Proceedings of International Conference on Applied Innovation in IT  ·  2026/06/12  ·  Vol. 14  ·  Issue 4  ·  pp. 371–381
New Convergence and Stability Results of Fixed-Point Iteration in Partial Metric Spaces with an Application
Ghaidaa Sadon Ashiaa and Salwa Salman Abed
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Abstract
This paper investigates the convergence properties of a new (uⓜ,u_0 )-three-step iterative algorithm for weakly (μⓜ,k)-nonexpansive mappings in convex partial metric spaces. The proposed algorithm is developed to improve convergence behavior and achieve faster approximation of fixed points compared with several classical iterative methods. First, examples are provided to demonstrate the efficiency of the proposed three-step algorithm. A comparative analysis is conducted with several well-known iterative schemes, including Mann, Ishikawa, S-Picard, JF, Agarwal, Thakur, M, M^*, and S-iteration methods. The results show improved convergence performance of the proposed method. Second, the stability of the new iterative process is established. Furthermore, several convergence results are obtained in uniformly convex complete partial metric spaces. As an application, the proposed algorithm is employed to obtain approximate solutions for a delay differential equation, supported by a numerical example. The obtained results extend existing fixed-point theory and provide new insights into the development of efficient iterative methods for nonlinear problems in partial metric spaces.
Keywords
Three-Step Iterative Algorithm Weakly K-Nonexpansive Mappings Generalized μ-Nonexpansive Mappings Partial Metric Spaces Convex Partial Metric Spaces Fixed Point Convergence
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