Existence and Convergence of Best Proximity Points for Semi Cyclic Contraction Pairs

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Balwant Singh Thakur
Ajay Sharma

Abstract

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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References

  1. Kirk, W.A., Srinivasan, P.S., Veeramani, P.: Fixed points for mappings satisfying cyclical contractive conditions. Fixed Point Theory 4, 79-89 (2003)
  2. Eldred, A.A., Veeramani, P.: Existence and convergence of best proximinity points. J. Math. Anal. Appl. 323, 1001-1006 (2006)
  3. Al-Thagafi, M.A., Shahzad, N.: Convergence and existence results for best proximity points. Nonlinear Anal. 70, 3665-3671 (2009)
  4. Gabeleh, M., Abkar, A.: Best proximity points for semi-cylic contractive pairs in Banach spaces, Int. Math. Forum 6(44), 2179-2186 (2011)
  5. Chandok, S., Postolache, M.: Fixed point theorem for weakly Chatterjea-type cyclic contractions. Fixed Point Theory Appl. ID: 2013:28, 9 pp. (2013)
  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)
  7. Clarkson, J.A.: Uniform convex spaces, Trans. Amer. Math. Soc. 40, 396-414 (1936)