Convergence of Tseng-type self-adaptive algorithms for variational inequalities and fixed point problems

 Yao, Yonghong, Shahzad, Naseer and Yao, Jen-Chih

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In this paper, we present a Tseng-type self-adaptive algorithm for solving a variational inequality and a fixed point problem involving pseudomonotone and pseudocontractive operators in Hilbert spaces. A weak convergent result for such algorithm is proved under a weaker assumption than sequentially weakly continuous imposed on the pseudomonotone operator. Some corollaries are also included.

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 Shahzad, Naseer,  Yao, Yonghong, Yao, Jen-Chih