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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
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
Journal Article
Journal of Inequalities and Applications, ISSN 1025-5834, 12/2014, Volume 2014, Issue 1, pp. 1 - 8
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
Journal Article
Fixed Point Theory and Applications, ISSN 1687-1820, 12/2012, Volume 2012, Issue 1, pp. 1 - 7
Journal Article
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
Journal Article
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
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
Journal Article
Fixed Point Theory and Applications, ISSN 1687-1820, 12/2016, Volume 2016, Issue 1, pp. 1 - 12
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 11/2012, Volume 219, Issue 5, pp. 2611 - 2617
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
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
Journal Article
by Xiu, ZY
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
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
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
Journal Article
Journal of Nonlinear and Convex Analysis, ISSN 1345-4773, 2015, Volume 16, Issue 9, pp. 1925 - 1936
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
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
Journal Article
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