$f$-CONSERVATIVE MATRIX SEQUENCES
Main Article Content
Abstract
The main purpose of this paper is to determine the necessary and sufficint conditions on the matrix sequence $\mathcal{A} = (A_p)$ in order that $\mathcal{A}$ contained in one of the classes $(f: f)$, $(f :f_s)$, $(f_s: f)$ and $(f_s: f_s)$, where $f$ and $f_s$ respectively denote the spares of all almost convergent real sequences and series. Our results are more general than those of Duran [3] and Solak [7]. Additionally, theorems of Steinhaus type concerning some subclasses of above matrix classes, are also given.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
References
S. Banach, Theorie des Operations Lineaires, (Warszawa-1932).
F. Basar, and I. Solak, Almost-coercive matrix sequences, Commun. Fae. Sci. Univ. Auk., Ser. Al, (to appear).
J. P. Duran, Infinite matrices and almost convergence, Math. Z., 128, (1972), 75-83.
J. P. King, Almost summable sequences, Proc. Amer. Math. Soc., 17, (1966), 1219-1225.
G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math., 80, (1948), 167- 190.
E. Öztürk, On strongly-regular dual summability methods, Conunun. Fae. Sci. Univ. Ank., Ser. Al , 32, (1983), 1-5.
I. Solak, f-conservative matrix transformations, (under communication).
M. Stieglitz, Eine verallgerneinerung des begriffs der fastkonvergenz, Math. Japon., 18, (1973), 53-70.