Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 18, Number 6 (2014), 1879-1895.
SUZUKI-WARDOWSKI TYPE FIXED POINT THEOREMS FOR $\alpha$-GF-CONTRACTIONS
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.  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.
Taiwanese J. Math., Volume 18, Number 6 (2014), 1879-1895.
First available in Project Euclid: 21 July 2017
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Zentralblatt MATH identifier
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
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