Fixed point theorems in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="double-struck">R</mml:mi></mml:math>-trees with applications to graph theory

Espínola, Rafael; Kirk, W. A.

doi:10.1016/j.topol.2005.03.001

Cited by 94 publications

(5 citation statements)

References 18 publications

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“…For example, Echenique [16] studied theory of fxed points in the setting of graph theory and obtained several new results. Similarly, Espinola and Kirk [17] obtained some novel fxed point results in the setting of graph theory. Alfuraidan and Khamsi [18] studied theory of fxed points for nonexpansive mappings in the setting of a hyperbolic space with direct graph.…”

Section: Introductionmentioning

confidence: 94%

Iterative Approximation of Common Fixed Points for Edge-Preserving Quasi-Nonexpansive Mappings in Hilbert Spaces along with Directed Graph

Dewangan¹,

Gurudwan²,

Ahmad

et al. 2023

Journal of Mathematics

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We present iterative approximation results of an iterative scheme for finding common fixed points of edge-preserving quasi-nonexpansive self-maps in Hilbert spaces along with directed graph. We obtain weak as well as strong convergence of our scheme under various assumptions. That is, we impose several possible mild conditions on the domain, on the mapping, or on the parameters involved in our scheme to prove convergence results. We support numerically our main outcome by giving an example. Eventually, an application is provided for solving a variational inequality problem. Our result are new/generalized some recently announced results of the literature.

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Section: Introductionmentioning

confidence: 94%

Iterative Approximation of Common Fixed Points for Edge-Preserving Quasi-Nonexpansive Mappings in Hilbert Spaces along with Directed Graph

Dewangan¹,

Gurudwan²,

Ahmad

et al. 2023

Journal of Mathematics

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“…Consequently, fixed point theorems in CAT(0) spaces have been developed by many mathematicians; see for example [8,29]. More so, some of these theorems in CAT(0) spaces are applicable in many fields of studies such as, graph theory, biology and computer science (see for example [9,18,20,31]).…”

Section: βY)mentioning

confidence: 99%

Split Variational Inclusion Problem and Fixed Point Problem for a Class of Multivalued Mappings in CAT(0) Spaces

et al. 2019

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The aim of this paper is to introduce a modified viscosity iterative method to approximate a solution of the split variational inclusion problem and fixed point problem for a uniformly continuous multivalued total asymptotically strictly pseudocontractive mapping in C A T ( 0 ) spaces. A strong convergence theorem for the above problem is established and several important known results are deduced as corollaries to it. Furthermore, we solve a split Hammerstein integral inclusion problem and fixed point problem as an application to validate our result. It seems that our main result in the split variational inclusion problem is new in the setting of C A T ( 0 ) spaces.

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“…Since then the fixed point theory for single-valued and multivalued mappings in CAT(0) spaces has been rapidly developed and many of papers have appeared (see e.g., [4][5][6][7][8][9][10][11][12][13][14] and the references therein). It is worth mentioning that fixed point theorems in CAT(0) spaces (specially in ℝ -trees) can be applied to graph theory, biology, and computer science (see e.g., [15][16][17][18][19][20]). …”

Section: D(t(x) Y) ≤ D(x Y) For All X ∈ K and Y ∈ Fix(t)mentioning

confidence: 99%

Common fixed points for some generalized multivalued nonexpansive mappings in uniformly convex metric spaces

Laowang

Panyanak

2011

Fixed Point Theory Appl

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Abkar and Eslamian (Nonlinear Anal. TMA, 74, 1835-1840 prove that if K is a nonempty bounded closed convex subset of a complete CAT(0) space X, t : K K is a single-valued quasi-nonexpansive mapping and T : K KC(K) is a multivalued mapping satisfying conditions (E) and (C l ) for some l (0, 1) such that t and T commute weakly, then there exists a point z K such that z = t(z) T(z). In this paper, we extend this result to the general setting of uniformly convex metric spaces. Nevertheless, condition (E) of T can be weakened to the strongly demiclosedness of I -T.

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Fixed point theorems inR-trees with applications to graph theory

Cited by 94 publications

References 18 publications

Iterative Approximation of Common Fixed Points for Edge-Preserving Quasi-Nonexpansive Mappings in Hilbert Spaces along with Directed Graph

Iterative Approximation of Common Fixed Points for Edge-Preserving Quasi-Nonexpansive Mappings in Hilbert Spaces along with Directed Graph

Split Variational Inclusion Problem and Fixed Point Problem for a Class of Multivalued Mappings in CAT(0) Spaces

Common fixed points for some generalized multivalued nonexpansive mappings in uniformly convex metric spaces

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