Author(s)

Md. Asraful Alom^1,2, Mohammed Harunor Rashid¹, Kalyan Kumer Dey¹

¹Department of Mathematics, University of Rajshahi, Rajshahi, Bangladesh.
²Department of Mathematics, Faculty of Civil Engineering, Khulna University of Engineering & Technology, Khulna, Bangladesh.

We introduce and study in the present paper the general version of Gauss-type proximal point algorithm (in short GG-PPA) for solving the inclusion , where T is a set-valued mapping which is not necessarily monotone acting from a Banach space X to a subset of a Banach space Y with locally closed graph. The convergence of the GG-PPA is present here by choosing a sequence of functions with , which is Lipschitz continuous in a neighbourhood O of the origin and when T is metrically regular. More precisely, semi-local and local convergence of GG-PPA are analyzed. Moreover, we present a numerical example to validate the convergence result of GG-PPA.

Set-Valued Mappings, Metrically Regular Mappings, Lipschitz-Like Mapping, Local and Semi-Local Convergence

Alom, M. , Rashid, M. and Dey, K. (2016) Convergence Analysis of General Version of Gauss-Type Proximal Point Method for Metrically Regular Mappings. Applied Mathematics, 7, 1248-1259. doi: 10.4236/am.2016.711110.