Generalized Wardowski type fixed point theorems via \(\alpha\)-admissible \(FG\)-contractions in \(b\)-metric spaces. (English) Zbl 1374.54056

Parvaneh, Vahid; Hussain, Nawab; Kadelburg, Zoran

Acta Math. Sci., Ser. B, Engl. Ed. 36, No. 5, 1445-1456 (2016).

Summary: Recently, a new contraction called \(F\)-contraction was introduced to prove a fixed point result as a generalization of the Banach contraction principle. In this paper, we introduce an \(\alpha\)-\(\beta\)-\(FG\)-contraction and generalize Wardowski’s fixed point result in \(b\)-metric and ordered \(b\)-metric spaces. As an application of our results, we deduce Suzuki type fixed point results for \(\beta\)-\(FG\)-contractions. Moreover, we discuss some illustrative examples to highlight the realized improvements.

MSC:

54H25	Fixed-point and coincidence theorems (topological aspects)
54E40	Special maps on metric spaces

Keywords:

\(\alpha\)-admissible mapping; \(F\)-contraction; \(\alpha\)-continuous function