On Some New Jungck–Fisher–Wardowski Type Fixed Point Results

Symmetry

Jelena Vujaković¹  Eugen Ljajko¹  Stojan Radenović²  Slobodan Radojević² 

[1] Department of Mathematics, Faculty of Sciences, University of Priština-Kosovska Mitrovica, Lole Ribara 29, 38200 Kosovska Mitrovica, Serbia;Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia;

关键词: banach contraction principle;    Fisher fixed point theorem;    Wardowski-type contractions;    compatible;    weakly compatible;    common fixed point;   

DOI  :  10.3390/sym12122048

来源: DOAJ

【 摘 要 】

Many authors used the concept of $\mathcal{F}-$contraction introduced by Wardowski in 2012 in order to define and prove new results on fixed points in complete metric spaces. In some later papers (for example Proinov P.D., J. Fixed Point Theory Appl. (2020)22:21, doi:10.1007/s11784-020-0756-1) it is shown that conditions (F2) and (F3) are not necessary to prove Wardowski’s results. In this article we use a new approach in proving that the Picard–Jungck sequence is a Cauchy one. It helps us obtain new Jungck–Fisher–Wardowski type results using Wardowski’s condition (F1) only, but in a way that differs from the previous approaches. Along with that, we came to several new contractive conditions not known in the fixed point theory so far. With the new results presented in the article, we generalize, extend, unify and enrich methods presented in the literature that we cite.

【 授权许可】

Unknown