• Nonlinear Functional Analysis and Applications
• /
• v.28 no.2
• /
• pp.383-394
• /
• 2023

In this paper, we shall introduce the new notions of ω-orbital admissible mappings, ω-interpolative Kannan type contraction and ω-interpolative Ciric-Reich-Rus type contraction. In the setting of these new contractions, we will prove some fixed point theorems in bipolar metric spaces. Some existing results from literature are also deduced from our main results. Some examples are also provided to illustrate the theorems.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.3
• /
• pp.649-672
• /
• 2024

This paper explores the significance and implications of fixed point results related to orbital contraction as a novel form of contraction in various fields. Theoretical developments and theorems provide a solid foundation for understanding and utilizing the properties of orbital contraction, showcasing its efficacy through numerous examples and establishing stability and convergence properties. The application of orbital contraction in control systems proves valuable in designing resilient and robust control strategies, ensuring reliable performance even in the presence of disturbances and uncertainties. In the realm of financial modeling, the application of fixed point results offers valuable insights into market dynamics, enabling accurate price predictions and facilitating informed investment decisions. The practical implications of fixed point results related to orbital contraction are substantiated through empirical evidence, numerical simulations, and real-world data analysis. The ability to identify and leverage fixed points grants stability, convergence, and optimal system performance across diverse applications.