TITLE:
Modification of the Convergence of GG-PPA for Solving Generalized Equations
AUTHORS:
Asraful Alom, Zaidur Rahman, Bayezid Gazi, Imran Hossain
KEYWORDS:
Set-Valued Mappings, Metrically Regular Mappings, Semi-Local Convergence, Lipschitz Continuous, Fixed Point Lemma
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.1,
January
31,
2023
ABSTRACT: A modified Gauss-type Proximal Point Algorithm (modified GG-PPA) is presented in this paper for solving the generalized equations like 0 ∈ T(x), where T is a set-valued mapping acts between two different Banach spaces X and Y. By considering some necessary assumptions, we show the existence of any sequence generated by the modified GG-PPA and prove the semi-local and local convergence results by using metrically regular mapping. In addition, we give a numerical example to justify the result of semi-local convergence.