## Banach Journal of Mathematical Analysis

- Banach J. Math. Anal.
- Volume 11, Number 3 (2017), 661-675.

### A hybrid shrinking projection method for common fixed points of a finite family of demicontractive mappings with variational inequality problems

Suthep Suantai and Withun Phuengrattana

#### Abstract

In this article, we prove some properties of a demicontractive mapping defined on a nonempty closed convex subset of a Hilbert space. By using these properties, we obtain strong convergence theorems of a hybrid shrinking projection method for finding a common element of the set of common fixed points of a finite family of demicontractive mappings and the set of common solutions of a finite family of variational inequality problems in a Hilbert space. A numerical example is presented to illustrate the proposed method and convergence result. Our results improve and extend the corresponding results existing in the literature.

#### Article information

**Source**

Banach J. Math. Anal., Volume 11, Number 3 (2017), 661-675.

**Dates**

Received: 7 July 2016

Accepted: 5 October 2016

First available in Project Euclid: 23 May 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.bjma/1495505201

**Digital Object Identifier**

doi:10.1215/17358787-2017-0010

**Mathematical Reviews number (MathSciNet)**

MR3679900

**Zentralblatt MATH identifier**

06754307

**Subjects**

Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.

Secondary: 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

**Keywords**

demicontractive mappings inverse strongly monotone mapping shrinking projection method variational inequality problems Hilbert spaces

#### Citation

Suantai, Suthep; Phuengrattana, Withun. A hybrid shrinking projection method for common fixed points of a finite family of demicontractive mappings with variational inequality problems. Banach J. Math. Anal. 11 (2017), no. 3, 661--675. doi:10.1215/17358787-2017-0010. https://projecteuclid.org/euclid.bjma/1495505201