Abstract:
We first introduce a modified proximal point algorithm formaximal monotone operators in a Banach space. Next, we obtain astrong convergence theorem for resolvents of maximal monotoneoperators in a Banach space which generalizes the previous resultby Kamimura and Takahashi in a Hilbert space. Using this result,we deal with the convex minimization problem and the variationalinequality problem in a Banach space.

Abstract:
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)-10, where f(t) is the set of fixed points of t and (a + b)-10 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.

Abstract:
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. 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.

Abstract:
Using the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of the mappings. Next, using this operator, we construct an iterative sequence to approximate common fixed points of the family. We finally apply our results to a convex feasibility problem in Banach spaces.

Abstract:
We introduce an implicit iterative process for a nonexpansive semigroup and then we prove a weak convergence theorem for the nonexpansive semigroup in a uniformly convex Banach space which satisfies Opial's condition. Further, we discuss the strong convergence of the implicit iterative process.

Abstract:
Using the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of the mappings. Next, using this operator, we construct an iterative sequence to approximate common fixed points of the family. We finally apply our results to a convex feasibility problem in Banach spaces.

Abstract:
We prove strong convergence theorems of Mann's type and Halpern's type for resolvents of accretive operators with compact domains and apply these results to find fixed points of nonexpansive mappings in Banach spaces.

Abstract:
We prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a relatively nonexpansive mapping in a Banach space by using a new hybrid method. Using this theorem, we obtain two new results for finding a solution of an equilibrium problem and a fixed point of a relatively nonexpnasive mapping in a Banach space.

Abstract:
We introduce an implicit iterative process for a nonexpansive semigroup and then we prove a weak convergence theorem for the nonexpansive semigroup in a uniformly convex Banach space which satisfies Opial's condition. Further, we discuss the strong convergence of the implicit iterative process.

Abstract:
We prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a relatively nonexpansive mapping in a Banach space by using a new hybrid method. Using this theorem, we obtain two new results for finding a solution of an equilibrium problem and a fixed point of a relatively nonexpnasive mapping in a Banach space.