We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined, embodying the equational properties of iteration theories. We prove a general completeness theorem for iteration operators, relying on a new, purely syntactic characterisation of the free iteration theory. We then show how iteration operators arise in axiomatic domain theory. One re...

This study presents a new one-parameter family of the well-known fixed point iteration method for solving nonlinear equations numerically. The proposed is derived by implementing approximation through straight line. presence an arbitrary parameter in improves convergence characteristic simple as it has wider domain convergence. Furthermore, we propose many two-step predictor–corrector iterative...

The purpose of this paper is to study the strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of asymptotically pseudocontractive mappings and nonexpansive mappings in normed linear spaces. The results in this paper improve and extend the corresponding results of Xu and Ori, Zhou and Chang, Sun, Yang and Yu in some aspects.