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arXiv · 1705.03699

A new contribution to discontinuity at fixed point

Nihal Taş·Nihal Yilmaz Özgür
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Abstract

The aim of this paper is to obtain new solutions to the open question on the existence of a contractive condition which is strong enough to generate a fixed point but which does not force the map to be continuous at the fixed point. To do this, we use the right-hand side of the classical Rhoades' inequality and the number $M(x,y)$ given in the definition of an $(\alpha ,\beta )$-Geraghty type-$I$ rational contractive mapping. Also we give an application of these new results to discontinuous activation functions.

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Nihal Taş, Nihal Yilmaz Özgür. 2017-05-10. A new contribution to discontinuity at fixed point. https://doi.org/10.24193/fpt-ro.2019.2.47

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