Author:
Dumitrescu Doru,Pitea Ariana
Abstract
<abstract><p>The aim of this article is to present some results regarding $ (\alpha, \psi) $-rational type contractions in the setting of the generalized metric spaces introduced by Jleli and Samet. By the nature of these types of contractions which use also comparison functions, new fixed point theorems are established. Already known facts appear as consequences of our outcomes. Examples and comments point out the applicability of our approach.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference27 articles.
1. V. Berinde, Iterative approximation of fixed point, Berlin: Springer, 2007.
2. M. Samreen, T. Kamran, M. Postolache, Extended $b$-metric space, extended $b$-comparison function and nonlinear contractions, U. Politech. Buch. Ser. A, 80 (2018), 21–28
3. E. Karapınar, D. O'Regan, A. Roldan, N. Shahzad, Fixed point theorems in new generalized metric spaces, Fixed Point Theory Appl., 18 (2016), 645–671, https://doi.org/10.1007/s11784-016-0301-4
4. D. Dumitrescu, A. Pitea, Fixed point theorems on almost $(\varphi, \theta)$-contractions in Jleli-Samet generalized metric spaces, Mathematics, 10 (2022). https://doi.org/10.3390/math10224239
5. H. H. Alsulami, S. Chandok, M. A. Taoudi, I. M. Erhan, Some fixed point theorems for $(\alpha, \psi)$-rational type contractive mappings, Fixed Point Theory Appl., 2015 (2015), 97. https://doi.org/10.1186/s13663-015-0332-3