Existence theorems for a unified interpolative Kannan contraction with an application on nonlinear matrix equations

Abstract

Introduction/purpose: This paper established a new mathematical framework by uncovering the relationships between Kannan contractions and interpolative Kannan contractions. The concept of unified interpolative Kannan contractions was introduced in the framework of a relational metric space. Additionally, the study aimed to broaden the concept of alpha admissibility by incorporating specific relational metric ideas. Methods: A detailed exploration of the properties and characteristics of Kannan contractions and interpolative Kannan contractions was conducted. The research introduced the concept of unified interpolative Kannan contractions and formulated new fixed point results for these mappings. Result: The study successfully established fixed point results for unified interpolative Kannan contractions within the framework of relational metric spaces. Additionally, an application of these results to solve a problem concerning nonlinear matrix equations was provided, further emphasizing their significance. Conclusion: The findings of this study significantly advanced the understanding of Kannan contractions and interpolative Kannan contractions, offering a unified framework for their analysis. The introduction of unified interpolative Kannan contractions and the expansion of alpha admissibility have broad implications for the field of mathematics.

Keywords

• unified interpolative kannan contraction
• r-admissible
• relational metric space