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On Some Fixed-Point Results in Cone Ab-Metric Space Over a Real Banach Algebra Without the Assumption of Normality of Cone

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  • Kumam Anthony Singh
  • K. Bala Devi
  • Konthoujam Sangita Devi

Abstract

In this paper, we introduce the concept of cone Ab-metric space over real Banach algebra and prove some fixed-point theorems of the Banach, Chatterjea, and Kannan types in such space without assuming normality of the cone. Our results extend and generalize many previously known results in the existing literature. An example is given to support our results. We also apply our result to examine the existence of unique solution for a nonlinear Fredholm integral equation.

Suggested Citation

  • Kumam Anthony Singh & K. Bala Devi & Konthoujam Sangita Devi, 2025. "On Some Fixed-Point Results in Cone Ab-Metric Space Over a Real Banach Algebra Without the Assumption of Normality of Cone," Journal of Mathematics, Hindawi, vol. 2025, pages 1-12, September.
    • Handle: RePEc:hin:jjmath:9077312
    DOI: 10.1155/jom/9077312
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