Advanced Search
Article Contents
Article Contents

Existence and convergence results for best proximity points in cone metric spaces

Abstract Related Papers Cited by
  • In this paper, the author introduces generalized cone proximal $\varphi$-cyclic contraction pairs in cone metric spaces and considers the existence and convergence of best proximity point for a pair in cone metric spaces. His results generalize the corresponding results in [1, 4, 5, 7, 8, 12, 13, 15].
    Mathematics Subject Classification: 47H10, 54H25.


    \begin{equation} \\ \end{equation}
  • [1]

    M. A. Al-Thagafi and N. Shahzad, Convergence and existence results for best proximity points, Nonlinear Analysis, 70 (2009), 3665-3671.doi: 10.1016/j.na.2008.07.022.


    M. A. Al-Thagafi and N. Shahzad, Best proximity sets and equilibrium pairs for a finite family of mulimaps, Fixed Point Theory Appl., Article ID 457069, 10 pages, 10 (2008).


    M. A. Al-Thagafi and N. Shahzad, Best proximity pairs and equilibrium pairs for Kakutani multimaps, Nonlinear Analysis, 70 (2009), 1209-1216.doi: 10.1016/j.na.2008.02.004.


    S. S. Basha, Best proximity point theorems: resolution of an important non-linear programming problem, Optim. Lett., 7 (2013), 1167-1177.doi: 10.1007/s11590-012-0493-5.


    A. A. Eldred and P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 232 (2006), 1001-1006.doi: 10.1016/j.jmaa.2005.10.081.


    K. Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z., 122 (1969), 234-240.


    M. Gabeleh and A. Abkar, Best proximity points for semi-cyclic contractive pairs in Banach spaces, Int. Math. Forum, 6 (2011), 2179-2186.


    L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476.doi: 10.1016/j.jmaa.2005.03.087.


    S. Karpagam and S. Agrawal, Best proximity point theorems for p-cyclic Meir-Keeler contraction, Fixed Point Theory Appl., Art. ID 197308, 9 (2009).


    W. K. Kim, S. Kum and K. H. Lee, On general best proximity pairs and equilibrium pairs in free abstract economies, Nonlinear Analysis, 68 (2008), 2216-2227.doi: 10.1016/j.na.2007.01.057.


    W. A. Kirk, S. Reich and P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer. Func. Anal. Optim., 24 (2003), 851-862.doi: 10.1081/NFA-120026380.


    B. S. Lee, Cone metirc version of existence and convergence for best proximity points, Universal J. Appl. Math., 2 (2014), 104-108.


    C. Mongkalkeha and P. Kumam, Some common best proximity points for proximity commuting mappings, Optim. Lett., 7 (2013), 1825-1826.doi: 10.1007/s11590-012-0525-1.


    D. Turkoglu, M. Abuloha and T. Abdeljawad, KKM mappings in cone metric spaces and some fixed point theorems, Nonlinear Analysis, 72 (2010), 348-353.doi: 10.1016/j.na.2009.06.058.


    D. Xu and L. Deng, Cone semi-metric spaces and fixed point theorems for generalized weak contractive mappings, Nonlinear Analysis Forum, 18 (2013), 57-64.

  • 加载中

Article Metrics

HTML views() PDF downloads(89) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint