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Search Results: 1 - 10 of 4002 matches for " Wataru Takahashi "
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Strong convergence of an iterative sequence for maximal monotone operators in a Banach space
Fumiaki Kohsaka,Wataru Takahashi
Abstract and Applied Analysis , 2004, DOI: 10.1155/s1085337504309036
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.
Weak Convergence Theorems for Maximal Monotone Operators with Nonspreading mappings in a Hilbert space
Manaka,Hiroko; Takahashi,Wataru;
Cubo (Temuco) , 2011, DOI: 10.4067/S0719-06462011000100002
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.
Weak Convergence Theorems for Maximal Monotone Operators with Nonspreading mappings in a Hilbert space
Hiroko Manaka,Wataru Takahashi
Cubo : A Mathematical Journal , 2011,
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.
Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces
Kohsaka Fumiaki,Takahashi Wataru
Fixed Point Theory and Applications , 2007,
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.
Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces
Atsushiba Sachiko,Takahashi Wataru
Fixed Point Theory and Applications , 2005,
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.
Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces
Fumiaki Kohsaka,Wataru Takahashi
Fixed Point Theory and Applications , 2007, DOI: 10.1155/2007/21972
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.
Approximating zero points of accretive operators with compact domains in general Banach spaces
Hiromichi Miyake,Wataru Takahashi
Fixed Point Theory and Applications , 2005, DOI: 10.1155/fpta.2005.93
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.
Strong Convergence Theorem by a New Hybrid Method for Equilibrium Problems and Relatively Nonexpansive Mappings
Wataru Takahashi,Kei Zembayashi
Fixed Point Theory and Applications , 2008, DOI: 10.1155/2008/528476
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.
Weak and strong convergence theorems for nonexpansive semigroups in Banach spaces
Sachiko Atsushiba,Wataru Takahashi
Fixed Point Theory and Applications , 2005, DOI: 10.1155/fpta.2005.343
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.
Strong Convergence Theorem by a New Hybrid Method for Equilibrium Problems and Relatively Nonexpansive Mappings
Takahashi Wataru,Zembayashi Kei
Fixed Point Theory and Applications , 2008,
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.
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