Picard-Mann hybrid iteration process for approximating f ixed points of contraction mappings - Ekuma-Okereke∗†, E.; Koko‡, O.D.; Okpako§, C.V.; Ogbodu¶, J.O. (International Journal of Mathematical Analysis and Modelling, 2025)
Fixed point theory has been very remarkable since its introduction and it has evolved greatly by hosting a great number of researches of many sort. Several mathematical problems have been solved by the fixed point method by transforming any of such problem into an operation of the fixed point equation. Fixed point theory is primarily concerned with finding conditions on the ambient space and also on the properties of the mapping so as to find results on the existence and uniqueness of fixed points. In this paper, we construct and introduce a new four-step iteration process called the Picard-Mann hybrid iteration process. We prove that this new iteration process converges to the unique fixed point of contraction mappings. We then show that it converges faster than several other iteration processes mentioned in the body of literature with numerical examples visualized in graphs and tables to substantiate our theoretical assertions. Data dependence and numerical stability is further established. Our results obtained in uniformly convex Banach space generalizes and extend other results cited in the literature.