Weak Convergence Theorems for Maximal Monotone Operators with Nonspreading mappings in a Hilbert space

• Hiroko Manaka ^[1] ; Wataru Takahashi ^[1]
  1. [1] Tokyo Institute of Technology

     Tokyo Institute of Technology

     Japón

     
• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 13, Nº. 1, 2011, págs. 11-24
• Idioma: inglés
• DOI: 10.4067/S0719-06462011000100002
• Enlaces
  • Texto completo
• Resumen
  • español

    Sea C un subconjunto convexo cerrado de un espacio real de Hilbert H. Sea T una asignación de C en sí mismo, sea A una asignación monótona α-inversa de C en H y sea B un operador monotono máximal en H tal que el dominio de B está incluido en C. Se introduce una secuencia iterativa para encontrar un punto de F(T) ∩ (A + B)(-1)0, donde F(T) es el conjunto de puntos fijos de T y (A + B)(-1)0 es el conjunto de los puntos cero de A + B. Entonces, se obtiene el resultado principal que se relaciona con la convergencia débil de la secuencia. Utilizando este resultado, obtenemos un teorema de convergencia para encontrar un punto común de una asignación fija y una asignación en un espacio de Hilbert. Además, consideramos el problema para encontrar un elemento común del conjunto de soluciones de un problema de equilibrio y el conjunto de puntos fijos de una asignación.

  • English

    Let C be a closed convex subset of a real Hilbert space H. Let T be a nonspreading mapping of C into itself, let A be an α-inverse strongly monotone mapping of C into H and let B be a maximal monotone operator on H such that the domain of B is included in C. We introduce an iterative sequence of finding a point of F(T)∩(A+B)(-1)0, where F(T) is the set of fixed points of T and (A + B)(-1)0 is the set of zero points of A + B. Then, we obtain the main result which is related to the weak convergence of the sequence. Using this result, we get a weak convergence theorem for finding a common fixed point of a nonspreading mapping and a nonexpansive mapping in a Hilbert space. Further, we consider the problem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonspreading mapping.

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