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2018-01-05 Nonlinear Seminar

Jian Meng (Tianjin University of Technology, China)
On some binomial difference sequence spaces

The matrix domains of Cesàro mean, Riesz mean $$ R_p $$, Nörlund mean $$ N_q $$ and Euler mean of order r in the sequence spaces $$ l_p $$, $$ l_\infty $$, c and $$ c_0 $$ have been studied by some authors. The Binomial mean is one of the most important methods in the summability theory, but the matrix domain of binomial mean has not been studied, until now. The aim of this talk is to introduce the binomial difference sequence spaces. We prove some basic properties of these spaces and some inclusion relations. Moreover, we obtain the Schauder bases of some of these spaces and compute the α-, β- and γ-duals of these sequence spaces.