Banach空间中完全广义混合隐似平衡问题的辅助原理和迭代算法(英文)

Auxiliary Principle and Iterative Algorithms for Completely Generalized Mixed Implicit Equilibrium-Like Problems in Banach Spaces

在Banach空间中利用双线性连续泛函F代替内积引进了新的一类完全广义混合隐似平衡问题,引进了F强单调的概念,提出了该平衡问题的广义辅助问题,证明了广义辅助问题的收敛定理,给出了新的算法和由此算法产生的迭代序列的收敛特征.

A new class of completely generalized mixed implicit equilibrium-like problems （CGMIELP） which do not contain inner product but replaced by a bilinear continuous function F is introduced in Banach space. Then, a concept called F-strongly monotonicity is defined. Next, a generalized auxiliary problem is suggested to study this class of equilibrium problem and the existence theorems of the solution of the generalized auxiliary problem is also proved. Finally, a novel and innovative iterative algorithm is given and the convergence criteria of iterative sequences generated by the algorithm is shown.