Iterative schemes for approximating solution of nonlinear operators in Banach spaces
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Author list: Saewan S., Kanjanasamranwong P., Kumam P., Cho Y.J.
Publisher: SpringerOpen
Publication year: 2013
Journal: Fixed Point Theory and Applications (1687-1820)
Volume number: 2013
ISSN: 1687-1820
eISSN: 1687-1812
Languages: English-Great Britain (EN-GB)
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Abstract
The purpose of this paper is to present a new modified Halpern-Mann type iterative scheme by using the generalized f-projection operator for finding a common element in the set of zeroes of a system of maximal monotone operators, the set of fixed points of a totally quasi-φ-asymptotically nonexpansive mapping and the set of solutions of a system of generalized Ky Fan's inequalities in a uniformly smooth and strictly convex Banach space with the Kadec-Klee property. Furthermore, we show that our proposed iterative scheme converges strongly to a common element of the sets mentioned above. © 2013 Saewan et al.; licensee Springer.
Keywords
Generalized f-projection operators, System of generalized Ky Fan's inequalities, Totally quasi-φ-asymptotically nonexpansive mapping
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