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Mann and Ishikawa Type Perturbed Iterative Algorithms for Generalized Quasivariational Inclusions

✍ Scribed by K.R. Kazmi

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 218 KB
Volume: 209
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.1997.5368

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✦ Synopsis

In this paper, we introduce a class of generalized quasivariational inclusions and show its equivalence with a class of fixed point problems by making use of the properties of proximal maps. Using this equivalence, we develop the Mann and Ishikawa type perturbed iterative algorithms for this class of generalized quasivariational inclusions. Further, using fixed point techniques, we prove the existence of solutions for the class of generalized quasivariational inclusions and discuss the convergence criteria for the perturbed algorithms. Our algorithms and results improve and generalize many known corresponding algorithms and results.

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## Abstract The concept of the operators of generalized monotone type is introduced and iterative approximation methods for a fixed point of such operators by the Ishikawa and Mann iteration schemes {xn} and {yn} with errors is studied. Let __X__ be a real Banach space and __T__ : __D__ ⊂ __X__ → 2