Best proximity points of contractive mappings on a metric space with a graph and applications

• Autores: Asrifa Sultana, V. Vetrivel
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 18, Nº. 1, 2017, págs. 13-21
• Idioma: inglés
• DOI: 10.4995/agt.2017.3424
• Enlaces
  • Texto completo
• Resumen

  • We establish an existence and uniqueness theorem on best proximity point for contractive mappings on a metric space endowed with a graph. As an application of this theorem, we obtain a result on the existence of unique best proximity point for uniformly locally contractive mappings. Moreover, our theorem subsumes and generalizes many recent  fixed point and best proximity point results.

• Referencias bibliográficas
  • T. Dinevari and M. Frigon, Fixed point results for multivalued contractions on a metric space with a graph, J. Math. Anal. Appl. 405 (2013),...
  • https://doi.org/10.1016/j.jmaa.2013.04.014
  • M. Edelstein, An extension of Banach's contraction principle, Proc. Amer. Math. Soc. 12 (1961), 7-10.
  • K. Fan, Extensions of two fixed point theorems of F. E. Browder, Math. Z. 122 (1969), 234-240.
  • https://doi.org/10.1007/BF01110225
  • J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc. 136 (2008), 1359-1373.
  • https://doi.org/10.1090/S0002-9939-07-09110-1
  • W. K. Kim and K. H. Lee, Existence of best proximity pairs and equilibrium pairs, J. Math. Anal. Appl. 316 (2006), 433-446.
  • https://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...
  • https://doi.org/10.1016/j.na.2007.01.057
  • W. A. Kirk, S. Reich and P. Veeramani, Proximinal retracts and best proximity pair theorems, Numer. Funct. Anal. Optim. 24 (2003), 851-862.
  • https://doi.org/10.1081/NFA-120026380
  • L. Máté, The Hutchinson-Barnsley theory for certain non-contraction mappings, Period. Math. Hungar. 27 (1993), 21-33.
  • https://doi.org/10.1007/BF01877158
  • J. J. Nieto and R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations,...
  • https://doi.org/10.1007/s11083-005-9018-5
  • V. Pragadeeswarar and M. Marudai, Best proximity points: approximation and optimization in partially ordered metric spaces, Optim. Lett. 7...
  • https://doi.org/10.1007/s11590-012-0529-x
  • V. Sankar Raj, Best proximity point theorems for non-self mappings, Fixed Point Theory 14 (2013), 447-454.
  • A. C. M. Ran and M. C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math....
  • https://doi.org/10.1090/S0002-9939-03-07220-4
  • A. Sultana and V. Vetrivel, Fixed points of Mizoguchi-Takahashi contraction on a metric space with a graph and applications, J. Math. Anal....
  • https://doi.org/10.1016/j.jmaa.2014.03.015
  • A. Sultana and V. Vetrivel, On the existence of best proximity points for generalized contractions, Appl. Gen. Topol. 15 (2014), 55-63.
  • https://doi.org/10.4995/agt.2014.2221