【摘要】 对映射引入了η-部分松弛Lipschitz连续的概念,应用这个概念和辅助变分不等式的技巧,在自反Banach空间中研究了一类广义集值非线性混合似变分不等式,给出了这类变分不等式解的存在性证明及算法,并讨论了算法的收敛性.更多还原

【Abstract】 The concept of η-partially relaxed Lipschitz continuity for mappings is introduced. By applying the concept and the auxiliary variational inequality technique, we study a new class of generalized set-valued nonlinear mixed variational-like inequalities in reflexive Banach spaces. We also prove an existence theorem of solutions for the class of generalized set-valued nonlinear mixed variational-like inequalities and suggest an innovative iterative algorithm to compute the approximate solutions of the class of variational inequalities. The convergence criteria of the iterative algorithm is also given.更多还原