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    Convergence Analysis of General Version of Gauss-Type Proximal Point Method for Metrically Regular Mappings

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    Date
    2016-07
    Author
    Alom, Md. Asraful
    Rashid, Mohammed H.
    Dey, Kalyan K.
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    Abstract
    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.
    URI
    http://dx.doi.org/10.4236/am.2016.711110
    http://hdl.handle.net/123456789/872
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