SOLVING EXISTENCE PROBLEMS VIA F-CONTRACTION IN MODIFIED b-METRIC SPACES

SOLVING EXISTENCE PROBLEMS VIA F-CONTRACTION IN MODIFIED b-METRIC SPACES

E. Karapinar, S. Sedghi, N. Shobe

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Abstract

In this paper, we introduce a new abstract structure, expanded b-metric, as an natural extension of b-metric. We also de ne basic topological notions in expanded b- metric to able to investigate the existence of  xed point for such mappings under various F-contractive conditions. We provide example to illustrate the results presented herein.

Keywords

b-metric, expanded b-metric,  xed point, contraction.