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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 \(\left(\mathfrak {\xi}, \mathfrak {\chi}\right) _{C}\) -contraction, a Ćirić type \(\left(\mathfrak {\xi},\mathfrak {\chi}\right) _{C}\) -contraction, a Rhoades type \(\left(\mathfrak {\xi},\mathfrak {\chi}\right) _{C}\) -contraction, a Sehgal type \(\left(\mathfrak {\xi},\mathfrak {\chi}\right) _{C}\) -contraction and Hardy-Rogers type \(\left(\mathfrak {\xi},\mathfrak {\chi}\right) _{C}\) -contraction. Employing these contractions, we establish several results concerning fixed circle and fixed disc supported by relevant examples and remarks.

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Some Fixed-Circle Results with Mix-Type Contractions

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  • 发表日期：

    2025年

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  • Nihal Taş,
  • Elif Kaplan

摘要

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 \(\left(\mathfrak {\xi}, \mathfrak {\chi}\right) _{C}\) -contraction, a Ćirić type \(\left(\mathfrak {\xi},\mathfrak {\chi}\right) _{C}\) -contraction, a Rhoades type \(\left(\mathfrak {\xi},\mathfrak {\chi}\right) _{C}\) -contraction, a Sehgal type \(\left(\mathfrak {\xi},\mathfrak {\chi}\right) _{C}\) -contraction and Hardy-Rogers type \(\left(\mathfrak {\xi},\mathfrak {\chi}\right) _{C}\) -contraction. Employing these contractions, we establish several results concerning fixed circle and fixed disc supported by relevant examples and remarks.