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In this work, general convergence theorems for -iterations scheme in some classes of multi-valued mappings are given. These results are included in four pivots. For the first time are dealt with this kind of scheme for the general quasi multi-valued mappings to prove new results in approximating fixed point theory. Other results have been dealing with multi-valued mappings, such as, general like-contraction, nonexpansive, Lipschitz -strictly pseudo contraction, -strictly pseudo contraction and monotone. The modification of - iteration, which is called -iteration, have been studied to obtain results about weak convergence for -strictly pseudo- contractive multi-valued mappings and strong convergence for -Lipschitz pseudo-contractive multi-valued mappings, quasi-contractive multi-valued mappings and generalized nonexpansive multi-valued mappings. Some comparisons have been studied. Here, - iteration method can be used to solve delay differential equations and solve a system of two multi-valued -accretive mappings with retarded argument.

Iterative Fixed Points Theorems for Set-Valued Mappings: Study s-iteration scheme involving various types of multivalued mappings