Convergence of fixed point iterative algorithm-CUIAN in various spaces

This paper introduces a new four-step fixed point iterative process called CUIAN-iteration which is an extension of CUIA-iteration. The CUIA-iteration was used to determine the FP (fixed point) of quasi-contractive operators and the same was utilized to show a strong convergence result for quasi contractive maps in the environment of Banach spaces. Here, we define a four-step CUIAN-iteration algorithm which converges with a rate better than some existing iteration procedures for self and non-self maps in the ambient spaces like Banach and Hilbert spaces. A theorem on strong convergence is established and one example is also proved in support of the theorem defined for quasi-contractive map satisfying Zamfirescu’s condition.