On cyclic relatively nonexpansive mappings in generalized semimetric spaces

• Autores: Moosa Gabeleh
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 16, Nº. 2, 2015, págs. 99-108
• Idioma: inglés
• DOI: 10.4995/agt.2015.2988
• Enlaces
  • Texto completo
• Resumen

  • In this article, we prove a fixed point theorem for cyclic relatively nonexpansive mappings in the setting of generalized semimetric spaces by using a geometric notion of seminormal structure and then we conclude some results in uniformly convex Banach spaces. We also discuss on the stability of seminormal structure in generalized semimetric spaces.

• Referencias bibliográficas
  • L. M. Blumenthal,Theory and applications of distance geometry, Oxford Univ. Press, London (1953).
  • M. S. Brodskii and D. P. Milman,On the center of a convex set, Dokl. Akad. Nauk. USSR 59(1948), 837-840 (in Russian). M. Gabeleh, Minimal...
  • A. A. Eldred, W. A. Kirk and P. Veeramani, Proximal normal structure and relatively nonexpansive mappings, Studia Math. 171(2005), 283-293.
  • http://dx.doi.org/10.4064/sm171-3-5
  • R. Espínola, A new approach to relatively nonexpansive mappings, Proc. Amer. Math. Soc. 136(2008), 1987-1996.
  • http://dx.doi.org/10.1090/S0002-9939-08-09323-4
  • R. Espínola and M. Gabeleh, On the structure of minimal sets of relatively nonexpansive mappings, Numer. Funct. Anal. Optim. 34 (2013), 845-860.
  • http://dx.doi.org/10.1080/01630563.2013.763824
  • M. Gabeleh and N. Shahzad, Seminormal structure and fixed points of cyclic relatively nonexpansive mappings, Abstract Appl. Anal. 2014 (2014),...
  • W. A. Kirk,A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004-1006.
  • http://dx.doi.org/10.2307/2313345
  • W. A. Kirk and B. G. Kang, A fixed point theorem revisited, J. Korean Math. Soc. 34(1997), 285-291.
  • W. A. Kirk, P. S. Srinivasan and P. Veeramani, Fixed points for mappings satisfying cyclic contractive conditions, Fixed Point Theory 4, no....