Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2013, Special Issue (2013), Article ID 761864, 21 pages.

Composite Iterative Algorithms for Variational Inequality and Fixed Point Problems in Real Smooth and Uniformly Convex Banach Spaces

Lu-Chuan Ceng and Ching-Feng Wen

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Abstract

We introduce composite implicit and explicit iterative algorithms for solving a general system of variational inequalities and a common fixed point problem of an infinite family of nonexpansive mappings in a real smooth and uniformly convex Banach space. These composite iterative algorithms are based on Korpelevich's extragradient method and viscosity approximation method. We first consider and analyze a composite implicit iterative algorithm in the setting of uniformly convex and 2-uniformly smooth Banach space and then another composite explicit iterative algorithm in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm. Under suitable assumptions, we derive some strong convergence theorems. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literatures.

Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 761864, 21 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394807739

Digital Object Identifier
doi:10.1155/2013/761864

Mathematical Reviews number (MathSciNet)
MR3074340

Zentralblatt MATH identifier
1271.47054

Citation

Ceng, Lu-Chuan; Wen, Ching-Feng. Composite Iterative Algorithms for Variational Inequality and Fixed Point Problems in Real Smooth and Uniformly Convex Banach Spaces. J. Appl. Math. 2013, Special Issue (2013), Article ID 761864, 21 pages. doi:10.1155/2013/761864. https://projecteuclid.org/euclid.jam/1394807739


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