在实自反Banach空间中, 引入并研究一类$k$-次增生型变分包含问题, 证明了这类变分包含解的存在与唯一性, 并在去掉${\alpha }_n\to 0,{\beta }_n\to 0\left(n\to \mathrm{\infty }\right)$以及序列$\{x_n\}$和$\left\{{\partial }_{\eta }\phi \left(g\left(x_n\right)\right)\right\}$有界限制的条件下,建立了$k$-次增生型 变分包含和变分不等式解的具有混合误差的多步迭代序列的强收敛性定理, 给出了收敛率的估计式,从而改进和推广了前人的研究结果.

The purpose of this paper is to introduce and study a new class of variational inclusion problems with Lipschitz k-subaccretive type mappings in real reflexive Banach spaces. The existence and uniqueness of such solutions are proved and convergence of the multi-step iterative sequences with mixed errors of solutions for the variational inclusions and variational inequalities with k-subaccretive type mappings are also established under removing some re- strictions. General convergence rate estimates are given in our results, which improve and extend the existing research results.