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

Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2008, Volume 136, Issue 5, pp. 1861 - 1869

We prove a fixed point theorem that is a very simple generalization of the Banach contraction principle and characterizes the metric completeness of the...

Euclidean space | Mathematical theorems | Mathematical completeness | Diagonal lemma | MATHEMATICS | MATHEMATICS, APPLIED | fixed point | SPACES | Banach contraction principle | metric completeness | Kannan mapping | MAPPINGS | FIXED-POINT THEOREM

Euclidean space | Mathematical theorems | Mathematical completeness | Diagonal lemma | MATHEMATICS | MATHEMATICS, APPLIED | fixed point | SPACES | Banach contraction principle | metric completeness | Kannan mapping | MAPPINGS | FIXED-POINT THEOREM

Journal Article

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2014, Volume 2014, Issue 1, pp. 1 - 8

We present a new generalization of the Banach contraction principle in the setting of Branciari metric spaces.

Banach contraction | fixed point | Analysis | generalized metric | Mathematics, general | Mathematics | Applications of Mathematics | Generalized metric | Fixed point | GAUGE SPACES | MATHEMATICS | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | ASYMPTOTIC CONTRACTIONS | MAPPINGS | COMPLETE METRIC-SPACES | CACCIOPPOLI TYPE

Banach contraction | fixed point | Analysis | generalized metric | Mathematics, general | Mathematics | Applications of Mathematics | Generalized metric | Fixed point | GAUGE SPACES | MATHEMATICS | MATHEMATICS, APPLIED | FIXED-POINT THEOREMS | ASYMPTOTIC CONTRACTIONS | MAPPINGS | COMPLETE METRIC-SPACES | CACCIOPPOLI TYPE

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2008, Volume 2008, Issue 1, pp. 1 - 8

Here we introduce a generalisation of the Banach contraction mapping principle. We show that the result extends two existing generalisations of the same...

Mathematical and Computational Biology | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | MATHEMATICS | FIXED-POINT THEOREMS | MAPS | ALTERING DISTANCES | Fixed point theory | Metric spaces | Banach spaces | Research | Properties | Mappings (Mathematics) | Contraction operators | Mathematical models | Algorithms

Mathematical and Computational Biology | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | MATHEMATICS | FIXED-POINT THEOREMS | MAPS | ALTERING DISTANCES | Fixed point theory | Metric spaces | Banach spaces | Research | Properties | Mappings (Mathematics) | Contraction operators | Mathematical models | Algorithms

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

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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

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

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

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2016, Volume 2016, Issue 1, pp. 1 - 12

The purpose of this paper is to introduce the notions of Θ-type contractions and Θ-type Suzuki contractions and to establish some new fixed point theorems for...

Mathematical and Computational Biology | Mathematics | Topology | Θ-type Suzuki contraction | Θ-type contraction | 47H10 | fixed point | Analysis | Banach contraction principle | 47H09 | Mathematics, general | 49M05 | Applications of Mathematics | Differential Geometry | Usage | Integral equations | Fixed point theory | Banach spaces | Contraction operators | Tests, problems and exercises | Paper | Theorems | Fixed points (mathematics) | Mapping | Metric space

Mathematical and Computational Biology | Mathematics | Topology | Θ-type Suzuki contraction | Θ-type contraction | 47H10 | fixed point | Analysis | Banach contraction principle | 47H09 | Mathematics, general | 49M05 | Applications of Mathematics | Differential Geometry | Usage | Integral equations | Fixed point theory | Banach spaces | Contraction operators | Tests, problems and exercises | Paper | Theorems | Fixed points (mathematics) | Mapping | Metric space

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 11/2012, Volume 219, Issue 5, pp. 2611 - 2617

The purpose of this paper is to introduce the concept of total asymptotically nonexpansive mappings and to prove the demiclosed principle for this kind of...

CAT space | Total asymptotically nonexpansive mappings | Krasnoselskii–Mann type iteration | Demiclosed principle | [formula omitted]-Convergence | Δ-Convergence | Krasnoselskii-Mann type iteration | MATHEMATICS, APPLIED | INVARIANT APPROXIMATIONS | METRIC-SPACES | Delta-Convergence | BANACH-SPACES | CAT-SPACES | FIXED-POINT SETS | CONTRACTIONS

CAT space | Total asymptotically nonexpansive mappings | Krasnoselskii–Mann type iteration | Demiclosed principle | [formula omitted]-Convergence | Δ-Convergence | Krasnoselskii-Mann type iteration | MATHEMATICS, APPLIED | INVARIANT APPROXIMATIONS | METRIC-SPACES | Delta-Convergence | BANACH-SPACES | CAT-SPACES | FIXED-POINT SETS | CONTRACTIONS

Journal Article

MATHEMATICS, ISSN 2227-7390, 09/2019, Volume 7, Issue 9, p. 862

The main purpose of the current work is to present firstly a new generalization of Caristi's fixed point result and secondly the Banach contraction principle....

MATHEMATICS | FIXED-POINT THEOREMS | integral equation | Banach contraction principle | MAPPINGS | Caristi fixed point | ITERATIVE APPROXIMATION | lower semi-continuous function

MATHEMATICS | FIXED-POINT THEOREMS | integral equation | Banach contraction principle | MAPPINGS | Caristi fixed point | ITERATIVE APPROXIMATION | lower semi-continuous function

Journal Article

Journal of Nonlinear Science and Applications, ISSN 2008-1898, 2016, Volume 9, Issue 6, pp. 3858 - 3863

The purpose of this note is to give a natural approach to the extensions of the Banach contraction principle in metric spaces endowed with a partial order, a...

