Viscosity approximation methods with a sequence of contractions

• Koji Aoyama ^[1] ; Yasunori Kimura ^[2]
  1. [1] Chiba University Department of Economics
  2. [2] Toho University Department of Information Science
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 16, Nº. 1, 2014, págs. 9-20
• Idioma: inglés
• DOI: 10.4067/S0719-06462014000100002
• Enlaces
  • Texto completo
• Resumen
  • español

    La meta de este artículo es probar en un marco de trabajo adecuado que cada sucesión iterativa generada por el método de aproximación de viscosidad con una sucesión cualquiera de contracciones es convergente como lo es cada sucesión iterativa generada por el método iterativo del tipo Halpern. Así, usando nuestro resultado mostramos algunos teoremas de convergencia para problemas de desigualdades variacionales, problemas de punto cero y problemas de punto fijo.

  • English

    The aim of this paper is to prove that, in an appropriate setting, every iterative sequence generated by the viscosity approximation method with a sequence of contractions is convergent whenever so is every iterative sequence generated by the Halpern type iterative method. Then, using our results, we show some convergence theorems for variational inequality problems, zero point problems, and fixed point problems.

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