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Fixed‐Point Results for Generalized α‐Admissible Hardy‐Rogers’ Contractions in Cone b2‐Metric Spaces over Banach’s Algebras with Application

Author

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  • Ziaul Islam
  • Muhammad Sarwar
  • Manuel de la Sen

Abstract

In the current manuscript, the notion of a cone b2‐metric space over Banach’s algebra with parameter b≻¯e is introduced. Furthermore, using α‐admissible Hardy‐Rogers’ contractive conditions, we have proven fixed‐point theorems for self‐mappings, which generalize and strengthen many of the conclusions in existing literature. In order to verify our key result, a nontrivial example is given, and as an application, we proved a theorem that shows the existence of a solution of an infinite system of integral equations.

Suggested Citation

  • Ziaul Islam & Muhammad Sarwar & Manuel de la Sen, 2020. "Fixed‐Point Results for Generalized α‐Admissible Hardy‐Rogers’ Contractions in Cone b2‐Metric Spaces over Banach’s Algebras with Application," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnlamp:v:2020:y:2020:i:1:n:8826060
    DOI: 10.1155/2020/8826060
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    References listed on IDEAS

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    1. Tanzeela Kanwal & Azhar Hussain & Poom Kumam & Ekrem Savas, 2019. "Weak Partial b -Metric Spaces and Nadler’s Theorem," Mathematics, MDPI, vol. 7(4), pages 1-12, April.
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