Extended quasi-metric space | Multivalued mapping | Contraction mapping | Monotone mapping | Banach contraction principle | Fixed point | monotone mapping | MATHEMATICS | FIXED-POINT THEOREMS | fixed point | contraction mapping | MAPPINGS | multivalued mapping | extended quasi-metric space

Extended quasi-metric space | Multivalued mapping | Contraction mapping | Monotone mapping | Banach contraction principle | Fixed point | monotone mapping | MATHEMATICS | FIXED-POINT THEOREMS | fixed point | contraction mapping | MAPPINGS | multivalued mapping | extended quasi-metric space

Journal Article

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, ISSN 1064-1246, 2017, Volume 33, Issue 3, pp. 1823 - 1830

In this paper, a new approach to Banach contraction principle in fuzzy metric space is provided. The concepts of convergent sequence, Cauchy sequence, complete...

PSEUDO-METRICS | FIXED-POINT THEOREMS | Fixed point theorem | Banach contraction principle | MAPPINGS | COINCIDENCE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | fuzzy metric space

PSEUDO-METRICS | FIXED-POINT THEOREMS | Fixed point theorem | Banach contraction principle | MAPPINGS | COINCIDENCE | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | fuzzy metric space

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2006, Volume 317, Issue 1, pp. 103 - 112

In this paper, the famous Banach contraction principle and Caristi's fixed point theorem are generalized to the case of multi-valued mappings. Our results are...

Complete metric space | Multi-valued mappings | Nadler's fixed point theorem | Banach contraction principle | Caristi's fixed point theorem | MATHEMATICS | complete metric space | MATHEMATICS, APPLIED | METRIC-SPACES | MAPS | multi-valued mappings

Complete metric space | Multi-valued mappings | Nadler's fixed point theorem | Banach contraction principle | Caristi's fixed point theorem | MATHEMATICS | complete metric space | MATHEMATICS, APPLIED | METRIC-SPACES | MAPS | multi-valued mappings

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

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

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2016, Volume 2016, Issue 1, pp. 1 - 19

In this paper, we establish the existence of a common fixed point of almost generalized contractions on modular spaces. As an application, we present some...

Banach G -contraction | 54E50 | modular space | Mathematical and Computational Biology | Mathematics | Topology | 54H25 | 47H10 | Analysis | almost contraction | Mathematics, general | Applications of Mathematics | Differential Geometry | Banach G-contraction | Fixed point theory | Usage | Graphic methods | Graphs | Mapping | Modular | Integrals

Banach G -contraction | 54E50 | modular space | Mathematical and Computational Biology | Mathematics | Topology | 54H25 | 47H10 | Analysis | almost contraction | Mathematics, general | Applications of Mathematics | Differential Geometry | Banach G-contraction | Fixed point theory | Usage | Graphic methods | Graphs | Mapping | Modular | Integrals

Journal Article

19.
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Saturated Contraction Principles for Non Self Operators, Generalizations and Applications

Filomat, ISSN 0354-5180, 1/2017, Volume 31, Issue 11, pp. 3391 - 3406

Let ( ) be a metric space, ⊂ a nonempty closed subset of and let : → be a non self operator. In this paper we study the following problem: under which...

Mathematical theorems | Approximation | Radii of convergence | Mathematical analysis | Diagonal lemma | Hilbert spaces | Mathematics | Banach space | Iterative methods | Operator theory | Basin of attraction | Retraction-displacement condition | Well posedness | Retraction | Metric space | Data dependence | Generalized metric space | Demicontractive mapping | Ostrowski property | Ulam stability | Fixed point | Non self operator | MATHEMATICS, APPLIED | non self operator | generalized metric space | STABILITY | retraction-displacement condition | EQUATIONS | well posedness | basin of attraction | metric space | MATHEMATICS | FIXED-POINT THEOREMS | RETRACTION METHODS | fixed point | retraction | demicontractive mapping | MAPPINGS | ITERATIVE APPROXIMATION | data dependence

Mathematical theorems | Approximation | Radii of convergence | Mathematical analysis | Diagonal lemma | Hilbert spaces | Mathematics | Banach space | Iterative methods | Operator theory | Basin of attraction | Retraction-displacement condition | Well posedness | Retraction | Metric space | Data dependence | Generalized metric space | Demicontractive mapping | Ostrowski property | Ulam stability | Fixed point | Non self operator | MATHEMATICS, APPLIED | non self operator | generalized metric space | STABILITY | retraction-displacement condition | EQUATIONS | well posedness | basin of attraction | metric space | MATHEMATICS | FIXED-POINT THEOREMS | RETRACTION METHODS | fixed point | retraction | demicontractive mapping | MAPPINGS | ITERATIVE APPROXIMATION | data dependence

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2010, Volume 2010, Issue 1, pp. 1 - 14

We prove the demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces. As a consequence, we obtain a -convergence theorem of the...

Mathematical and Computational Biology | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | MATHEMATICS | SEMIGROUPS | MATHEMATICS, APPLIED | INVARIANT APPROXIMATIONS | METRIC-SPACES | BANACH-SPACES | BEHAVIOR | THEOREMS | CAT-SPACES | FIXED-POINT SETS | CONVERGENCE | CONTRACTIONS

Mathematical and Computational Biology | Analysis | Mathematics, general | Mathematics | Applications of Mathematics | Topology | Differential Geometry | MATHEMATICS | SEMIGROUPS | MATHEMATICS, APPLIED | INVARIANT APPROXIMATIONS | METRIC-SPACES | BANACH-SPACES | BEHAVIOR | THEOREMS | CAT-SPACES | FIXED-POINT SETS | CONVERGENCE | CONTRACTIONS

Journal Article

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