Generalized set-valued variational-like inclusions involving -η-cocoercive operator in Banach spaces
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- 作者：Rais Ahmad (1)
Mohd Dilshad (1)
Mu-Ming Wong (2)
Jen-Chin Yao (3) (4) - 关键词：η ; cocoercive ; Lipschitz continuity ; algorithm ; variational ; like inclusion
- 刊名：Journal of Inequalities and Applications
- 出版年：2012
- 出版时间：December 2012
- 年：2012
- 卷：2012
- 期：1
- 全文大小：218KB
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Mohd Dilshad (1)
Mu-Ming Wong (2)
Jen-Chin Yao (3) (4)
1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
2. Department of Applied Mathematics, Chung Yuan Christain University, Chung Li, 32023, Taiwan
3. Center for General Education, Kaohsiung Medical University, Kaohsiung, 807, Taiwan
4. Department of Applied Mathematics, National Sun-Yat Sen University, Kaohsiung, 804, Taiwan - ISSN：1029-242X
文摘
The aim of this paper is to introduce a new -η-cocoercive operator and its resolvent operator. We study some of the properties of -η-cocoercive operator and prove the Lipschitz continuity of resolvent operator associated with -η-cocoercive operator. Finally, we apply the techniques of resolvent operator to solve a generalized set-valued variational-like inclusion problem in Banach spaces. Our results are new and generalize many known results existing in the literature. Some examples are given in support of definition of -η-cocoercive operator. MSC: 47H19, 49J40.