On Stability of Iterative Sequences with Error

Abstract

Iterative methods were employed to obtain solutions of linear and non-linear systems of equations, solutions of differential equations, and roots of equations. In this paper, it was proved that s-iteration with error and Picard–Mann iteration with error converge strongly to the unique fixed point of Lipschitzian strongly pseudo-contractive mapping. This convergence was almost F-stable and F-stable. Applications of these results have been given to the operator equations Fx=f and x+Fx=f, where F is a strongly accretive and accretive mappings of X into itself.

A Computational Approach to Solve a System of Transcendental Equations with Multi-Functions and Multi-Variables

“…For non-zero SoTEs, a range of value of a parameter or variable can be simulated. The solution may require an iterative process [20] with a range of values of the parameters and variables of the system. The parameters or variables chosen depend on the aspect of the system under investigation.…”

Some Results on Normalized Duality Mappings and Approximating Fixed Points in Convex Real Modular Spaces

“…Theorem 9: Let be a uniformly smooth space, ∅ ≠ ⊂ , be a convex and bounded subset of and : → 2 be a strongly pseudo contraction mapping. Assume that { } , { } be two sequences in (0,1)such that (i) Later, in this direction, it is possible to study the results in (13)(14)(15) in modular spaces and compression all results.…”

A-contraction mappings of integral type in n-normed spaces

“…If for all ∈ B, B is -bounded then B is called a bounded set. Definition (1.9) [11,17]: Let (H,‖. , … , .…”

“…Next, some research works have been executed to extending contractive conditions of integral type for distinct contractive mappings satisfying appropriate properties, see, Rhoades [20], Tarsh [17], Lazam and Abed [12]. Inspired and motivated by these consequent works, similarly, some results are presented in complete -normed spaces which in turn generalize fixed point results.…”