Approximating Fixed Points of The General Asymptotic Set Valued Mappings
Keywords:Asymptotically Non- Expansive Set-Valued Mappings, Demi-Closeness, Fixed Points, Iterative Schemes
The purpose of this paper is to introduce a new generalization of asymptotically non-expansive set-valued mapping and to discuss its demi-closeness principle. Then, under certain conditions, we prove that the sequence defined by yn+1 = tn z+ (1-tn )un , un in Gn( yn ) converges strongly to some fixed point in reflexive Banach spaces. As an application, existence theorem for an iterative differential equation as well as convergence theorems for a fixed point iterative method designed to approximate this solution is proved
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