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Convergence Analysis of Extended Hummel–Seebeck-Type Method for Solving Variational Inclusions

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Abstract

In this paper, we introduce and study an extended Hummel–Seebeck-type method for solving the variational inclusions 0 ∈ f(x) + F(x), where f: Ω ⊆ X → Y is a Fréchet differentiable function in an open subset Ω of X and F is a set-valued mapping acting between Banach space X and the subsets of Y with closed graph. We prove the existence of the sequence {x k } generated by this method and analyze its semilocal and local convergence.

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Acknowledgments

The author thanks the referees for their valuable comments and constructive suggestions which improved the presentation of this manuscript.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Rajshahi, Rajshahi, 6205, Bangladesh

    Mohammed Harunor Rashid

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  1. Mohammed Harunor Rashid
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Correspondence to Mohammed Harunor Rashid.

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Rashid, M.H. Convergence Analysis of Extended Hummel–Seebeck-Type Method for Solving Variational Inclusions. Vietnam J. Math. 44, 709–726 (2016). https://doi.org/10.1007/s10013-015-0179-2

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  • DOI: https://doi.org/10.1007/s10013-015-0179-2

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