Title: Existence and Convergence of Best Proximity Points for Semi Cyclic Contraction Pairs
Author(s): Balwant Singh Thakur, Ajay Sharma
Pages: 33-44
Cite as:
Balwant Singh Thakur, Ajay Sharma, Existence and Convergence of Best Proximity Points for Semi Cyclic Contraction Pairs, Int. J. Anal. Appl., 5 (1) (2014), 33-44.


In this article, we introduce the notion of a semi cyclic ϕ-contraction pair of mappings, which contains semi cyclic contraction pairs as a subclass. Existence and convergence results of best proximity points for semi cyclic ϕ- contraction pair of mappings are obtained.

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  1. Kirk, W.A., Srinivasan, P.S., Veeramani, P.: Fixed points for mappings satisfying cyclical contractive conditions. Fixed Point Theory 4, 79-89 (2003) Google Scholar

  2. Eldred, A.A., Veeramani, P.: Existence and convergence of best proximinity points. J. Math. Anal. Appl. 323, 1001-1006 (2006) Google Scholar

  3. Al-Thagafi, M.A., Shahzad, N.: Convergence and existence results for best proximity points. Nonlinear Anal. 70, 3665–3671 (2009) Google Scholar

  4. Gabeleh, M., Abkar, A.: Best proximity points for semi-cylic contractive pairs in Banach spaces, Int. Math. Forum 6(44), 2179–2186 (2011) Google Scholar

  5. Chandok, S., Postolache, M.: Fixed point theorem for weakly Chatterjea-type cyclic contractions. Fixed Point Theory Appl. ID: 2013:28, 9 pp. (2013) Google Scholar

  6. Shatanawi, W., Postolache, M.: Common fixed point results of mappings for nonlinear contractions of cyclic form in ordered metric spaces. Fixed Point Theory Appl. ID: 2013:60, 13 pp. (2013) Google Scholar

  7. Clarkson, J.A.: Uniform convex spaces, Trans. Amer. Math. Soc. 40, 396–414 (1936) Google Scholar


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