Abstract
In this manuscript, we present some results related to fixed-discs of self-mappings in rectangular metric spaces. To do this, we give new techniques modifying some classical notions such as Banach contraction principle, α-admissible mappings and Brianciari type contractions. We give necessary illustrative examples to show the validity of our obtained theoretical theorems. Our results are generalizations of some fixed-circle results existing in the literature.
Highlights
Introduction and PreliminariesIt is well known that some applications of the Banach fixed point theorem and its generalizations have been widely studied in various disciplines of mathematics, engineering, economics and statistics.An interesting application of the Banach fixed point theorem has been obtained in the study of the graph neural network model [1]
Discontinuous activation functions are extensively used in neural networks
Considering the above literature, the study of new fixed-disc results and fixed-circle results on a rectangular metric space gains an importance because a rectangular metric is a generalization of a metric and there exist some examples of a rectangular metric that is not a metric
Summary
It is well known that some applications of the Banach fixed point theorem and its generalizations have been widely studied in various disciplines of mathematics, engineering, economics and statistics. Considering the above literature, the study of new fixed-disc results and fixed-circle results on a rectangular metric space gains an importance because a rectangular metric is a generalization of a metric and there exist some examples of a rectangular metric that is not a metric (see the following two examples). We provide some results on fixed-discs for different contraction mappings in the setting of rectangular metric spaces. To derive new fixed-disc results, we modify some known techniques and introduce new contractive conditions such as an α-ξ 0 -contractive condition, an Fd -contractive condition, a Ćirić type Fd -contractive condition, a Branciari Fd -contraction and a Branciari Fd -rational contraction on a rectangular metric space. Using these new contractive conditions, we prove some fixed-disc (fixed-circle) theorems and discuss some related results
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