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ICMRA Seminar Series
ICMRA Seminar Series
Convergence and applications of an efficient iterative scheme for generalized $\alpha$-Reich-Suzuki nonexpansive mappings
Convergence and applications of an efficient iterative scheme for generalized $\alpha$-Reich-Suzuki nonexpansive mappings
Organizers
Sohail Farhangi
,
Xiaoming John Zhang
Speaker
Time
Monday, May 18, 2026 3:30 PM - 4:30 PM
Venue
A3-3-301
Online
Zoom 204 323 0165
(BIMSA)
Abstract
In this study, a brief survey of the fixed point theory, methods and applications is discussed. The convergence behavior of the UO iterative scheme for approximating fixed points of generalized $\alpha$-Reich--Suzuki nonexpansive mappings in Banach spaces is presented. Weak and strong convergence theorems are established under appropriate conditions. The practical performance of the scheme is illustrated through numerical examples, demonstrating faster convergence compared to the $F^{\ast}$, Uddin et al., and Picard--S iterative methods. Polynomiographs for a sextic polynomial are generated to visualize the global convergence dynamics and the basins of attraction, highlighting the scheme's stability and wide attraction regions. Furthermore, the method is applied to solve a nonlinear fractional differential equation and to analyze an SVIR epidemic model with immigration across compartments. The results confirm that the UO iterative scheme is an efficient and reliable tool for solving nonlinear problems in applied mathematics, extending and generalizing existing findings in the literature.