On fixed point theorems of Leray–Schauder type

Borkowski, Marcin; Bugajewski, Dariusz

doi:10.1090/s0002-9939-07-09023-5

Cited by 3 publications

(3 citation statements)

References 16 publications

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“…As a corollary of this theorem and Theorem 3.1, we have the fixed point result for nonexpansive multivalued mappings (for more on this see [21,Section 9] Different interesting papers on extensions of the above result have appeared after the publication of [21]; some of them are [11,14,19,34,46]. Also a number of works have been published about KKM mappings on hyperconvex spaces after [33] as, for instance, [15].…”

Section: Definition 32 Givenmentioning

confidence: 89%

Metric fixed point theory on hyperconvex spaces: recent progress

Espínola

Lorenzo

2012

Arab. J. Math.

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In this survey we present an exposition of the development during the last decade of metric fixed point theory on hyperconvex metric spaces. Therefore we mainly cover results where the conditions on the mappings are metric. We will recall results about proximinal nonexpansive retractions and their impact into the theory of best approximation and best proximity pairs. A central role in this survey will be also played by some recent developments on R-trees. Finally, some considerations and new results on the extension of compact mappings will be shown. Mathematics Subject Classification

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Section: Definition 32 Givenmentioning

confidence: 89%

Metric fixed point theory on hyperconvex spaces: recent progress

Espínola

Lorenzo

2012

Arab. J. Math.

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“…Note that there exists a hyperconvex counterpart of the nonlinear alternative (Theorem 5.6); see [7]. There arises a natural question whether one could apply it in a similar way as in Theorem 5.7 to obtain an analogous result for hyperconvex spaces.…”

Section: Theorem 57 Let C Be An Open Convex Subset Of a Banach Spacmentioning

confidence: 99%

“…Also, the notion of hyperconvexity has gained some interest for graph theorists, since Kirk proved in [17] that a hyperconvex metric space with unique metric segments is an R-tree. From the point of view of fixed-point theory it is interesting to emphasize that the fixed-point property holds for nonexpansive mappings in bounded hyperconvex spaces (see [25] and [26] and also [5] for complete generality) as well as that many fixed-point results have been shown to hold in hyperconvex spaces (see, e.g., references given in [7] and [8]). Our new results from Section 5 extend some theorems from [11] and [16].…”

Section: Introductionmentioning

confidence: 99%

On some fixed-point theorems for generalized contractions and their perturbations

Borkowski

Bugajewski

Zima

2010

Journal of Mathematical Analysis and Applications

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The aim of this paper is to prove a collection of fixed-point theorems for mappings which can be roughly called generalized contractions or their perturbations. In particular, we are going to consider operators (single-valued or multi-valued) in Banach spaces with a quasimodulus, in hyperconvex subsets of normed spaces, or finally in non-Archimedean spaces. A particular attention will be paid to Krasnoselskii-type fixed-point theorems as well as to a Schaefer-type fixed-point theorem. Some applications to nonlinear functionalintegral equations will be given. Our results extend and complement some commonly known theorems.

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Positive solution for a class of nonlinear fourth-order boundary value problem

Zhang¹,

Chen

2023

MATH

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<abstract>In this paper, we are concerned with the existence of positive solutions for boundary value problems of nonlinear fourth-order differential equations <disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{eqnarray*} &&u^{(4)}+c(x)u = \lambda a(x)f(u), \; \; x\in (0,1),\\ &&u(0) = u(1) = u''(0) = u''(1) = 0, \end{eqnarray*} $\end{document} </tex-math></disp-formula> where $ a(x) $ may change signs. The proof of main results is based on Leray-Schauder's fixed point theorem and the properties of Green's function of the fourth-order differential operator $ L_cu = u^{(4)}+c(x)u $.</abstract>

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On fixed point theorems of Leray–Schauder type

Abstract: Abstract. In this paper we prove a few fixed points theorems of LeraySchauder type in hyperconvex metric spaces.

Cited by 3 publications

References 16 publications

Metric fixed point theory on hyperconvex spaces: recent progress

Metric fixed point theory on hyperconvex spaces: recent progress

On some fixed-point theorems for generalized contractions and their perturbations

Positive solution for a class of nonlinear fourth-order boundary value problem

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