(𝛅,Ü ) Convex Structure on Partial B-Metric Space Concerning Quasi Contraction and Fixed-Point Results - UmaShanker; Naval Singh; Ruchi Singh (Recent Trends in Mathematics, 2024)
This work introduces the concept of (δ,Ü )– Convex Partial b-Metric Spaces using convex structure. Motivated by this approach, we demonstrated fixed point results and their uniqueness, as well as quasi contraction, and provided some supporting instances for the established results. Our findings expand prior fixed-point results to a novel concept (δ,Ü )– Convex Partial b-Metric Spaces. To support our theoretical findings, we provide several instances that exemplify the established results, including concrete examples to illustrate the practical applicability and relevance of our work. Our findings significantly extend prior fixed-point results to the novel concept of (δ,Ü)-Convex Partial b-Metric Spaces. By extending traditional fixed point theory to (δ,Ü)– Convex Partial b-Metric Spaces, this research not only deepens our theoretical understanding but also broadens the scope of applications across diverse fields. In scientific and engineering disciplines, where complex systems and nonlinear dynamics are prevalent, the conceptual framework introduced here offers new tools for analyzing and solving problems. The ability to model and analyze phenomena with convexity considerations opens avenues for more accurate representations of real-world scenarios, potentially leading to more effective solutions and insights This extension not only enhances the understanding of fixed-point theory but also creates new opportunities for its application in more complex and diverse mathematical settings. Consequently, our research advances the field, offering a robust foundation for future studies and potential applications across various scientific and engineering disciplines
Keywords: (δ; Common fixed point; Convex partial b-metric space. Quasi contraction; Fixed Point; Ü )– Convex Structure