GENERAL GAUSS-TYPE PROXIMAL POINT METHOD AND ITS CONVERGENCE ANALYSIS FOR SMOOTH GENERALIZED EQUATIONS

Let X and Y be Banach spaces and Ω be an open subset of X. In the present paper, a general Gauss-type Proximal Point Algorithm (GGPPA) is introduced for approximating the solution of a generalized equation 0∈f(x)+F(x), where f:X→ Y is a differentiable function on Ω and F:X⇉2^Y is a set valued mapping with closed graph. Semilocal and local convergences of the GGPPA are presented by considering a sequence of Lipschitz continuous functions gk:X→ Y such that gk (0)=0 around the origin with positive Lipschitz constants λk and the metric regularity condition of F. Finally, we give a numerical example to verify the convergence results of the GGPPA.