Existence theorems for a unified interpolative Kannan contraction with an application on nonlinear matrix equations - Vara Prasad, Koti N. V . V.; Mishra, Vinay; Radenović, Stojan (Vojnotehnički glasnik / Military Technical Courier, 2024)
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 Kan- nan 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.