Remarks on F-weak contractions and discontinuity at the fixed point

The aim of this paper is to generalize celebrated results due to Wardowski[8, 9] and also to provide yet new solutions to the once open problem[6, p.242] on the existence of a contractive mapping which possesses a fixed point but is not continuous at the fixed point via generalized F**-weak contractions. Finally, an example is given to illustrate our results. The aim of this paper is to generalize celebrated results due to Wardowski[8, 9] and also to provide yet new solutions to the once open problem[6, p.242] on the existence of a contractive mapping which possesses a fixed point but is not continuous at the fixed point via generalized F**-weak contractions. Finally, an example is given to illustrate our results.

Keywords:

F-contraction, F-weak contraction, F**-weak contraction, contractive mapping, fixed point theorem discontinuity at the fixed point,

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