STABILITY AND DATA DEPENDENCE OF FIXED POINTS IN METRIC SPACES RELATIONS
Priyanka ,Research Scholar,
Dr. Narendra Swami ,Research Guide,
Department of Mathematics, Shri JJT University, Jhunjhunu, Rajasthan, India
Abstract : In this paper, we investigate the stability and data dependence of fixed points for various classes of relations and operators in metric spaces. By employing generalized contractive conditions and comparison functions, we establish sufficient criteria for the existence and uniqueness of fixed points. Furthermore, we analyze how perturbations in the underlying mappings or relations affect the location of fixed points, providing explicit estimates that describe their continuous dependence on data. Several stability results, including Ulam–Hyers type stability, are derived to illustrate the robustness of fixed point solutions under small deviations. The obtained results extend and unify a number of well-known fixed point theorems in metric spaces and offer a useful framework for applications in nonlinear analysis and applied mathematics.
Keywords: Fixed point, metric space, stability, data dependence, contractive conditions, nonlinear analysis
