The Study On The Convergence Of Generalized Nonexpansive Semigroups And Generalized Pseudocontractive Semigroups

The aim of this paper is to study the strong and weak convergence for the modified Ishikawa type iterative sequences of totally asymptotically strict pseudo-contractive semigroups, and to give the strong convergence for the generalized f-projection itera-tive algorithm of totally quasi-G-asymptotically nonexpansive semigroups.The first result introduce a new modified Ishikawa type iteration algorithm for common fixed point of total asymptotically strict pseudo-contractive semigroups in a real Banach space. The iteration sequences{xn} defined as follows: and prove strong convergence of it under reduction of some conditions.By using the principal of demiclosedness, the second result give the weak conver-gence for the sequence{xn} in a reflexive Banach space satisfying the Opial condition.The third result introduce a new generalized f-projection iterative sequences for the totally quasi-G-asymptotically nonexpansive semigroups in the uniformly convex and uniformly smooth Banach space, the sequence{xn} defined by: where, ξn=μnsupp€F(J)T(G(p, Jxn))+δn,{αn} C (0,1). we prove that{xn} converges strongly to пfF(J)x1.The results in the present paper extend some resent results of other authors.In the first chapter, we introduce some related research background, some relevant knowledge, some basic concepts and notations.In the second chapter, we study the strong convergence for the modified Ishikawa type iterative sequences of totally asymptotically strict pseudo-contractive semigroups.In the third chapter, we study the weak convergence for the modified Ishikawa type iterative sequences of totally asymptotically strict pseudo-contractive semigroups.In the fourth chapter, we study the strong convergence for the generalized f-projection iterative algorithm of totally quasi-G-asymptotically nonexpansive semi-groups.