Noncyclic Meir-Keeler contractions and best proximity pair theorems

• Autorzy: Gabeleh M. , Markin J.

Identyfikatory

DOI

10.1515/dema-2018-0017

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

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

PL

przestrzenie CAT(0); przestrzeń Banacha; przestrzeń jednostajnie wypukła; odwzorowanie; kontrakcja Meir-Keelera

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2018
• Tom: Vol. 51, nr 1
• Strony: 171--181
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Gabeleh M.

• Department of Mathematics, Ayatollah Boroujerdi University, Boroujerd, Iran

autor

Markin J.

• 528 Rover Blvd., Los Alamos, NM 87544, USA

Bibliografia

• [1] Meir A., Keeler, E., A theorem on contraction mappings, J. Math. Anal. Appl., 1969, 28(2), 326-329
• [2] Di Bari C., Suzuki T., Vetro C., Best proximity points for cyclic Meir-Keeler contractions, Nonlinear Anal., 2008, 69(11), 3790-3794
• [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), 2918-2926
• [4] Eldred A. A., Kirk W. A., Veeramani P., Proximal normal structure and relatively nonexpansive mappings, Studia Math., 2005, 171, 283-293
• [5] Abkar A., Gabeleh M., Global optimal solutions of noncyclic mappings in metric spaces, J. Optim. Theory Appl., 2012, 153(2), 298-305
• [6] Chen C., A note on asymptotic pointwise weaker Meir-Keeler-type contractions, App. Math. Lett., 2012, 25(10), 1267-1269
• [7] Bridson M. R., Haefliger A., Metric Spaces of Non-positive Curvature, Springer-Verlag, Berlin Heidelberg, 1999
• [8] Kirk W. A., Shahzad N., Fixed Point Theory in Distance Spaces, Springer, New York, 2014
• [9] Fernández-León A., Nicolae A., Best proximity pair results for relatively nonexpansive mappings in geodesic spaces, Numerical Funct. Ananl. Optim., 2014, 35(11), 1399-1418
• [10] Gabeleh M., Common best proximity pairs in strictly convex Banach spaces, Georgian Math. J., 2017, 24(3), 363-372
• [11] Gabeleh M., Otafudu O. O., Markov-Kakutani’s theorem for best proximity pairs in Hadamard spaces, Indag. Math. (N.S.), 2017, 28(3), 680-693
• [12] Eldred A. A., Veeramani P., Existence and convergence of best proximity points, J. Math. Anal. Appl., 2006, 323(2), 1001-1006
• [13] Espínola R., Fernández-León A., On best proximity points in metric and Banach spaces, Canad. J. Math., 2011, 63, 533-550
• [14] Gabeleh M., Convergence of Picard’s iteration using projection algorithm for noncyclic contractions, (preprint)
• [15] Espínola R., Lorenzo P., Metric fixed point theory on hyperconvex spaces: recent progress, Arab J. Math., 2012, 1(4), 439-463
• [16] Gabeleh M., Lakzian H., Shahzad N., Best proximity points for asymptotic pointwise contractions, J. Nonlinear Convex Anal., 2015, 16, 83-93
• [17] Markin J., Shahzad N., Best proximity points for relatively u-continuous mappings in Banach and hyperconvex spaces, Abstract Appl. Anal., 2013, Article ID 680186
• [18] Eldred A. A., Sankar Raj V., Veeramani P., On best proximity pair theorems for relatively u-continuous mappings, Nonlinear Anal., 2011, 74(12), 3870-3875
• [19] Niculescu C. P., Roventa I., Schauder fixed point theorem in spaces with global nonpositive curvature, Fixed Point Theory Appl., 2009, 2009: 906727

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).