SUZUKI-WARDOWSKI TYPE FIXED POINT THEOREMS FORα-GF-CONTRACTIONS - Hussain, N.; Salimi, P. (Taiwanese journal of mathematics, 2014)
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 anα-GF-contraction with respect to a general family of functionsGand 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. 2010Mathematics Subject Classification: 46N40, 47H10, 54H25, 46T99. Key words and phrases: Fixed point,α-GF-contraction,α-η-Continous function, Orbitally continuous function.