On the existence of best proximity points for generalized contractions

• Vetrivel, V. ^[1] ; Sultana, Asrifa ^[1]
  1. [1] Indian Institute of Technology Madras

     Indian Institute of Technology Madras

     India

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 15, Nº. 1, 2014, págs. 55-63
• Idioma: inglés
• DOI: 10.4995/agt.2014.2221
• Enlaces
  • Texto completo
• Resumen

  • In this article we establish the existence of a unique best proximity point for some generalized non self contractions on a metric space in a simpler way using a geometric result. Our results generalize some recent best proximity point theorems and several fixed point theorems proved by various authors.

• Referencias bibliográficas
  • D. W. Boyd and J.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458-464.
  • http://dx.doi.org/10.1090/S0002-9939-1969-0239559-9
  • V. Sankar Raj and P. Veeramani, Best proximity pair theorems for relatively
  • nonexpansive mappings, Appl. General Topology 10 (2009), 21-28.
  • J. Anuradha and P. Veeramani, Proximal pointwise contraction, Topology Appl. 156 (2009), 2942-2948.
  • http://dx.doi.org/10.1016/j.topol.2009.01.017
  • A. Abkar and M. Gabeleh, Global optimal solutions of noncyclic mappings in metric spaces, J. Optim. Theory Appl. 153 (2012), 298-305.
  • http://dx.doi.org/10.1007/s10957-011-9966-4
  • A. A. Eldred and P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl. 323 (2006), 1001-1006.
  • http://dx.doi.org/10.1016/j.jmaa.2005.10.081
  • A. Amini Harandi, Best proximity points for proximal generalized contractions in metric spaces, Optim Lett. 7 (2013), 913-921
  • http://dx.doi.org/10.1007/s11590-012-0470-z
  • W. A. Kirk, S. Reich and P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer. Funct. Anal. Optim. 24 (2003), 851-862.
  • http://dx.doi.org/10.1081/NFA-120026380
  • A. Granas and J. Dugundji, Fixed Point Theory, Springer Monographs in Mathematics, Springer-Verlag, New York, 2003.
  • http://dx.doi.org/10.1007/978-0-387-21593-8
  • B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226 (1977), 257-290.
  • http://dx.doi.org/10.1090/S0002-9947-1977-0433430-4
  • K. Fan, Extensions of two fixed point theorems of F.E. Browder, Math. Z. 122 (1969), 234-240
  • http://dx.doi.org/10.1007/BF01110225
  • W. K. Kim and K. H. Lee, Existence of best proximity pairs and equilibrium pairs, J. Math. Anal. Appl. 316 (2006), 433-446.
  • http://dx.doi.org/10.1016/j.jmaa.2005.04.053
  • W. K. Kim, S. Kum and K. H. Lee, On general best proximity pairs and equilibrium pairs in free abstract economies, Nonlinear Anal. TMA 68...
  • http://dx.doi.org/10.1016/j.na.2007.01.057