Generalized H-η-Accretive Operators in Banach Spaces With an Application to Variational Inclusions

LUO Xue-ping; HUANG Nan-jing

doi:10.3879/j.issn.1000-0887.2010.04.009

Volume 31 Issue 4

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LUO Xue-ping, HUANG Nan-jing. Generalized H-η-Accretive Operators in Banach Spaces With an Application to Variational Inclusions[J]. Applied Mathematics and Mechanics, 2010, 31(4): 472-480. doi: 10.3879/j.issn.1000-0887.2010.04.009

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Generalized H-η-Accretive Operators in Banach Spaces With an Application to Variational Inclusions

doi: 10.3879/j.issn.1000-0887.2010.04.009

Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China

Received Date: 1900-01-01
Rev Recd Date: 2010-02-10
Publish Date: 2010-04-15

Abstract

Abstract

A new notion of generalizedH-η-accretive operator which provided a unifying framework for the generalizedm-accretive operator and theH-η-mono tone operator in Banach spaces was introduced and studied.A resolvent operator associated with the generalizedH-η-accretive operator was defined and its Lipschitz continuity was shown.As an application,the solvability for a class of variational inclusion sinvolving the generalizedH-η-accretive operators in Banach spaces was considered.By using the technique of resolvent mapping,aniterative algorithm for solving the variational inclusion in Banach space was constructed.Under some suitable conditions,the existence of solution for the variational inclusion and the convergence of iterative sequence generated by the algorithm were proved.
- generalizedH-η-accretive operator,
- resolvent operator,
- variational inclusion,
- iterative algorithm,
- convergence

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References(35)

References

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