Some fixed point theorems on non-convex sets

• Autores: Mohanasundaram Radhakrishnan, S. Rajesh, Sushama Agrawal
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 18, Nº. 2, 2017, págs. 377-390
• Idioma: inglés
• DOI: 10.4995/agt.2017.7452
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we prove that if $K$ is a nonempty weakly compact set in a Banach space $X$, $T:K\to K$ is a nonexpansive map satisfying $\frac{x+Tx}{2}\in K$ for all $x\in K$ and if $X$ is $3-$uniformly convex or $X$ has the Opial property, then $T$ has a fixed point in $K.$

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