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Volume 7, Issue 3, Article 91 |
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New Perturbed Iterations for a Generalized Class of Strongly Nonlinear Operator Inclusion Problems in Banach Spaces
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Authors: |
Heng-you Lan, Huang-Lin Zeng, Zuo-An Li, |
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Keywords:
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Generalized $m$-accretive mapping; Generalized strongly nonlinear operator inclusion problems; Perturbed iterative algorithm with errors; Existence; Convergence and stability |
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Date Received:
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05/03/06 |
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Date Accepted:
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19/03/06 |
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Subject Codes: |
68Q25, 49J40, 47H19, 47H12.
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Editors: |
Ram U. Verma, |
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Abstract: |
The purpose of this paper is to introduce and study a new kind of generalized strongly nonlinear operator inclusion problems involving generalized m-accretive mapping in Banach spaces. By using the resolvent operator technique for generalized m-accretive mapping due to Huang and Fang, we also prove the existence theorem of the solution for this kind of operator inclusion problems and construct a new class of perturbed iterative algorithm with mixed errors for solving this kind of generalized strongly nonlinear operator inclusion problems in Banach spaces. Further, we discuss the convergence and stability of the iterative sequence generated by the perturbed algorithm. Our results improve and generalize the corresponding results of [3,6,11,12].
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