A Two-step Fixed Point Iteration: Stability and Data Dependence Analysis
Vivek Kumar
Department of Mathematics, KLP College, Rewari-123401, Haryana, India.
Poonam Gupta
Department of Mathematics, I.B. (PG) College, Panipat, India.
Kapil Kumar *
Department of Mathematics, All India Jat Heroes Memorial College, Rohtak-124001, Haryana, India.
*Author to whom correspondence should be addressed.
Abstract
Fixed point iterative methods play an important role in various branches of mathematics and their applications including optimization theory, nonlinear equations, numerical analysis, differential equations, and computational sciences. The convergence behaviour of these iterative schemes is significantly influenced by variations in the data and associated parameters. This study investigates the strong convergence, stability and data dependence of a two-step fixed point iteration under suitable contractive conditions in hyperbolic spaces. The variations of the fixed point to data dependence are analysed using the established error bounds. A numerical example supported by graphical and tabular representations illustrates the effect of data dependence on the convergence behaviour. Moreover, this study provides a practical use of an iterative scheme to find the solution of an integral equation.
Keywords: Strong convergence, boundary value problem, integral equation