×
Jeddi, Jaauad; Kabil, Mustapha; Lazaiz, Samih

Some fixed point theorems in modular function spaces endowed with a graph. (English) Zbl 1480.47073

Abstr. Appl. Anal. 2020, Article ID 2135859, 7 p. (2020).
Summary: The aim of this paper is to give fixed point theorems for \(G\)-monotone \(\rho \)-nonexpansive mappings over \(\rho \)-compact or \(\rho \)-a.e.compact sets in modular function spaces endowed with a reflexive digraph not necessarily transitive. Examples are given to support our work.

Cited in 2 Documents

MSC:

47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H04 Set-valued operators
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords:

fixed point theorems; \(G\)-monotone \(\rho \)-nonexpansive mappings; modular function spaces
PDF BibTeX XML Cite
\textit{J. Jeddi} et al., Abstr. Appl. Anal. 2020, Article ID 2135859, 7 p. (2020; Zbl 1480.47073)
Full Text: DOI

References:

[1] Ran, A. C. M.; Reurings, M. C. B., A fixed point theorem in partially ordered sets and some applications to matrix equations, Proceedings of the American Mathematical Society, 1435-1443 (2004) · Zbl 1060.47056
[2] Jachymski, J., The contraction principle for mappings on a metric space with a graph, Proceedings of the American Mathematical Society, 136, 4, 1359-1373 (2008) · Zbl 1139.47040
[3] Nadler, S. B., Multi-valued contraction mappings, Pacific Journal of Mathematics, 30, 2, 475-488 (1969) · Zbl 0187.45002
[4] Nakano, H., Modulared sequence spaces, Proceedings of the Japan Academy, 27, 9, 508-512 (1951) · Zbl 0044.11302
[5] Nakano, H., Topology of Linear Topological Spaces (1951), Tokyo: Maruzen Co., Ltd, Tokyo
[6] Chen, S., Geometry of orlicz spaces, Journal of Baoji Teachers College, 12, 2, 22-28 (1989)
[7] Khamsi, M. A.; Kozlowski, W. M.; Reich, S., Fixed point theory in modular function spaces, Nonlinear Analysis: Theory, Methods & Applications, 14, 11, 935-953 (1990) · Zbl 0714.47040
[8] Alfuraidan, M. R., Fixed points of multivalued mappings in modular function spaces with a graph, Fixed Point Theory and Applications, 2015, 1 (2015) · Zbl 1311.54031
[9] Souayah, N.; Mlaiki, N.; Mrad, M., The G_M-contraction principle for mappings on an M-metric spaces endowed with a graph and fixed point theorems, IEEE Access, 6, 1, 25178-25184 (2018)
[10] Souayah, N.; Aydi, H.; Abdeljawad, T.; Mlaiki, N., Best proximity point theorems on rectangular metric spaces endowed with a graph, Axioms, 8, 1, 17 (2019) · Zbl 1432.54083
[11] Khamsi, M. A.; Kozlowski, W. M., Fixed Point Theory in Modular Function Spaces (2015), Birkhäuser · Zbl 1318.47002
[12] Kozłowski, W. M., Notes on modular function spaces I. Notes on modular function spaces. II, Commentationes Mathematicae, 28, 1, 91-120 (1988)
[13] Domínguez Benavides, T.; Khamsi, M. A.; Samadi, S., Uniformly lipschitzian mappings in modular function spaces, Nonlinear Analysis: Theory, Methods & Applications, 46, 2, 267-278 (2001) · Zbl 1001.47039
[14] Rigo, M., Advanced Graph Theory and Combinatorics (2016), John Wiley & Sons · Zbl 1369.05001
[15] Brezis, H., Analyse Fonctionnelle: Théorie et Applications (1983), Paris: Masson, Paris · Zbl 0511.46001
[16] Dominguez-Benavides, T.; Khamsi, M. A.; Samadi, S., Asymptotically nonexpansive mappings in modular function spaces, Journal of Mathematical Analysis and Applications, 265, 249-263 (2002) · Zbl 1014.47031
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.