IMPROVED GRAOIENT METHOD FOR MONOTONE AND LIPSCHITZ CONTINUOUS MAPPINGS IN BANACH SPACES

doi:10.1016/S0252-9602(17)30006-1

Abstract

Abstract:

Let C be a nonempty closed convex subset of a 2-uniformly convex and uniformly smooth Banach space C and {A_n}_n∈N be a family of monotone and Lipschitz continuos mappings of C into E^*. In this article, we consider the improved gradient method by the hybrid method in mathematical programming[10] for solving the variational inequality problem for {A_n} and prove strong convergence theorems. And we get several results which improve the well-known results in a real 2-uniformly convex and uniformly smooth Banach space and a real Hilbert space.

Key words: Variational inequality problem, gradient method, monotone operators, 2-uniformly convex Banach space, hybrid method

Kazuhide NAKAJO. IMPROVED GRAOIENT METHOD FOR MONOTONE AND LIPSCHITZ CONTINUOUS MAPPINGS IN BANACH SPACES[J].Acta mathematica scientia,Series B, 2017, 37(2): 342-354.

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