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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

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Volume 19, Issue 2


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


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.

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