A new contribution to discontinuity at fixed point


	Open access
	A new contribution to discontinuity at fixed point


	Fixed Point Theory, Volume 20, No. 2, 2019, 715-728, June 1st, 2019 DOI: 10.24193/fpt-ro.2019.2.47 Authors: N. Taș and N. Yilmaz Özgür 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 (α,β)-Geraghty type-I rational contractive mapping. Also we give an application of these new results to discontinuous activation functions. Key Words and Phrases: Discontinuity, fixed point, fixed circle, metric space, activation function. 2010 Mathematics Subject Classification: 47H10, 54H25, 47H09. Published on-line: June 1st, 2019. Abstract pdf Fulltext pdf Back to volume's table of contents