boundary value problems | BOUNDARY-VALUE-PROBLEMS | SYSTEMS | fractional differential equations | Caputo fractional derivative | impulsive differential equations

Schaefer's fixed point theorem | EXISTENCE | MATHEMATICS | Banach contraction mapping principle | boundary value problems | BOUNDARY-VALUE-PROBLEMS | SYSTEMS | fractional differential equations | Caputo fractional derivative | impulsive differential equations

Journal Article

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