Advances in Nonlinear Analysis, ISSN 2191-9496, 08/2018, Volume 7, Issue 3, pp. 307 - 311

We give a generalized version of the well-known Borsuk’s antipodal fixed point theorem for a large class of antipodally approachable condensing or compact set...

47H10 | approximative selection | compact set-valued maps | Borsuk’s antipodal fixed point theorem | antipodally approximable set-valued maps | 54C60 | measure of non-compactness | condensing set-valued maps | Borsuk's antipodal fixed point theorem | MATHEMATICS | MATHEMATICS, APPLIED | HOMOTOPY METHOD | Economics and Finance | Mathematics | Humanities and Social Sciences

47H10 | approximative selection | compact set-valued maps | Borsuk’s antipodal fixed point theorem | antipodally approximable set-valued maps | 54C60 | measure of non-compactness | condensing set-valued maps | Borsuk's antipodal fixed point theorem | MATHEMATICS | MATHEMATICS, APPLIED | HOMOTOPY METHOD | Economics and Finance | Mathematics | Humanities and Social Sciences

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 1/2019, Volume 180, Issue 1, pp. 34 - 47

In the case of Banach spaces, there are theorems stating the invariance of the fixed point property of mappings under a homotopy...

Mathematics | Theory of Computation | Coincidence point | Optimization | Isotone mapping | 54H25 | Order homotopy | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | 06A06 | Partial order | Fixed point | EXISTENCE | MATHEMATICS, APPLIED | SERIES | METRIC-SPACES | APPROXIMATION | SEARCH | STABILITY | VALUED MAPPINGS | PRINCIPLE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COVERING MAPPINGS | SUBORDINATE | Theorems | Fixed points (mathematics) | Coincidences | Preservation | Banach space

Mathematics | Theory of Computation | Coincidence point | Optimization | Isotone mapping | 54H25 | Order homotopy | Calculus of Variations and Optimal Control; Optimization | Operations Research/Decision Theory | Applications of Mathematics | Engineering, general | 06A06 | Partial order | Fixed point | EXISTENCE | MATHEMATICS, APPLIED | SERIES | METRIC-SPACES | APPROXIMATION | SEARCH | STABILITY | VALUED MAPPINGS | PRINCIPLE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | COVERING MAPPINGS | SUBORDINATE | Theorems | Fixed points (mathematics) | Coincidences | Preservation | Banach space

Journal Article

Journal of Mathematical Economics, ISSN 0304-4068, 12/2014, Volume 55, Issue 1, pp. 186 - 189

Let X be a convex subset of a locally convex topological vector space, let U⊂X be open with U¯ compact, let F:U¯→X be an upper semicontinuous convex valued correspondence with no fixed points in U...

Fixed point index | Kohlberg–Mertens stability | Fixed points | Stochastic games | Essential sets | Homotopy | Kohlberg-Mertens stability | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | EQUILIBRIA | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS

Fixed point index | Kohlberg–Mertens stability | Fixed points | Stochastic games | Essential sets | Homotopy | Kohlberg-Mertens stability | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | EQUILIBRIA | SOCIAL SCIENCES, MATHEMATICAL METHODS | ECONOMICS

Journal Article

Order, ISSN 0167-8094, 11/2015, Volume 32, Issue 3, pp. 301 - 311

A topological space has the fixed point property if every continuous self-map of that space has at least one fixed point...

Geometry | Discrete Mathematics in Computer Science | Finite poset | Homotopy | Kolmogorov space | Mathematics | Theory of Computation | Fixed point property | MATHEMATICS | PRODUCTS | THEOREM | PARTIALLY ORDERED SETS

Geometry | Discrete Mathematics in Computer Science | Finite poset | Homotopy | Kolmogorov space | Mathematics | Theory of Computation | Fixed point property | MATHEMATICS | PRODUCTS | THEOREM | PARTIALLY ORDERED SETS

Journal Article

5.
Full Text
An infeasible homotopy method for solving fixed point problems on a general unbounded set

Journal of Applied Mathematics and Computing, ISSN 1598-5865, 2/2015, Volume 47, Issue 1, pp. 277 - 289

In this paper, we consider an infeasible homotopy method to solve fixed point problems on a general unbounded set...

