The modified viscosity implicit rules for uniformly L-Lipschitzian asymptotically pseudocontractive mappings in Banach spaces

Volume 10, Issue 4, pp 1582--1592 http://dx.doi.org/10.22436/jnsa.010.04.24

Publication Date: April 20, 2017 Submission Date: January 12, 0017

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Authors

Yuanheng Wang - Department of Mathematics, Zhejiang Normal University, Jinhua, China. Chanjuan Pan - Department of Mathematics, Zhejiang Normal University, Jinhua, China.

Abstract

The aim of this paper is to establish the modified viscosity implicit rules for uniformly L-Lipschitzian asymptotically pseudocontractive mappings in Banach spaces. The strong convergence theorems of the rules are proved under certain assumptions imposed on the sequences of parameters. As an application, we apply our main results to solve some variational inequalities in Banach spaces, provided T is asymptotically regular. Our results extend the previous known results from Hilbert spaces to Banach spaces and from non-expansive mappings to asymptotically pseudocontractive mappings.

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Keywords

• Viscosity implicit rule
• variational inequality
• strong convergence
• asymptotically pseudo-contractions
• Banach space.

MSC

•  47H05
•  47H09
•  47H10
•  54H25

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