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Spingarn, J.E. (1981/82) Submonotone Mappings and the Proximal Point Algorithm. Numerical Functional Analysis and Optimization, 4, 123-150.
https://doi.org/10.1080/01630568208816109

has been cited by the following article:

• 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.