A new class of g-eta-accretive mappings is introduced and studied in Banach space. By using the properties of g-eta-accretive mappings, the concept of resolventoperators associated with the classical m-accretive oper...
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A new class of g-eta-accretive mappings is introduced and studied in Banach space. By using the properties of g-eta-accretive mappings, the concept of resolventoperators associated with the classical m-accretive operators is extended. And an iterative algorithm for a new class of generalized implicit variational-like inclusion involving g-eta-accretive mappings and its convergence results are established in Banach space. (c) 2006 Elsevier Inc. All rights reserved.
In this paper, we introduce a new class of monotone operators-H-monotone operators. The resolventoperator associated with an H-monotone operator is defined and its Lipschitz continuity is presented. We also introduce...
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In this paper, we introduce a new class of monotone operators-H-monotone operators. The resolventoperator associated with an H-monotone operator is defined and its Lipschitz continuity is presented. We also introduce and study a new class of variational inclusions involving H-monotone operators and construct a new algorithm for solving this class of variational inclusions by using the resolvent operator technique. (C) 2003 Elsevier Inc. All rights reserved.
In this paper, we first introduce a new class of generalized accretive operators named H-accretive operators in Banach spaces. By studying the properties of H-accretive operators, we extend the concept of resolvent op...
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In this paper, we first introduce a new class of generalized accretive operators named H-accretive operators in Banach spaces. By studying the properties of H-accretive operators, we extend the concept of resolventoperators associated with the classical m-accretive operators to the new H-accretive operators. In terms of the new resolvent operator technique, we give the approximate solution for a class of variational inclusions involving H-accretive operators in Banach spaces. (C) 2004 Elsevier Ltd. All rights reserved.
A new system of generalized nonlinear variational-like inclusions involving A- maximal m-relaxed η-accretive （so-called, （A, η）-accretive in [36]） mappings in q-uniformly smooth Banach spaces is introduced, and ...
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A new system of generalized nonlinear variational-like inclusions involving A- maximal m-relaxed η-accretive （so-called, （A, η）-accretive in [36]） mappings in q-uniformly smooth Banach spaces is introduced, and then, by using the resolvent operator technique associated with A-maximal m-relaxed ~/-accretive mappings due to Lan et al., the exis- tence and uniqueness of a solution to the aforementioned system is established. Applying two nearly uniformly Lipschitzian mappings 81 and 82 and using the resolvent operator technique associated with A-maximal m-relaxed ~？-accretive mappings, we shall construct a new perturbed N-step iterative algorithm with mixed errors for finding an element of the set of the fixed points of the nearly uniformly Lipschitzian mapping Q = （S1, S2） which is the unique solution of the aforesaid system. We also prove the convergence and stability of the iterative sequence generated by the suggested perturbed iterative algorithm under some suitable conditions, The results presented in this paper extend and improve some known results in the literature.
In this paper, we introduce and study a new system of generalized mixed quasi-variational inclusions with (A, eta)-accretive operators in q-uniformly smooth Banach spaces. By using the resolvent operator technique ass...
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In this paper, we introduce and study a new system of generalized mixed quasi-variational inclusions with (A, eta)-accretive operators in q-uniformly smooth Banach spaces. By using the resolvent operator technique associated with (A, eta)-accretive operators, we construct a new p-step iterative algorithm for solving this system of generalized mixed quasi-variational inclusions in real q-uniformly smooth Banach spaces. We also prove the existence of solutions for the generalized mixed quasi-variational inclusions and the convergence of iterative sequences generated by algorithm. Our results improve and generalize many known corresponding results. (C) 2007 Elsevier B.V. All rights reserved.
The main purpose of this paper is to construct a new iterative algorithm using the notion of P-eta-resolventoperator for solving a new system of generalized multi-valued variational-like inclusions in the setting of ...
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The main purpose of this paper is to construct a new iterative algorithm using the notion of P-eta-resolventoperator for solving a new system of generalized multi-valued variational-like inclusions in the setting of Banach spaces. As an application of the constructed algorithm, the strong convergence of the sequences generated by our proposed iterative algorithm to a solution of the system of generalized multi-valued variational-like inclusions is proved.
In this paper, we introduce and study a new system of variational inclusions involving H-eta-monotone operators in Banach space. Using the resolventoperator associated with H-eta-monotone operators, we prove the exis...
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In this paper, we introduce and study a new system of variational inclusions involving H-eta-monotone operators in Banach space. Using the resolventoperator associated with H-eta-monotone operators, we prove the existence and uniqueness of solutions for this new system of variational inclusions. We also construct a new algorithm for approximating the solution of this system and discuss the convergence of the sequence of iterates generated by the algorithm. (C) 2007 Elsevier Ltd. All rights reserved.
A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolventoperator tech...
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A new system of the set-valued mixed quasi-variational-like inclusions （SSMQVLI） involving H-η-monotone operators is studied in general Banach spaces without uniform smoothness. By using the resolvent operator technique of H-η-monotone operators, a new iterative algorithm for finding approximate solutions to SSMQVLI is proposed. It is shown that the iterative sequences generated by the algorithm converge strongly to the exact solution of SSMQVLI under appropriate assumptions. These obtained new results have extended and improved previous results.
In this paper, we consider a system of nonlinear variational inclusions involving H-accretive operators studied by Huang and Fang in q-uniformly smooth Banach spaces. Using resolvent operator technique, we suggest an ...
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In this paper, we consider a system of nonlinear variational inclusions involving H-accretive operators studied by Huang and Fang in q-uniformly smooth Banach spaces. Using resolvent operator technique, we suggest an iterative algorithm for finding all approximate solution to the system of variational inclusions. Further, we discuss convergence criteria for the approximate solution of the system of variational inclusions. The theorems presented in this paper improve and unify many known results of variational inclusions. (c) 2006 Elsevier B.V. All rights reserved.
In this work, we introduce a new concept of (A, eta)-accretive mappings, study some properties of (A, eta)-accretive mappings and define resolventoperators associated with (A, eta)-accretive mappings which include th...
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In this work, we introduce a new concept of (A, eta)-accretive mappings, study some properties of (A, eta)-accretive mappings and define resolventoperators associated with (A, eta)-accretive mappings which include the existing resolventoperators as special cases. By using the new resolvent operator technique, we also construct a new class of iterative algorithms for a class of relaxed cocoercive variational inclusions involving non-accretive set-valued mappings and study applications of (A, eta)-accretive mappings to the approximation-solvability of the relaxed cocoercive variational inclusions in q-uniformly smooth Banach spaces. Our results generalize and improve the corresponding results of recent works. (C) 2006 Elsevier Ltd. All rights reserved.
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