Existence and iterative approximations of solutions for mixed quasi-variational-like inequalities in Banach spaces |
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| Authors: | Zeqing Liu Zhengsheng Chen Shin Min Kang Jeong Sheok Ume |
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| Institution: | 1. Department of Mathematics, Liaoning Normal University, P.O. Box 200, Dalian, Liaoning 116029, People’s Republic of China;2. Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Chinju 660-701, Republic of Korea;3. Department of Applied Mathematics, Changwon National University, Changwon 641-773, Republic of Korea |
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| Abstract: | In this paper, we introduce and investigate a new class of mixed quasi-variational-like inequalities in reflexive Banach spaces. By applying a minimax inequality due to Ding–Tan and a lemma due to Chang, we establish some existence and uniqueness results of solution for the mixed quasi-variational-like inequality. Next, by using a KKM theorem due to Fan and an auxiliary principle technique due to Cohen, we suggest two iterative algorithms and study the convergence criteria of iterative sequences generated by the iterative algorithms. Our results extend, improve and unify several known results in the literature. |
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| Keywords: | 47J20 49J40 |
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