期刊论文详细信息
Journal of inequalities and applications
General variational inclusions involving difference of operators
Muhammad Aslam Noor1 
关键词: monotone operators;    iterative method;    resolvent operator;    convergence;   
DOI  :  10.1186/1029-242X-2014-98
学科分类:数学(综合)
来源: SpringerOpen
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【 摘 要 】

In this paper, we introduce and consider a new class of general variational inclusions involving the difference of operators in a Hilbert space. We establish the equivalence between the general variational inclusions and the fixed point problems as well as with a new class of resolvent equations using the resolvent operator technique. We use this alternative formulation to discuss the existence of a solution of the general variational inclusions. We again use this alternative equivalent formulation to suggest and analyze a number of iterative methods for finding a zero of the difference of operators. We also discuss the convergence of the iterative method under suitable conditions. Our methods of proofs are very simple as compared with other techniques. Several special cases of these problems are also considered. The results proved in this paper may be viewed as a refinement and an improvement of the known results in this area.

【 授权许可】

CC BY   

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