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