Caristi-type nonunique fixed-point results and fixed-circle problem on bv(s)-metric spaces

Abstract

Fixed-point theory has been comprehensively studied with several methods. One of these methods is to generalize the used metric space such as bv(s)-metric spaces. Another method is to analyze the geometric features of the fixed-point set. In the light of these methods, in this chapter, we prove Caristi’s fixed-point theorem and new fixed-figure theorems in bv(s)-metric spaces. We present some examples to emphasize the significance of geometrical results. To further strengthen the obtained theoretical results, we establish an application to S-Shaped Rectified Linear Unit (SReLU) activation functions.