Multivalued fixed point theorems in terms of weak topology and measure of weak noncompactness

Cardinali, Tiziana; Rubbioni, Paola

doi:10.1016/j.jmaa.2013.03.045

Cited by 14 publications

(4 citation statements)

References 11 publications

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“…Remark 3.15. Theorem 3.14 generalizes Theorem 3.18 in [9] and Theorem 4.1 in [15] to the case of countably Meir-keeler condensing mapping. The condition that X is separable in the statement of this Theorem is not needed.…”

Section: Definition 32 [27]mentioning

confidence: 56%

Solutions of Neutral Differential Inclusions

AMOR

REMADI

2022

Advances in the Theory of Nonlinear Analysis and Its Application

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Section: Definition 32 [27]mentioning

confidence: 56%

Solutions of Neutral Differential Inclusions

AMOR

REMADI

2022

Advances in the Theory of Nonlinear Analysis and Its Application

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“…Several fixed point theorems based on the De Blasi measure of noncompactness are known, see e.g. [9]. However, we need a variant where this measure occurs only indirectly in a countable form.…”

Section: Fixed Point Theorems and Condensing Mapsmentioning

confidence: 99%

Semilinear inclusions with nonlocal conditions without compactness in non-reflexive spaces

Benedetti¹,

Väth²

2016

TMNA

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An existence result for an abstract nonlocal boundary value problem, is given, where A(t) determines a linear evolution operator, L is linear, and F and B are multivalued. To avoid compactness conditions, the weak topology is employed. The result applies also in nonreflexive spaces under a hypothesis concerning the De Blasi measure of noncompactness. Even in the case of initial value problems, the required condition is essentially milder than previously known results.

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“…Leray-Schauder type alternatives for weakly compact, weakly condensing and weakly Mönch type maps were established in the literature in a variety of settings, see for example [1,2,5] and the references therein. Using the notion of an essential map (originally introduced by Granas, see [3]) we present general Leray-Schauder alternative type theorems for general weakly Mönch type maps (see [4,5]) and our results generalize those in the literature.…”

Section: Introductionmentioning

confidence: 99%