Taiwanese Journal of Mathematics

SUZUKI-WARDOWSKI TYPE FIXED POINT THEOREMS FOR $\alpha$-GF-CONTRACTIONS

N. Hussain and P. Salimi Salimi

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Abstract

Recently, Wardowski [Fixed Point Theory Appl. 2012:94, 2012] introduced and studied a new contraction called F-contraction to prove a fixed point result as a generalization of the Banach contraction principle. Abbas et al. [2] further generalized the concept of F-contraction and proved certain fixed and common fixed point results. In this paper, we introduce an $\alpha$-GF-contraction with respect to a general family of functions $G$ and establish Wardowski type fixed point results in metric and ordered metric spaces. As an application of our results we deduce Suzuki type fixed point results for GF-contractions. We also derive certain fixed and periodic point results for orbitally continuous generalized F-contractions. Moreover, we discuss some illustrative examples to highlight the realized improvements.

Article information

Source
Taiwanese J. Math., Volume 18, Number 6 (2014), 1879-1895.

Dates
First available in Project Euclid: 21 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500667501

Digital Object Identifier
doi:10.11650/tjm.18.2014.4462

Mathematical Reviews number (MathSciNet)
MR3284036

Zentralblatt MATH identifier
1357.54033

Subjects
Primary: 46N40: Applications in numerical analysis [See also 65Jxx] 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 54H25: Fixed-point and coincidence theorems [See also 47H10, 55M20] 46T99: None of the above, but in this section

Keywords
fixed point $\alpha$-GF-contraction $\alpha$-$\eta$-Continous function orbitally continuous function

Citation

Hussain, N.; Salimi Salimi, P. SUZUKI-WARDOWSKI TYPE FIXED POINT THEOREMS FOR $\alpha$-GF-CONTRACTIONS. Taiwanese J. Math. 18 (2014), no. 6, 1879--1895. doi:10.11650/tjm.18.2014.4462. https://projecteuclid.org/euclid.twjm/1500667501


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