Finding Fixed Points for Set-Valued Mappings by Graph Concepts
DOI:
https://doi.org/10.23851/mjs.v31i4.894Abstract
The researchers have presented some theorems of the fixed points of single-valued mappings by defining known contractive conditions on those points in the same path from a given graph. Here, this procedure will be modified and used to find fixed points of order-preserve mappings in a complete partially ordered g-metric space.
References
S. B. Nadler, "Multivalued contraction mappings", Pacific Journal of Mathematics, 30(2), pp.475-488, 1969.
S. Reich, "Some remarks concerning contraction mappings", Canadian Mathematical Bulletin, 14(1), pp.121-124, 1971.
A. Azam, M. Arshad, " Fixed points of a sequence of locally contractive multivalued maps". Computers & Mathematics with Applications, 57(1), pp.96-100, 2009.
I. Beg, AR. Butt, " Fixed point of set-valued graph contractive mappings ", Journal of Inequalities and Applications, 2013(1), pp.1-7, 2013.
I. Beg A. Butt, S. Radojevi?, " The contraction principle for set-valued mappings on a metric space with a graph ", Computers & Mathematics with Applications, 60(5), pp.1214-1219,2010.
D. Klim, D. Wardowski, " Fixed point theorems for set-valued contractions in complete metric spaces ". Journal of Mathematical Analysis and Applications, 334(1), pp.132-139, 2007.
S.S.Abed, " Fixed point principles in general b-metric Spaces and b-Menger probabilistic spaces ", Journal of Al-Qadisiyah for Computer Science and Mathematics, 10(2), pp.42-53,2018.
Z.Mustafa, A new structure for generalized metric spaces-with applications to fixed point theory. Ph.D. thesis, the University of Newcastle, Australia (2005)
S. S. Abed, H.A. Jabbar, " Coupled points for total weakly contraction mappings via ? distance", Int. J. Basic Appl. Sci, 5(3), pp.164-171,2016.
S. S. Abed, " Approximating fixed points of the general asymptotic set-valued mappings", Journal of Advances in Mathematics, 18, pp.52-59,2020.
A.N.Faraj, S.S.Abed, " Fixed points results in G-metric spaces", Ibn AL-Haitham Journal For Pure And Applied Science, 32(1), pp.139-146, 2019.
Sh. Q. Latif, S. S. Abed, " Types of fixed points of set-valued contraction conditions for comparable elements" , Iraqi Journal of Science, Special Issue ,190-195, 2020.
J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proceedings of the American Mathematical Society, 136(4), pp.1359-1373, 2008.
Downloads
Published
How to Cite
Issue
Section
License
Articles accepted for publication in Al-Mustansiriyah Journal of Science (MJS) are protected under the Creative Commons Attribution 4.0 International License (CC-BY-NC). Authors of accepted articles are requested to sign a copyright release form prior to their article being published. All authors must agree to the submission, sign copyright release forms, and agree to be included in any correspondence between MJS and the authors before submitting a work to MJS. For personal or educational use, permission is given without charge to print or create digital copies of all or portions of a MJS article. However, copies must not be produced or distributed for monetary gain. It is necessary to respect the copyright of any parts of this work that are not owned by MJS.
