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

Analele Universitatii "Ovidius" Constanta - Seria Matematica

The Journal of "Ovidius" University of Constanta

Editor-in-Chief: Flaut, Cristina

1 Issue per year

IMPACT FACTOR 2016: 0.422

CiteScore 2016: 0.56

SCImago Journal Rank (SJR) 2016: 0.346
Source Normalized Impact per Paper (SNIP) 2016: 0.966

Mathematical Citation Quotient (MCQ) 2016: 0.10

Open Access
See all formats and pricing
More options …

Best proximity points of Kannan type cyclic weak ϕ-contractions in ordered metric spaces

Erdal Karapınar
Published Online: 2013-05-21 | DOI: https://doi.org/10.2478/v10309-012-0055-y


In this manuscript, the existence of the best proximity of Kannan Type cyclic weak ϕ-contraction in ordered metric spaces is investigated. Some results of Rezapour-Derafshpour-Shahzad [22] are generalized.

Keywords: ϕ-contraction; best proximity; ordered metric spaces

  • [1] Ya. I. Alber, S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert space In: New Results in Operator Theory, Advances and Appl. (Eds: I. Gohberg and Yu. Lyubich,) 722, Birkh¨auser, Basel, Oper. Theory Adv. Appl.,98, (1997).Google Scholar

  • [2] M.A. Al-Thafai, N. Shahzad, Convergence and existence for best proximity points, Nonlinear Analysis, 70(2009) 3665-3671 .Google Scholar

  • [3] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations itegrales, Fund. Math., 3(1922)133-181 .Google Scholar

  • [4] K.C.Border, Fixed Point Theorems with Applications to Economics and Game Theory , Cambridge University Press, Newyork,1985.Google Scholar

  • [5] D.W. Boyd, and S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969) 458-464.CrossrefGoogle Scholar

  • [6] Lj. B. ´Ciri´c, On contraction type mappings Math. Balkanica, 1(1971) 52-57 .Google Scholar

  • [7] Lj. B. ´Ciri´c, On some maps with a nonunique fixed point. Publ. Inst. Math., 17(1974) 52-58 .Google Scholar

  • [8] H.S.Ding,L. Li, and S. Radenovic, Bhaskar-Lakshmikantham-Ciric-type theorems in partially ordered metric space, preprint.Google Scholar

  • [9] A.A.Eldered, P.Veeramani, Proximal pointwise contraction. Topology andits Applications, 156 (2009) 2942-2948.Web of ScienceGoogle Scholar

  • [10] A.A.Eldered, P.Veeramani, Convergence and existence for best proximity points. J. Math. Anal. Appl., 323 (2006)1001-1006.Google Scholar

  • [11] N.Hussain, G. Jungck, Common fixed point and invariant approximation results for noncommuting generalized (f, g)-nonexpansive maps, J. Math. Anal. Appl., 321(2006) 851-861.Google Scholar

  • [12] E.Karapınar, Some Nonunique Fixed Point Theorems of ´Ciri´c type on Cone Metric Spaces Abst. Appl. Anal., 2010, Article id 123094, 14 pages (2010), doi:10.1155/2010/123094 .CrossrefGoogle Scholar

  • [13] E.Karapınar, Fixed point theory for cyclic weak ϕ-contraction, Appl.Math.Lett., 24(2011),no : 6, 822-825.CrossrefWeb of ScienceGoogle Scholar

  • [14] E.Karapınar, Best proximity points of cyclic mappings, Appl.Math.Lett., Volume 335, Issue 1, 1 November 2007, Pages 79-92.Web of ScienceGoogle Scholar

  • [15] E.Karapınar, ˙I.M. Erhan and A.Y.Ulus.: Fixed Point Theorem for Cyclic Maps on Partial Metric Spaces, Appl. Math. Inf. Sci., 6 (2012), no:1, 239-244.Google Scholar

  • [16] W.A. Kirk, P.S. Srinavasan,and P. Veeramani, Fixed Points for mapping satisfying cylical contractive conditions Fixed Point Theory, 4 (2003)79-89.Google Scholar

  • [17] Mitrovic,Z. D.: A coupled best approximations theorem in normed spaces, Nonlinear Anal. 72 (2010), 4049-4052.Google Scholar

  • [18] J.J.Nieto,R.L. and Pouso,R. Rodriguez-Lopez, Fixed point theorems in ordered abstract spaces, Proc. Amer. Math. Soc., 137 (2007) 2505-2517.Web of ScienceGoogle Scholar

  • [19] E.A.Ok, Real Analysis with Economic Applications, Princeton University Press, 2007.Google Scholar

  • [20] G.Petru¸sel, Cyclic representations and periodic points, Studia Univ. Babes-Bolyai Math., 50 (2005) 107-112.Google Scholar

  • [21] G. Petru¸sel and I.A. Rus, Fixed point theorems in ordered L-spaces Proc. Amer. Math. Soc., 134(2006) 411-418.Google Scholar

  • [22] Sh.Rezapour, M. Derafshpour, N. Shahzad, Best proximity point of cyclic φ-contractions in ordered metric spaces, Topological Methods in Nonlinear Analysis,37(2011)193-202.Google Scholar

  • [23] Sh.Rezapour, M. Derafshpour, N. Shahzad, Best Proximity Points of Cyclic φ-Contractions on Reflexive Banach Spaces, Fixed Point Theory and Applications, 2010, Article id 946178, 7 pages,(2010). Google Scholar

  • [24] B. E. Rhoades, Some theorems on weakly contractive maps. NonlinearAnal., 47 (2001), no:4, 2683-2693.Google Scholar

  • [25] Y. Song, Coincidence points for noncommuting f-weakly contractive mappings, Int. J. Comput. Appl. Math., 2(2007),no:1, 51-57 .Google Scholar

  • [26] Y.Song, S. Xu, A note on common fixed-points for Banach operator pairs, Int. J. Contemp. Math. Sci., 2(2007) 1163-1166.Google Scholar

  • [27] Q. Zhang, and Y. Song, Fixed point theory for generalized φ-weak contractions, Appl. Math. Lett., 22(2009),no:1, 7578.Web of ScienceGoogle Scholar

About the article

Published Online: 2013-05-21

Published in Print: 2012-12-01

Citation Information: Analele Universitatii "Ovidius" Constanta - Seria Matematica, Volume 20, Issue 3, Pages 51–64, ISSN (Online) 1844-0835, DOI: https://doi.org/10.2478/v10309-012-0055-y.

Export Citation

This content is open access.

Comments (0)

Please log in or register to comment.
Log in