An Analytical Study of the Convergence and Stability of the New Four-Step Iterative Schemes

Abstract

Based on the needs of the scientific community, researchers tended to find new iterative schemes or develop previous iterative schemes that would help researchers reach the fixed point with fewer steps and with stability, will be define in this paper the multi_implicit four-step iterative (MIFSI) which is development to four-step implicit fixed point iterative, to develop the aforementioned iterative scheme, we will use a finite set of projective functions ,nonexpansive function and finite set from a new functions called generalized quasi like contractive which is an amalgamation of quasi contractive function and contractive like function , by the last function and a set of sequential organized steps, we will be able to prove the existence of the fixed point(f-point) of the MIFSI and four-step iterative(FSI), furthermore, we shall show that MIFSI faster than FSI. From another hand we state and prove the stability for the new iterative .