Some Fixed-Circle Theorems on Metric Spaces

A new generalization of metric spaces: rectangular M-metric spaces

“…Therefore, it is important to study fixed-point theorems using different contractive conditions on a rectangular Mmetric space even if a rectangular M-metric and a rectangular metric generate same topology. Furthermore, in the last section, we have given an introduction to the fixedcircle problem [8]. On this new space, it is possible to study some fixed-circle results by various aspects.…”

S-metrik uzaylar üzerinde sabit-nokta teoremlerinin çeşitli türleri

“…Recently, a new approach is being studied to do geometric interpretations for fixed points which is called fixed-circle problem [14]. The notions of a circle and a fixed circle were defined on S-metric spaces as follows:…”

“…Using the above definitions, some fixed-circle results were obtained on S-metric spaces (see [15] and [16] for more details).…”

Meir-Keeler type and Caristi type fixed point theorems

“…Fixed point theorems for discontinuous mappings have found wide applications, for example application of such theorems in the study of neural networks with discontinuous activation functions is a very active area of research (e. g. Ding et al [5], Forti and Nistri [6], Nie and Zheng [8,9,10], Wu and Shan [16]). Recently Ozgur and Tas [11,12] have obtained application of the results on discontinuity at the fixed point in neural networks with discontinuous activation functions.…”