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Existence of Solutions of New Generalized Mixed Vector Variational-Like Inequalities in Reflexive Banach Spaces

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Abstract

In this paper, we extend the concept of monotonicity for a vector set-valued map** to semimonotonicity for a vector set-valued map**. Then, we prove solvability results for a class of new generalized mixed vector variational-like inequalities by applying the Fan-KKM theorem and Nadler’s result. On the other hand, we introduce the concepts of complete semicontinuity and strong semicontinuity for vector multivalued map**s. Moreover, by using the Brouwer fixed point theorem, we prove the solvability for the class of generalized vector variational-like inequalities without monotonicity assumption. Using this result, we obtain a theorem and corollary that improve and extend some known results.

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Acknowledgements

Supported by The Royal Golden Jubilee Program under Grant PHD/0117/2549, Thailand.

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  1. Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand

    Somyot Plubtieng & Tipphawan Thammathiwat

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  1. Somyot Plubtieng
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  2. Tipphawan Thammathiwat
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Correspondence to Somyot Plubtieng.

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Plubtieng, S., Thammathiwat, T. Existence of Solutions of New Generalized Mixed Vector Variational-Like Inequalities in Reflexive Banach Spaces. J Optim Theory Appl 162, 589–604 (2014). https://doi.org/10.1007/s10957-013-0322-8

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  • DOI: https://doi.org/10.1007/s10957-013-0322-8

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