渐近伪压缩半群公共不动点的强收敛结果（英文）

Strong convergence results on the common fixed points of asymptotically pseudocontractive semigroups

在实Banach空间中研究渐近伪压缩半群公共不动点的强收敛性问题,提出黏制迭代算法,并且证明了该公共不动点是一个变分不等式的唯一解.所得结果将文献[8]中的结果从Halpern迭代算法推广到了粘制迭代算法,将文献[9]中的结果从非扩张半群推广到了渐近伪压缩半群.

In order to study the strong convergence of asymptotically pseudocontractive semig- roups in a real Banach space, a viscosity iteration algorithm for approximating the common fixed point of asymptotically pseudocontractive semigroups is proposed, and it is proved that the common fixed point is also unique solution to a variational inequality. The results mainly extend the results of Ref.[8] from the Halpern iteration algorithm to viscosity iteration algo- rithm, and also extend the results of Ref.[9] from nonexpansive semigroups to asymptotically pseudocontractive semigroups.