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Este resumen es generado por máquina.

Este estudio introduce un nuevo mapeo en espacios de Banach para encontrar soluciones comunes para mapeos no expansivos y estrictamente pseudocontractivos. Establece fuertes teoremas de convergencia para puntos fijos y problemas de desigualdad variacional.

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Área de la Ciencia:

  • Análisis funcional
  • Análisis no lineal
  • Teoría de la optimización

Sus antecedentes:

  • La teoría del punto fijo y los problemas de desigualdad variacional son cruciales en varios campos matemáticos.
  • Los métodos existentes a menudo se enfrentan a limitaciones con tipos específicos de mapeos y espacios.
  • Los espacios de Banach uniformemente convexos y uniformemente lisos proporcionan un marco robusto para resolver estos problemas.

Objetivo del estudio:

  • Introducir un nuevo mapeo dentro de 2 espacios de Banach uniformemente lisos y uniformemente convexos.
  • Determinar soluciones comunes para conjuntos de puntos fijos de mapeos enriquecidos no expansivos y estrictamente pseudocontractivos.
  • Establecer conjuntos de soluciones para problemas de desigualdad variacional relacionados.

Principales métodos:

  • Utilizando un marco de espacio de Banach uniformemente liso y uniformemente convexo.
  • Desarrollo y aplicación de una nueva cartografía para el análisis de convergencia.
  • Empleando el método iterativo de tipo Mann-Halpern.

Principales resultados:

  • Se obtuvieron soluciones comunes para conjuntos de puntos fijos de familias finitas de mapeos enriquecidos no expansivos y estrictamente pseudocontractivos.
  • Se proporcionan conjuntos de soluciones para problemas de desigualdad variacional.
  • Demostró teoremas de convergencia fuertes para estos conjuntos de soluciones utilizando el método Mann-Halpern.

Conclusiones:

  • El mapeo y los métodos introducidos dan lugar a avances significativos en la búsqueda de soluciones comunes.
  • Los teoremas de fuerte convergencia generalizan y mejoran los resultados existentes en la literatura.
  • Este trabajo contribuye a la comprensión teórica y la aplicación práctica de los métodos iterativos en los espacios de Banach.