A Related Fixed Point Theorem for F-Contractions on Two Metric Spaces

Olgun, Murat; Biçer, Özge; Alyıldız, Tuğçe; Altun, İshak

doi:10.15672/hjms.2017.517

Cited by 1 publication

(1 citation statement)

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“…In the last few decades, the Banach contraction principle has been generalized and studied by different approaches such as to generalize the used contractive condition (see [1], [4], [5], [6], [7], [8], [11], [18], [19] and [26] for more details) and to generalize the used metric space (see [2], [3], [9], [12], [14], [17], [25], [27] and [28] for more details). Recently, some fixed-circle theorems have been introduced as a geometrical direction of generalization of the fixed-point theorems (see [20], [21], [22] and [23] for more details).…”

Section: Introductionmentioning

confidence: 99%

New fixed-circle results related to Fc-contractive and Fc-expanding mappings on metric spaces

Mlaiki,

Ozgur,

Tas

2021

Preprint

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The fixed-circle problem is a recent problem about the study of geometric properties of the fixed point set of a self-mapping on metric (resp. generalized metric) spaces. The fixed-disc problem occurs as a natural consequence of this problem. Our aim in this paper, is to investigate new classes of self-mappings which satisfy new specific type of contraction on a metric space. We see that the fixed point set of any member of these classes contains a circle (or a disc) called the fixed circle (resp. fixed disc) of the corresponding self-mapping. For this purpose, we introduce the notions of an F c -contractive mapping and an F c -expanding mapping. Activation functions with fixed circles (resp. fixed discs) are often seen in the study of neural networks. This shows the effectiveness of our fixed-circle (resp. fixed-disc) results. In this context, our theoretical results contribute to future studies on neural networks.

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