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Advances in Inequalities and Applications ISSN 2050-7461

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Adv. Inequal. Appl. 2014 (2014), Article ID 40

Strong convergence theorems for finding a common solution of a variational inequality problem and a fixed point problem in a uniformly convex and 2-smooth Banach spaces

Renu Chugh, Rekha Rani, Sanjay Kumar

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Abstract

In this paper, we generalize α-inverse strongly accretive mapping to accretive and Lipschitz continuous mapping in uniformly convex and 2-smooth Banach space and prove a strong convergence result for finding common element of the set of fixed points of strictly pseudocontractive mappings and the set of solutions of variational inequality problem. With the help of an example, we find a common solution of a variational inequality problem and a fixed point problem.

Published
25 October 2014
Volume
2014 (2014)
License
CC BY 3.0

Copyright © 2014 Renu Chugh, Rekha Rani, Sanjay Kumar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Cite this article

R. Chugh, R. Rani, S. Kumar, Strong convergence theorems for finding a common solution of a variational inequality problem and a fixed point problem in a uniformly convex and 2-smooth Banach spaces, Adv. Inequal. Appl. 2014 (2014), 40.

BibTeX
@article{Chugh2014,
  author  = {Chugh, Renu and Rani, Rekha and Kumar, Sanjay},
  title   = {Strong convergence theorems for finding a common solution of a variational inequality problem and a fixed point problem in a uniformly convex and 2-smooth Banach spaces},
  journal = {Adv. Inequal. Appl.},
  volume  = {2014},
  year    = {2014},
  pages   = {40},
  doi     = {}
}