## Journal of Applied Mathematics

- J. Appl. Math.
- Volume 2012, Special Issue (2012), Article ID 401960, 20 pages.

### Hybrid Algorithm for Common Fixed Points of Uniformly Closed Countable Families of Hemirelatively Nonexpansive Mappings and Applications

#### Abstract

The authors have obtained the following results: (1) the definition of uniformly closed countable family of nonlinear mappings, (2) strong convergence theorem by the monotone hybrid algorithm for two countable families of hemirelatively nonexpansive mappings in a Banach space with new method of proof, (3) two examples of uniformly closed countable families of nonlinear mappings and applications, (4) an example which is hemirelatively nonexpansive mapping but not weak relatively nonexpansive mapping, and (5) an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping. Therefore, the results of this paper improve and extend the results of Plubtieng and Ungchittrakool (2010) and many others.

#### Article information

**Source**

J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 401960, 20 pages.

**Dates**

First available in Project Euclid: 3 January 2013

**Permanent link to this document**

https://projecteuclid.org/euclid.jam/1357180279

**Digital Object Identifier**

doi:10.1155/2012/401960

**Mathematical Reviews number (MathSciNet)**

MR2889114

**Zentralblatt MATH identifier**

1295.47070

#### Citation

Ai, Sumei; Su, Yongfu. Hybrid Algorithm for Common Fixed Points of Uniformly Closed Countable Families of Hemirelatively Nonexpansive Mappings and Applications. J. Appl. Math. 2012, Special Issue (2012), Article ID 401960, 20 pages. doi:10.1155/2012/401960. https://projecteuclid.org/euclid.jam/1357180279