Suzuki-Wardowski Type Theorems for Generalized $\alpha$-$\eta$-$GF$-Contractions

Vo Thi Le Hang, Kanokwan Sitthithakerngkiet

Abstract

The notion of a generalized $\alpha$-$\eta$-$GF$-contraction is introduced and Suzuki-Wardowski type theorems for generalized $\alpha$-$\eta$-$GF$-contractions are proved. These results generalize and improve the main results of [D. Wardowski, N.V. Dung, Fixedpoints of $F$-weak contractions on complete metric spaces, Demonstratio Math. 47 (1) (2014) 146--155, N.V. Dung, V.T.L. Hang, A fixed point theorem for generalized $F$-contractions on complete metric spaces, Vietnam J. Math. 43 (4) (2015) 743--753, N. Hussain, P. Salimi, Suzuki-Wardowski type fixed point theorems for $\alpha$-$GF$-contractions, Taiwanese J. Math. 18 (6) (2014) 879--1895]. An application to the Urysohn integral equation is obtained. Examples are also given to illustrate obtained results.