Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero


Covered by:
Web of Science - Emerging Sources Citation Index
Scopus
MathSciNet


CiteScore 2018: 0.47
SCImago Journal Rank (SJR) 2018: 0.265
Source Normalized Impact per Paper (SNIP) 2018: 0.714

Mathematical Citation Quotient (MCQ) 2018: 0.17

ICV 2018: 121.16

Open Access
Online
ISSN
2391-4661
See all formats and pricing
More options …
Volume 51, Issue 1

Issues

Noncyclic Meir-Keeler contractions and best proximity pair theorems

Moosa Gabeleh / Jack Markin
Published Online: 2018-08-28 | DOI: https://doi.org/10.1515/dema-2018-0017

Abstract

In this article, we consider the class of noncyclic Meir-Keeler contractions and study the existence and convergence of best proximity pairs for such mappings in the setting of complete CAT(0) spaces. We also discuss asymptotic pointwise noncyclic Meir-Keeler contractions in the framework of uniformly convex Banach spaces and generalize a main result of Chen [Chen C. M., A note on asymptotic pointwise weaker Meir-Keeler type contractions, Appl. Math. Lett., 2012, 25, 1267-1269]. Examples are given to support our main results.

Keywords: best proximity pair; CAT(0) space; uniformly convex Banach space; projection mapping; noncyclic Meir-Keeler contraction

MSC 2010: 47H10; 47H09; 46B20

References

  • [1] Meir A., Keeler, E., A theorem on contraction mappings, J. Math. Anal. Appl., 1969, 28(2), 326-329CrossrefGoogle Scholar

  • [2] Di Bari C., Suzuki T., Vetro C., Best proximity points for cyclic Meir-Keeler contractions, Nonlinear Anal., 2008, 69(11), 3790-3794Google Scholar

  • [3] Suzuki T., Kikkawa M., Vetro C., The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal., 2009, 71(7), 2918-2926Google Scholar

  • [4] Eldred A. A., KirkW. A., Veeramani P., Proximal normal structure and relatively nonexpansivemappings, StudiaMath., 2005, 171, 283-293Google Scholar

  • [5] Abkar A., Gabeleh M., Global optimal solutions of noncyclicmappings in metric spaces, J. Optim. Theory Appl., 2012, 153(2), 298-305Google Scholar

  • [6] Chen C., A note on asymptotic pointwise weaker Meir-Keeler-type contractions, App. Math. Lett., 2012, 25(10), 1267-1269Web of ScienceGoogle Scholar

  • [7] Bridson M. R., Haefliger A., Metric Spaces of Non-positive Curvature, Springer-Verlag, Berlin Heidelberg, 1999Google Scholar

  • [8] Kirk W. A., Shahzad N., Fixed Point Theory in Distance Spaces, Springer, New York, 2014Google Scholar

  • [9] Fernández-León A., Nicolae A., Best proximity pair results for relatively nonexpansive mappings in geodesic spaces, Numerical Funct. Ananl. Optim., 2014, 35(11), 1399-1418Google Scholar

  • [10] Gabeleh M., Common best proximity pairs in strictly convex Banach spaces, Georgian Math. J., 2017, 24(3), 363-372Web of ScienceGoogle Scholar

  • [11] Gabeleh M., Otafudu O. O., Markov-Kakutani’s theorem for best proximity pairs in Hadamard spaces, Indag. Math. (N.S.), 2017, 28(3), 680-693Web of ScienceGoogle Scholar

  • [12] Eldred A. A., Veeramani P., Existence and convergence of best proximity points, J.Math. Anal. Appl., 2006, 323(2), 1001-1006Google Scholar

  • [13] Espínola R., Fernández-León A., On best proximity points in metric and Banach spaces, Canad. J. Math., 2011, 63, 533-550Google Scholar

  • [14] Gabeleh M., Convergence of Picard’s iteration using projection algorithm for noncyclic contractions, (preprint)Google Scholar

  • [15] Espínola R., Lorenzo P., Metric fixed point theory on hyperconvex spaces: recent progress, Arab J.Math., 2012, 1(4), 439-463Google Scholar

  • [16] Gabeleh M., Lakzian H., Shahzad N., Best proximity points for asymptotic pointwise contractions, J. Nonlinear Convex Anal., 2015, 16, 83-93Google Scholar

  • [17] Markin J., Shahzad N., Best proximity points for relatively u-continuous mappings in Banach and hyperconvex spaces, Abstract Appl. Anal., 2013, Article ID 680186Google Scholar

  • [18] Eldred A. A., Sankar Raj V., Veeramani P., On best proximity pair theorems for relatively u-continuous mappings, Nonlinear Anal., 2011, 74(12), 3870-3875Google Scholar

  • [19] Niculescu C. P., Roventa I., Schauder fixed point theorem in spaces with global nonpositive curvature, Fixed Point Theory Appl., 2009, 2009: 906727.Web of ScienceGoogle Scholar

About the article

Received: 2017-05-09

Accepted: 2018-07-24

Published Online: 2018-08-28


Citation Information: Demonstratio Mathematica, Volume 51, Issue 1, Pages 171–181, ISSN (Online) 2391-4661, DOI: https://doi.org/10.1515/dema-2018-0017.

Export Citation

© by Moosa Gabeleh and Jack Markin, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

Comments (0)

Please log in or register to comment.
Log in