## Abstract and Applied Analysis

### Discussion on Generalized-(αψ, β$\phi$)-Contractive Mappings via Generalized Altering Distance Function and Related Fixed Point Theorems

#### Abstract

We extend the notion of (α ψ, β $\phi$)-contractive mapping, a very recent concept by Berzig and Karapinar. This allows us to consider contractive conditions that generalize a wide range of nonexpansive mappings in the setting of metric spaces provided with binary relations that are not necessarily neither partial orders nor preorders. Thus, using this kind of contractive mappings, we show some related fixed point theorems that improve some well known recent results and can be applied in a variety of contexts.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 259768, 12 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412273187

Digital Object Identifier
doi:10.1155/2014/259768

Mathematical Reviews number (MathSciNet)
MR3176729

Zentralblatt MATH identifier
07022026

#### Citation

Berzig, Maher; Karapınar, Erdal; Roldán-López-de-Hierro, Antonio-Francisco. Discussion on Generalized-( α ψ , β $\phi$ )-Contractive Mappings via Generalized Altering Distance Function and Related Fixed Point Theorems. Abstr. Appl. Anal. 2014 (2014), Article ID 259768, 12 pages. doi:10.1155/2014/259768. https://projecteuclid.org/euclid.aaa/1412273187

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