Existence of Solutions of a Nonlinear Hammerstein Integral Equation

Jeribi, Aref; Krichen, Bilel; Mefteh, Bilel

doi:10.1080/01630563.2014.884582

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2015

2022

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Cited by 7 publications

(4 citation statements)

References 18 publications

(14 reference statements)

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“…The main goal of the present section is to establish new variants of Theorem 1.1 for three operators acting on WC-Banach algebras, without using the sequential condition (P). This result can be considered an extension of [7,12,15,17].…”

mentioning

confidence: 79%

Fixed point theory in WC--Banach algebras

Jeribi¹,

Krichen²,

Mefteh³

2016

Turk J Math

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mentioning

confidence: 79%

Fixed point theory in WC--Banach algebras

Jeribi¹,

Krichen²,

Mefteh³

2016

Turk J Math

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“…Further applications to nonlinear Volterra and Hammerstein equations can be found, e.g., in [2,45,62,63]. …”

Section: Applicationsmentioning

confidence: 98%

Fixed Point Theory for 1-Set Contractions: a Survey

Djebali¹

2015

Applied Mathematics in Tunisia

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In this report, we first review some classical results concerning the fixed point theory for an important class of mappings for which the Banach contraction principle fails, namely nonexpansive mappings. Both metric and topological fixed point theory will be surveyed. We will also discuss some known results regarding the extension to nonlinear contractions and to˛-contractive mappings with respect to some measure of noncompactness˛. The second part of this survey paper will be devoted to some recent progress and development of the fixed point theory of 1-set contractions that have been achieved during the last couple of years. The theory for different boundary conditions and when the corresponding space is endowed with the weak topology are also discussed. Finally, some applications to equations of Krasnosels'kȋi type and to the solvability of nonlinear integral equations of Volterra type are presented.

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“…On the other hand, to the best of our knowledge, the use of fixed point theorems under the weak topology in the study of fractional differential equations is still not sufficiently generalized. However although, fixed point theory with weak topology has been investigated in several papers and monographs for integral equations to prove the existence of solutions [11,14] and the monograph [9] and the references therein.…”

Section: Introductionmentioning

confidence: 99%