Stability and modified new results for the iterative approximations
Intelligent Systems and Simulation: Mathematical and Environmental Modeling, CRC Press, ss.22-47, 2025
- Yayın Türü: Kitapta Bölüm / Araştırma Kitabı
- Basım Tarihi: 2025
- Doi Numarası: 10.1201/9781003638414-3
- Yayınevi: CRC Press
- Sayfa Sayıları: ss.22-47
- Kırklareli Üniversitesi Adresli: Evet
Özet
This chapter explores the approximation of common fixed points within iterative sequences, focusing on modified iterations designed for generalized Lipschitzian mappings in Hilbert spaces. It presents an analysis of stability within these iterations, providing theoretical proofs and numerical examples to illustrate the concepts. By examining nonexpansive semigroups, the study delves into the intricacies of convergence and stability in iterative approximation methods. The modified iterative processes introduced offer novel insights into the dynamics of fixed point approximation, particularly in the context of generalized Lipschitzian mappings. Theoretical results establish stability criteria, enhancing understanding and applicability in various mathematical settings. Numerical demonstrations further validate the theoretical constructs, offering practical insights into the efficacy of the proposed methods. Overall, this chapter contributes to the advancement of iterative approximation techniques and their stability analysis, with implications for diverse fields reliant on fixed-point computation. The study considers the approximation of common fixed points in iterative sequences and demonstrates the modified versions of iterative processes for generalized Lipschitzian mappings in Hilbert spaces. Additionally, several results on the stability of these iterations are proved, and some numerical examples are presented.