Block methods for a convex feasibility problem in a Banach space

Volume 9, Issue 6, pp 4897--4908 http://dx.doi.org/10.22436/jnsa.009.06.125

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Authors

Mingliang Zhang - School of Mathematics and Statistics, Henan University, Kaifeng, China. Ravi P. Agarwal - Department of Mathematics, Texas A&M University, Kingsville, U. S. A..

Abstract

In this paper, a convex feasibility problem is investigated based on a block method. Strong convergence theorems for common solutions of equilibrium problems and generalized asymptotically quasi-\(\phi\)- nonexpansive mappings are established in a strictly convex and uniformly smooth Banach space which also has the Kadec-Klee property. The results obtained in this paper unify and improve many corresponding results announced recently.

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Keywords

• Banach space
• block method
• equilibrium problem
• convex feasibility problem
• variational inequality.

MSC

•  90C33
•  47H05

References

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