New fixed point iteration and its rate of convergence

Abstract

In the present paper, we introduce a new three-step fixed point iteration called SNIA-iteration (Naveen et al. iteration) which converges faster than the original iteration. It is possible by introducing a contraction operator on the existing iteration algorithm where the coefficients of the new iterative process are chosen in $(\frac{1}{2},1)$ instead of [0, 1]. The strong convergence result for the SNIA-iteration method is also proved by showing the convergence of this iteration method towards its fixed point. Further, the coefficients involved in SNIA-iteration have been interchanged, and then the result is compared with the original iteration. It is found that the new result is better than the previous one in the sense of its rate of convergence for contraction mappings.

Keywords:

• Contractive mapping
• convex metric space
• fixed point
• rate of convergence
• convexity structure

2000 AMS classifications:

• 47H10
• 54H25
• 46L07

Disclosure statement

No potential conflict of interest was reported by the authors.