Fixed Point Results in Hilbert Space via Altering Distance Functions

Drawing on the principles of functional analysis within the framework of Hilbert space, this research aims to establish fixed point results for distinct mappings under newly proposed rational contractions employing altering distance functions. The study employs specific mathematical techniques, including Banach Contraction Principle, iterative methods, and relational mappings that incorporate partial orders and metric spaces. In particular, we construct appropriate complete metric spaces and apply rational expressions to define contraction conditions. The methods also involve proving convergence through iterative sequences and leveraging the properties of partial orders to manage relational structures. Additionally, the findings are illustrated with examples to enhance understanding. The paper further explores the derivation of corollaries, which serve as specialized instances of the main results. Through iterative processes and methodological rigor, this work advances understanding in the field, providing valuable insights into the properties of fixed points under the specified rational contractions.