Discontinuity at fixed points with applications

R. P. Pant; Nihal Yilmaz Özgür; Nihal Taş

doi:10.36045/BBMS/1576206358

Discontinuity at fixed points with applications

R. P. Pant, Nihal Yilmaz Özgür, Nihal Taş

Research output: Contribution to journal › Article › peer-review

30 Citations (Scopus)

Abstract

In this paper, we study new contractive conditions which are strong enough to generate fixed points but which do not force the map to be continuous at fixed points. In this context, we give new results on the fixed-circle problem. We investigate some applications to complex-valued metric spaces and to discontinuous activation functions in real and complex valued neural networks.

Original language	English
Pages (from-to)	571-589
Number of pages	19
Journal	Bulletin of the Belgian Mathematical Society - Simon Stevin
Volume	26
Issue number	4
DOIs	https://doi.org/10.36045/BBMS/1576206358
Publication status	Published - 2019
Externally published	Yes

Keywords

Activation function
Complex-valued neural network
Discontinuity
Fixed circle
Fixed point
Real-valued neural network

ASJC Scopus subject areas

General Mathematics

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10.36045/BBMS/1576206358

Cite this

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title = "Discontinuity at fixed points with applications",

abstract = "In this paper, we study new contractive conditions which are strong enough to generate fixed points but which do not force the map to be continuous at fixed points. In this context, we give new results on the fixed-circle problem. We investigate some applications to complex-valued metric spaces and to discontinuous activation functions in real and complex valued neural networks.",

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AU - Özgür, Nihal Yilmaz

AU - Taş, Nihal

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AB - In this paper, we study new contractive conditions which are strong enough to generate fixed points but which do not force the map to be continuous at fixed points. In this context, we give new results on the fixed-circle problem. We investigate some applications to complex-valued metric spaces and to discontinuous activation functions in real and complex valued neural networks.

KW - Activation function

KW - Complex-valued neural network

KW - Discontinuity

KW - Fixed circle

KW - Fixed point

KW - Real-valued neural network

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Discontinuity at fixed points with applications

Abstract

Keywords

ASJC Scopus subject areas

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