Stability Analysis of Modified General Version of Gauss-type Proximal Point Method for Solving Generalized Equations Using Metrically Regular Mapping
Md. Asraful Alom *
Department of Mathematics, Khulna University of Engineering and Technology, Khulna-9203, Bangladesh.
Md. Zaidur Rahman
Department of Mathematics, Khulna University of Engineering and Technology, Khulna-9203, Bangladesh.
*Author to whom correspondence should be addressed.
Abstract
A modified general version of Gauss-type proximal point algorithm (GGPPA) is presented in this article for solving the parameterized generalized equation y ∈ F(x), where y is a parameter and a set-valued mapping F: X ⇉ 2Y is acting between two different Banach spaces X and Y. We demonstrate the existence of any sequence produced by the modified GGPPA by taking certain presumptions into account, and we use metrically regular mapping to demonstrate the uniformity of semi-local and local convergence findings. Finally, we present a numerical experiment to verify the uniformity of semi-local convergence result.
Keywords: Set-valued mapping, metrically regular mapping, semi-local convergence, uniform convergence, lipschitz continuity, fixed point lemma