## Abstract and Applied Analysis

### Fixed Point Results for α-ψ-Contractive Mappings Including Almost Contractions and Applications

#### Abstract

In the recent paper (B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for $\alpha$-$\psi$-contractive type mappings, Nonlinear Analysis. Theory, Methods and Applications, 75 (2012), 2154-2165.), the authors introduced the concept of $\alpha$-admissible maps on metric spaces. Using this new concept, they presented some nice fixed point results. Also, they gave an existence theorem for integral equation to show the usability of their result. Then, many authors focused on this new concept and obtained a lot of fixed point results, which are used for existence theorems. In this paper, we not only extend some of the recent results about this direction but also generalize them. Then, we give some examples to show our results are proper extensions. Furthermore, we use our results to obtain the existence and uniqueness result for a solution of fourth order two-point boundary value problem.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 869123, 10 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412606561

Digital Object Identifier
doi:10.1155/2014/869123

Mathematical Reviews number (MathSciNet)
MR3246363

Zentralblatt MATH identifier
07023226

#### Citation

Durmaz, Gonca; Mınak, Gülhan; Altun, Ishak. Fixed Point Results for α - ψ -Contractive Mappings Including Almost Contractions and Applications. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 869123, 10 pages. doi:10.1155/2014/869123. https://projecteuclid.org/euclid.aaa/1412606561

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