Some Fixed-Circle Results with Mix-Type Contractions

Abstract

In this chapter, we give fixed-circle results as a geometric approach to the fixed-point theory (FPT) on metric spaces using the mix-type contractions with two different function families. We define ξ,χ<inf>C</inf>-contraction, a Ćirić type ξ,χ<inf>C</inf>-contraction, a Rhoades type ξ,χ<inf>C</inf>-contraction, a Sehgal type ξ,χ<inf>C</inf>-contraction and Hardy-Rogers type ξ,χ<inf>C</inf>-contraction. Employing these contractions, we establish several results concerning fixed circle and fixed disc supported by relevant examples and remarks. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.