Viscosity like implicit methods for zeros of monotone operators in Banach spaces

Document Type : Original Article

Authors

John T Mendy ¹

Rahul Shukla ²

¹ University of the Gambia, Brikama Campus, Gambia

² Department of Mathematics & Applied Mathematics, University of Johannesburg, Kingsway Campus, Auckland Park 2006, South Africa

10.22034/kjm.2021.247019.1991

Abstract

In this paper, we present some implicit methods to approximate the zeros of monotone operators in the setting of Banach spaces. The methods considered herein converge strongly to the desired solutions under certain assumptions. As applications, we employ our methods to obtain solutions of convex minimization problems and Fredholm integral equations. Finally, we show the effectiveness and efficiency of the algorithm considered herein.

Keywords

Viscosity approximation method

Lipschitz mapping

Banach space

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