A new iterative method based on the modified proximal-point algorithm for finding a common null point of an infinite family of accretive operators in Banach spaces
- Autores: T.M.M. Sow
- Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 22, Nº. 2, 2020, págs. 155-175
- Idioma: inglés
- DOI: 10.4067/S0719-06462020000200155
- Enlaces
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Resumen
- español
Resumen En este artículo, introducimos y estudiamos un nuevo método iterativo para encontrar un cero común de una familia infinita de operadores acretivos con un operador Lischitziano fuertemente acretivo, usando el algoritmo punto-proximal. También demostramos que el cero común es la única solución de una desigualdad variacional sin imponer ninguna condición de tipo compacidad en ninguno de los operadores o los espacios considerados. Finalmente, se entregan algunas aplicaciones de los resultados principales a problemas de equilibrio y problemas de punto fijo con una familia infinita de aplicaciones pseudo-contractivas. El resultado principal es una generalización y mejora de numerosos resultados bien conocidos en la literatura disponible.
- English
Abstract In this paper, we introduce and study a new iterative method for finding a common null point of an infinite family of accretive operators with a strongly accretive and Lipschitzian operator, by using the proximal-point algorithm. And also we prove that the common null point is a unique solution of variational inequality without imposing any compactness-type condition on either the operators or the space considered. Finally, some applications of the main results to equilibrium problems and fixed point problems with an infinite family of pseudocontractive mappings are given. The main result is a generalization and improvement of numerous well-known results in the available literature.
- español
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