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

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 sequen...

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Detalles Bibliográficos
Autores principales:	Manaka,Hiroko, Takahashi,Wataru
Lenguaje:	English
Publicado:	Universidad de La Frontera. Departamento de Matemática y Estadística. 2011
Materias:	Nonspreading mapping maximal monotone operator inverse strongly-monotone mapping fixed point iteration procedure
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000100002
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spelling	oai:scielo:S0719-064620110001000022018-10-08Weak Convergence Theorems for Maximal Monotone Operators with Nonspreading mappings in a Hilbert spaceManaka,HirokoTakahashi,Wataru Nonspreading mapping maximal monotone operator inverse strongly-monotone mapping fixed point iteration procedure 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.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.13 n.1 20112011-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000100002en10.4067/S0719-06462011000100002
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Nonspreading mapping maximal monotone operator inverse strongly-monotone mapping fixed point iteration procedure
spellingShingle	Nonspreading mapping maximal monotone operator inverse strongly-monotone mapping fixed point iteration procedure Manaka,Hiroko Takahashi,Wataru Weak Convergence Theorems for Maximal Monotone Operators with Nonspreading mappings in a Hilbert space
description	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.
author	Manaka,Hiroko Takahashi,Wataru
author_facet	Manaka,Hiroko Takahashi,Wataru
author_sort	Manaka,Hiroko
title	Weak Convergence Theorems for Maximal Monotone Operators with Nonspreading mappings in a Hilbert space
title_short	Weak Convergence Theorems for Maximal Monotone Operators with Nonspreading mappings in a Hilbert space
title_full	Weak Convergence Theorems for Maximal Monotone Operators with Nonspreading mappings in a Hilbert space
title_fullStr	Weak Convergence Theorems for Maximal Monotone Operators with Nonspreading mappings in a Hilbert space
title_full_unstemmed	Weak Convergence Theorems for Maximal Monotone Operators with Nonspreading mappings in a Hilbert space
title_sort	weak convergence theorems for maximal monotone operators with nonspreading mappings in a hilbert space
publisher	Universidad de La Frontera. Departamento de Matemática y Estadística.
publishDate	2011
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462011000100002
work_keys_str_mv	AT manakahiroko weakconvergencetheoremsformaximalmonotoneoperatorswithnonspreadingmappingsinahilbertspace AT takahashiwataru weakconvergencetheoremsformaximalmonotoneoperatorswithnonspreadingmappingsinahilbertspace
_version_	1714206770599034880

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

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