THE SPACE L_q OF DOUBLE SEQUENCES

The spaces BS, BS(t), CSp, CSbp, CSr and BV of double sequences have recently been studied by Altay and Ba¸sar [J. Math. Anal. Appl. 309(1)(2005), 70–90]. In this work, following Altay and Ba¸sar [1], we introduce the Banach space Lq of double sequences corresponding to the well-known space &#8467;q of single sequences and examine some properties of the space Lq. Furthermore, we determine the &#946;(&#965;)-dual of the space and establish that the &#945;- and &#947;-duals of the space Lq coincide with the &#946;(&#965;)-dual; where 1 &#8804; q &#60; &#8734; and &#965; 2 {p, bp, r}.</p

The Fine Spectra of the Cesàro Operator C 1 over the Sequence Space bvp, (1 &#8804; p &#8734;)

The sequence space bvp consisting of all sequences (xk) such that (xk - xk-1) in the sequence space lp has recently been introduced by Basar and Altay [Ukrainian Math. J. 55(1)(2003), 136-147]; where 1 &#8804; p &#8804; &#8734;. In the present paper, the norm of the Ces&#224;ro operator C1 acting on the sequence space bvp has been found and the fine spectrum of the Ces&#224;ro operator C1 over the sequence space bvp has been determined, where 1 &#8804; p &#60; &#8734;.</p

Summability theory and its applications

The theory of summability has many uses throughout analysis and applied mathematics. Engineers and physicists working with Fourier series or analytic continuation will also find the concepts of summability theory valuable to their research. The concepts of summability have been extended to the sequences of fuzzy numbers and also to the theorems of ergodic theory. This e-book explains various aspects of summability and demonstrates applications in a coherent manner. The content can readily serve as a useful series of lecture notes on the subject. This e-book comprises of 8 chapters startin

A Study on Certain Kothe Spaces

3rd International Conference on Analysis and Applied Mathematics (ICAAM) -- SEP 07-10, 2016 -- Almaty, KAZAKHSTANWOS: 000439421100005Let A = (a(nk)) be a Kothe matrix. In this paper, we introduce the space lambda(bs)(A) and we emphasize on some topological properties of the spaces c(0)(A), lambda(bs)(A) and lambda(p)(A) together with some inclusion relations, where 1 <= p <= infinity.Inst Math & Math Modeling, Al Farabi Kazakh Natl Univ, L N Gumilyov Eurasian Natl Uni

On The Paranormed Spaces of Regularly Convergent Double Sequences

In Hardy (Proc Camb Philos 19:86-95, 1916), Hardy defined the normed spaces C-r and C-ro of all regularly convergent and regularly null double sequences and made convergence factor calculations (i.e. some beta-dual calculations). In this paper, we extend these spaces to the paranormed spaces and C-r(t)and C-ro(t). Also, we define the paranormed spaces C-tr(t) and C-tro(t) of all totally regularly convergent and totally regularly null double sequences. We examine some topological properties of these spaces and determine their alpha-, beta- and gamma-duals

On the Paranormed Space L(t) of Double Sequences

In this paper, we introduce the paranormed sequence space L(t) which is the generalization of the space L q of all absolutely q summable double sequences. We examine some topological properties of the space L(t) and determine its alpha-, beta -and gamma-duals. Finally, we characterize some classes of four-dimensional matrix transformations from the space L(t) into some spaces of double sequences

Almost convergence and generalized difference matrix

Let f denotes the space of almost convergent sequences introduced by Lorentz [G.G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80 (1948), 167-190] and (f) over cap also be the domain of the generalized difference matrix B(r, s) in the sequence space f. In this paper, the beta- and gamma-duals of the spaces f, fs and (f) over cap are determined. Furthermore, two basic results on the space f are proved and the classes ((f) over cap: mu) and (mu: (f) over cap) of infinite matrices are characterized, and the characterizations of some other classes are also given as an application of those main results, where mu is any given sequence space. (C) 2010 Elsevier Ltd. All rights reserved

Some new sequence spaces derived by the domain of generalized difference matrix

Let lambda denote any one of the classical spaces l(infinity), c, c(0) and l(p) of bounded, convergent, null and absolutely p-summable sequences, respectively, and (lambda) over cap. also be the domain of the generalized difference matrix B(r, s) in the sequence space lambda, where 1 are determined, and the Schauder bases for the spaces (c) over cap, (C-0) over cap and (l(p)) over cap are given, and some topological properties of the spaces (c(0)) over cap, (l(1)) over cap and (l(p)) over cap are examined. Finally, the classes ((lambda(1)) over cap, : lambda(2)) and ((lambda(1)) over cap : (lambda(2)) over cap) of infinite matrices are characterized, where lambda(1) is an element of {l(infinity), c, c(0), l(p), l(1)) and lambda(2) is an element of {l(infinity), c, c(0), l(1)). Published by Elsevier Lt

A SURVEY FOR PARANORMED SEQUENCE SPACES GENERATED BY INFINITE MATRICES

WOS: 000467698500001In the present paper, we summarize the recent literature concerning the domains of triangles in Maddox's sequence spaces l(infinity)(p), c(p), c(0)(p) and l(p), and related topics