## Abstract and Applied Analysis

### The Existence of Fixed Point Theorems via $w$-Distance and $\alpha$-Admissible Mappings and Applications

#### Abstract

We introduce the concept of the generalized ${w}_{\alpha }$-contraction mappings and establish the existence of fixed point theorem for such mappings by using the properties of $w$-distance and $\alpha$-admissible mappings. We also apply our result to coincidence point and common fixed point theorems in metric spaces. Further, the fixed point theorems endowed with an arbitrary binary relation are also derived from our results. Our results generalize the result of Kutbi, 2013, and several results in the literature.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 165434, 8 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393442135

Digital Object Identifier
doi:10.1155/2013/165434

Mathematical Reviews number (MathSciNet)
MR3121524

Zentralblatt MATH identifier
1300.54075

#### Citation

Kutbi, Marwan Amin; Sintunavarat, Wutiphol. The Existence of Fixed Point Theorems via $w$ -Distance and $\alpha$ -Admissible Mappings and Applications. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 165434, 8 pages. doi:10.1155/2013/165434. https://projecteuclid.org/euclid.aaa/1393442135

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