65L05 | Computational Mathematics and Numerical Analysis | Global convergence | Infeasible homotopy method | Mathematics | Theory of Computation | 65C20 | 90C30 | Mathematics of Computing | 90C33 | Appl.Mathematics/Computational Methods of Engineering | Unbounded set | Fixed point problems | Studies | Mathematical analysis | Set theory | Fixed points (mathematics) | Perturbation methods | Computation | Texts | Mathematical models | Computational efficiency | Expansion | Convergence

65L05 | Computational Mathematics and Numerical Analysis | Global convergence | Infeasible homotopy method | Mathematics | Theory of Computation | 65C20 | 90C30 | Mathematics of Computing | 90C33 | Appl.Mathematics/Computational Methods of Engineering | Unbounded set | Fixed point problems | Studies | Mathematical analysis | Set theory | Fixed points (mathematics) | Perturbation methods | Computation | Texts | Mathematical models | Computational efficiency | Expansion | Convergence

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2009, Volume 222, Issue 1, pp. 151 - 171

In this paper, when G is the circle S 1 and M is a G-space, we study the rational homotopy type of the fixed point set M G , the homotopy fixed point set M h G...

Space of sections | Fixed point set | Homotopy fixed point set | Rational homotopy | BUNDLE | MATHEMATICS | FUNCTION-SPACES | MAPS

Space of sections | Fixed point set | Homotopy fixed point set | Rational homotopy | BUNDLE | MATHEMATICS | FUNCTION-SPACES | MAPS

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2016, Volume 2016, Issue 1, pp. 1 - 20

Based on the notions of both contractibility and local contractibility, many works were done in fixed point theory...

68U10 | Schauder’s fixed point theorem | Mathematical and Computational Biology | Khalimsky homotopy | Mathematics | local contractibility | Topology | Khalimsky topology | 55N35 | Analysis | Mathematics, general | fixed point property | Applications of Mathematics | Differential Geometry | contractibility | Digital | Maps | Categories | Digital mapping

68U10 | Schauder’s fixed point theorem | Mathematical and Computational Biology | Khalimsky homotopy | Mathematics | local contractibility | Topology | Khalimsky topology | 55N35 | Analysis | Mathematics, general | fixed point property | Applications of Mathematics | Differential Geometry | contractibility | Digital | Maps | Categories | Digital mapping

Journal Article

8.
Full Text
A boundary perturbation interior point homotopy method for solving fixed point problems

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 05/2011, Volume 377, Issue 2, pp. 683 - 694

In this paper, a boundary perturbation interior point homotopy method is proposed to give a constructive proof of the general Brouwer fixed point theorem and thus solve fixed point problems in a class of nonconvex sets...

Nonconvex sets | Brouwer fixed point theorem | Boundary perturbation interior point homotopy method | Initial points | MATHEMATICS | MATHEMATICS, APPLIED | THEOREM | CONSTRUCTIVE PROOF | Analysis | Methods | Algorithms

Nonconvex sets | Brouwer fixed point theorem | Boundary perturbation interior point homotopy method | Initial points | MATHEMATICS | MATHEMATICS, APPLIED | THEOREM | CONSTRUCTIVE PROOF | Analysis | Methods | Algorithms

Journal Article

Journal of the European Mathematical Society : JEMS, ISSN 1435-9855, 2020, Volume 22, Issue 6, pp. 1971 - 2046

We consider self-homeomorphisms h of some surface S. A subset F of the fixed point set of h is said to be unlinked if there is an isotopy from the identity to h that fixes every point of F...

