Jong Kyu Kim, Anu K. Khanna, Tirth Ram, On $\eta$-generalized operator variational-like inequalities, Vol. 2018 (2018), Article ID 14, pp. 1-11

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DOI: 10.23952/cot.2018.14

Received April 17, 2018; Accepted May 7, 2018; Published June 4, 2018

Abstract. In this paper, we introduce and study a class of $\eta$ -generalized operator variational-like inequalities (for short, $\eta$ -GOVLI) and $\eta$ -generalized strong operator variational-like inequalities (for short, $\eta$ -GSOVLI) in Hausdorff topological vector spaces. An equivalence result concerned with these two classes of $\eta$ -generalized operator variational-like inequalities is proved under suitable conditions. Some new existence results for $\eta$ -generalized operator variational-like inequalities and $\eta$ -generalized strong operator variational-like inequalities are proved by using the Fan KKM theorem.

How to Cite this Article:
Jong Kyu Kim, Anu K. Khanna, Tirth Ram, On $\eta$ -generalized operator variational-like inequalities, Communications in Optimization Theory, Vol. 2018 (2018), Article ID 14, pp. 1-11.