A simultaneous iterative method for split equality problems of two finitefamilies of strictly pseudononspreading mappings without prior knowledge ofoperator norms

摘要

In this article, we first introduce the concept of T-mapping of a finitefamily of strictly pseudononspreading mapping , and we show that the fixed point set of theT-mapping is the set of common fixed points of and T is a quasi-nonexpansive mapping.Based on the concept of a T-mapping, we propose a simultaneousiterative algorithm to solve the split equality problem with a way of selectingthe stepsizes which does not need any prior information about the operatornorms. The sequences generated by the algorithm weakly converge to a solution ofthe split equality problem of two finite families of strictly pseudononspreadingmappings. Furthermore, we apply our iterative algorithms to some convex andnonlinear problems. MSC: 47H09, 47H05, 47H06, 47J25.