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | HOMEOMORPHISMS | Surface homeomorphism | 2-MANIFOLDS | fixed point | RESIDUAL FINITENESS | isotopy | TRANSVERSE | homotopy | CURVES

EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | HOMEOMORPHISMS | Surface homeomorphism | 2-MANIFOLDS | fixed point | RESIDUAL FINITENESS | isotopy | TRANSVERSE | homotopy | CURVES

Journal Article

1988, Lecture notes in mathematics, ISBN 3540501878, Volume 1343, 147

..., continuous submersions, and fibre bundles. It thus addresses equivariant point set topology as well as equivariant homotopy theory...

Fixed point theory | Homotopy theory | Mappings (Mathematics) | Algebraic topology

Fixed point theory | Homotopy theory | Mappings (Mathematics) | Algebraic topology

Book

2006, Topological fixed point theory and its applications, ISBN 9781402039300, Volume 3, xi, 319

.... A modern exposition of the classical topological fixed-point theory with a complete set of all the necessary notions as well as new proofs of the Lefschetz-Hopf and Wecken theorems are included...

Fixed point theory | Homotopy theory | Algebraic topology | Dynamical Systems and Ergodic Theory | Algebraic Topology | Mathematics

Fixed point theory | Homotopy theory | Algebraic topology | Dynamical Systems and Ergodic Theory | Algebraic Topology | Mathematics

Book

Journal of Inequalities and Applications, ISSN 1025-5834, 12/2019, Volume 2019, Issue 1, pp. 1 - 8

As is well known, fixed point theorems and problems play important roles in differential equations, mathematical programming, control, and so on...

34B15 | 35A01 | 39B05 | Mathematics | Constructive proofs | 90C30 | Inequality techniques | Analysis | Mathematics, general | 65H10 | Applications of Mathematics | Fixed point problems | Homotopy methods | MATHEMATICS | MATHEMATICS, APPLIED | THEOREMS | CONSTRUCTIVE PROOF | CONVERGENCE | Fixed points (mathematics) | Convexity | Differential equations | Mathematical programming

34B15 | 35A01 | 39B05 | Mathematics | Constructive proofs | 90C30 | Inequality techniques | Analysis | Mathematics, general | 65H10 | Applications of Mathematics | Fixed point problems | Homotopy methods | MATHEMATICS | MATHEMATICS, APPLIED | THEOREMS | CONSTRUCTIVE PROOF | CONVERGENCE | Fixed points (mathematics) | Convexity | Differential equations | Mathematical programming

Journal Article

Mathematics (Basel), ISSN 2227-7390, 06/2020, Volume 8, Issue 6, p. 921

The present paper investigates digital topological properties of an alignment of fixed point sets which can play an important role in fixed point theory from the viewpoints of computational or digital topology...

digital image | k-contractibility | alignment | k-homotopy | digital wedge | normal adjacency

digital image | k-contractibility | alignment | k-homotopy | digital wedge | normal adjacency

Journal Article

Fixed Point Theory and Applications, ISSN 1687-1820, 12/2015, Volume 2015, Issue 1, pp. 1 - 14

Let T : X → X $T: X\to X$ be a given operator and F T $F_{T}$ be the set of its fixed points...

Mathematical and Computational Biology | Mathematics | Topology | partial metric | 54H25 | 47H10 | fixed point | Analysis | φ -admissible | Mathematics, general | Applications of Mathematics | homotopy result | Differential Geometry | φ-admissible | MATHEMATICS | PARTIAL METRIC-SPACES | GENERALIZED CONTRACTIONS | THEOREMS | MAPPINGS | phi-admissible | Texts | Operators | Theorems | Fixed points (mathematics)

Mathematical and Computational Biology | Mathematics | Topology | partial metric | 54H25 | 47H10 | fixed point | Analysis | φ -admissible | Mathematics, general | Applications of Mathematics | homotopy result | Differential Geometry | φ-admissible | MATHEMATICS | PARTIAL METRIC-SPACES | GENERALIZED CONTRACTIONS | THEOREMS | MAPPINGS | phi-admissible | Texts | Operators | Theorems | Fixed points (mathematics)

Journal Article

Lobachevskii Journal of Mathematics, ISSN 1995-0802, 11/2017, Volume 38, Issue 6, pp. 1069 - 1074

In this paper sufficient conditions are presented for the least element existence in the common fixed point set of a family of multivalued mappings on ordered sets...

