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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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