To Define the Hybrid Generalized Multi-Valued Contraction Mapping |

ABSTRACT:

It is the object in the present research to survey,systematize, and extend a number of recent results concerning the existence offixed points of noncompact mappings of a subset C of a Hilbert space H into H.The purpose of this research is to define the hybrid generalized multi-valuedcontraction mapping which is more general than various mappings in literatureand to give some properties of this mapping. We also establish the common fixedpoint theorem. been largely motivated and dominated by questions from nonlinearproblems in practice, such as problems of geometric group theory, and others.However, so far, we have seen not many results for the approximation iterationof multi-valued non-expansive mappings in terms of Hausdorff metrics for fixedpoints in the existing literature. The purpose of this research is to extendthe iteration scheme of multi-valued non-expansive mappings from a Banach spaceto a hyperbolic space by proving Δ-convergence theorems for two multi-valuednonexpansive mappings in terms of mixed type iteration processes to approximatea common fixed point of two multi-valued non-expansive mappings in hyperbolicspaces.