Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique s...Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique solution of Ax (?) f. The conclusion in this paper weakens the stronger conditions about errors in Chidume and Moore's theorem (J. Math. Anal. Appl, 245(2000), 142-160).展开更多
Letq>1,and let E be a real q-uniformly smooth Banach space. Let T: E→E be a continuous φstrongly accretive operator.For a given f E,let x*denote the unique solution of the equation Tx=f.Define the operator H:E→E...Letq>1,and let E be a real q-uniformly smooth Banach space. Let T: E→E be a continuous φstrongly accretive operator.For a given f E,let x*denote the unique solution of the equation Tx=f.Define the operator H:E→E by Hx=f+x-Tx,and suppose that the range of H is bounded. for any x1 E let {xn}∞n=qin E be the Ishikawa iterative process defined by Under suitable comditions,the Ishikawa iterative process strongly converges to the unique solution of Tx=f.the related result deals with the problems that Ishikawa iterative process strongly converges to the unique fixed point of -hemicontractive mappings.These results generalize results of Osilike [2],Chidume[4,5]and Tan[10],Zeng[11]and several other results from the class of strongly assertive operators and the class of strongly pseudocontractive operators to the much more general class of -trongly accrtive and class of -hemicontractive maps.展开更多
Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Ou...Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Our results improve and extend thecorresponding results of Noor and Chang-Huang. Moreover, a more general iterativealgorithm for finding the approximate solution of generalized strongly nonlinear quasi-complementarity problems is also given. It is shown that the approximate solution ob-tained by the iterative scheme converges to the exact solution of this quasi-com-plementarity problem.展开更多
文摘Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique solution of Ax (?) f. The conclusion in this paper weakens the stronger conditions about errors in Chidume and Moore's theorem (J. Math. Anal. Appl, 245(2000), 142-160).
基金the National Natural Science Foundation of China under Grant No. 19801017 andthe Foundation for University Key Teacher by th
文摘Letq>1,and let E be a real q-uniformly smooth Banach space. Let T: E→E be a continuous φstrongly accretive operator.For a given f E,let x*denote the unique solution of the equation Tx=f.Define the operator H:E→E by Hx=f+x-Tx,and suppose that the range of H is bounded. for any x1 E let {xn}∞n=qin E be the Ishikawa iterative process defined by Under suitable comditions,the Ishikawa iterative process strongly converges to the unique solution of Tx=f.the related result deals with the problems that Ishikawa iterative process strongly converges to the unique fixed point of -hemicontractive mappings.These results generalize results of Osilike [2],Chidume[4,5]and Tan[10],Zeng[11]and several other results from the class of strongly assertive operators and the class of strongly pseudocontractive operators to the much more general class of -trongly accrtive and class of -hemicontractive maps.
文摘Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Our results improve and extend thecorresponding results of Noor and Chang-Huang. Moreover, a more general iterativealgorithm for finding the approximate solution of generalized strongly nonlinear quasi-complementarity problems is also given. It is shown that the approximate solution ob-tained by the iterative scheme converges to the exact solution of this quasi-com-plementarity problem.
