Analyzing the Convergence of the Adapted General Gauss-type Proximal Point Approach for Smooth Generalized Equations

This work analyzed the adapted general Gauss-type proximal point approach for solving smooth generalized equations like , where is a set-valued mapping with closed graph and is a single-valued mapping acting between two general Banach spaces and . To confirm the existence and convergence of any sequence produced by this technique under appropriate assumptions, we develop the convergence criteria of this approach by utilizing metrically regular mapping and gathered both semi-local as well as local convergence results. Lastly, we plot a numerical example to compare the semi-local convergence result of this technique.