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

Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

Online
ISSN
1572-9176
See all formats and pricing
More options …
Volume 19, Issue 2

Issues

Convergence and existence results for best C-proximity points

Hemant Kumar Pathak / Naseer Shahzad
Published Online: 2012-05-30 | DOI: https://doi.org/10.1515/gmj-2012-0012

Abstract.

We provide a positive answer to a question raised by Al-Thagafi and Shahzad [Nonlinear Anal. 70 (2009), 3665–3671] about the existence of a best proximity point for a cyclic -contraction map in a reflexive Banach space by using appreciable generalized notions. In turn, this also gives a positive answer to a question raised by Eldred and Veeramani [J. Math. Anal. Appl. 323 (2006), 1001–1006]. To this end, we introduce a new concept of C-proximity point and a new class of maps, called cyclic -contractions, which contains cyclic contraction maps and cyclic -contraction maps as subclasses. Convergence and existence results of best C-proximity points for cyclic -contraction maps are also obtained.

Keywords: Best proximity point; fixed point; cyclic -contraction map; cyclic -contraction map; metric space; Banach space

About the article

Received: 2011-02-28

Revised: 2011-11-21

Published Online: 2012-05-30

Published in Print: 2012-06-01


Citation Information: Georgian Mathematical Journal, Volume 19, Issue 2, Pages 301–316, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2012-0012.

Export Citation

© 2012 by Walter de Gruyter Berlin Boston.Get Permission

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Poom Kumam, Peyman Salimi, and Calogero Vetro
Fixed Point Theory and Applications, 2014, Volume 2014, Number 1
[2]
Leila Gholizadeh and Erdal Karapınar
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2017
[3]
Moosa Gabeleh and Naseer Shahzad
Journal of Applied Mathematics, 2013, Volume 2013, Page 1

Comments (0)

Please log in or register to comment.
Log in