Geometry | Algebra | order-homotopy | concordantly isotone mappings | Common fixed point | Analysis | Mathematics, general | Probability Theory and Stochastic Processes | Mathematics | partial order | Mathematical Logic and Foundations

Geometry | Algebra | order-homotopy | concordantly isotone mappings | Common fixed point | Analysis | Mathematics, general | Probability Theory and Stochastic Processes | Mathematics | partial order | Mathematical Logic and Foundations

Journal Article

Mathematical Notes, ISSN 0001-4346, 9/2019, Volume 106, Issue 3, pp. 591 - 601

.... We study the problem as to whether the existence of a fixed point (or a coincidence point...

fixed point | coincidence point | Mathematics, general | Mathematics | multivalued homotopy | ordered set | pair of equilibrium strategies

fixed point | coincidence point | Mathematics, general | Mathematics | multivalued homotopy | ordered set | pair of equilibrium strategies

Journal Article

TOPOLOGY AND ITS APPLICATIONS, ISSN 0166-8641, 08/2014, Volume 173, pp. 240 - 263

The main purpose of this work is to study the minimal fixed point set of fiber-preserving maps for spaces which are fiber bundles over the circle and the fiber is the torus...

MATHEMATICS | MATHEMATICS, APPLIED | Fiberwise homotopy | Fiber bundle | One-parameter fixed point theory | Minimal fixed point set

MATHEMATICS | MATHEMATICS, APPLIED | Fiberwise homotopy | Fiber bundle | One-parameter fixed point theory | Minimal fixed point set

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 11/2011, Volume 218, Issue 6, pp. 2398 - 2406

In this paper, common fixed point theorems for four mappings satisfying a generalized nonlinear contraction type condition on partial metric spaces are proved...

Coincidence point | Partial metric space | Common fixed point | Homotopy | Weakly compatible pair of mappings | MATHEMATICS, APPLIED | THEOREM | Mechanical engineering | Operators | Theorems | Fixed points (mathematics) | Metric space | Computation | Nonlinearity | Mathematical models | Mapping | Topology

Coincidence point | Partial metric space | Common fixed point | Homotopy | Weakly compatible pair of mappings | MATHEMATICS, APPLIED | THEOREM | Mechanical engineering | Operators | Theorems | Fixed points (mathematics) | Metric space | Computation | Nonlinearity | Mathematical models | Mapping | Topology

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 01/2018, Volume 328, pp. 302 - 313

The purpose of this paper is to obtain some common fixed point results for two mappings satisfying various contractive conditions in metric-like spaces...

Metric-like spaces | Coincidence point | Common fixed point | Adomian | Homotopy | MATHEMATICS, APPLIED | SET | FIXED-POINTS | CONTRACTIONS

Metric-like spaces | Coincidence point | Common fixed point | Adomian | Homotopy | MATHEMATICS, APPLIED | SET | FIXED-POINTS | CONTRACTIONS

Journal Article

Nonlinear analysis, ISSN 0362-546X, 2009, Volume 70, Issue 9, pp. 3371 - 3377

...) of the fixed point theory for a new type contractive multivalued operator. The results complement and extend some very recent results proved by M. Kikkawa...

Generalized contraction | Multivalued operator | Data dependence | Homotopy result | Multivalued weakly Picard operator | Nonself multivalued operator | Fixed point | Strict fixed point | Well-posedness | MATHEMATICS, APPLIED | SET | METRIC-SPACES | MATHEMATICS

Generalized contraction | Multivalued operator | Data dependence | Homotopy result | Multivalued weakly Picard operator | Nonself multivalued operator | Fixed point | Strict fixed point | Well-posedness | MATHEMATICS, APPLIED | SET | METRIC-SPACES | MATHEMATICS

Journal Article

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