Inertial algorithm for solving split inclusion problem in Banach spaces

• Autores: Ajay Kumar, Ekta Tamrakar
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 25, Nº. 1, 2023, págs. 67-88
• Idioma: inglés
• DOI: 10.56754/0719-0646.2501.067
• Enlaces
  • Texto completo
• Resumen
  • español

    El propósito de este artículo es proponer un algoritmo para encontrar un elemento común del conjunto de puntos fijos de aplicaciones relativamente no-expansivas y el conjunto de soluciones de problemas de inclusión escindidos con una manera de seleccionar el tamaño del paso sin conocimiento previo de la norma del operador en el contexto de espacios de Banach. Luego, el resultado principal se usa para los problemas de punto fijo común de una familia de aplicaciones relativamente no expansivas y el problemas del equilibrio escindido. Finalmente, se entrega un ejemplo numérico para ilustrar el resultado principal.

  • English

    The purpose of this paper is to propose an algorithm for finding a common element of the set of fixed points of relatively nonexpansive mapping and the set of solutions of split inclusion problem with a way of selecting the stepsize without prior knowledge of the operator norm in the framework of Banach spaces. Then, the main result is used to the common fixed point problems of a family of relatively nonexpansive mappings and split equilibrium problem. Finally, a numerical example is provided to illustrate the main result.

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