scholarly journals A New Outlook for Almost Convergent Sequence Spaces

2018 ◽  
pp. 34-46 ◽  
Author(s):  
Murat CANDAN
2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Orhan Tug

Das and Patel (1989) introduced two new sequence spaces which are called lacunary almost convergent and lacunary strongly almost convergent sequence spaces. Móricz and Rhoades (1988) defined and studied almost P-convergent double sequences spaces. Savaş and Patterson (2005) introduce the almost lacunary strong P-convergent double sequence spaces by using Orlicz functions and examined some properties of these sequences spaces. In this paper, some almost lacunary double sequences spaces are given by using 2-normed spaces.


Author(s):  
Mustafa Cemil Bişgin

AbstractIn this work, we construct the sequence spaces f(Q(r, s, t, u)), f0(Q(r, s, t, u)) and fs(Q(r, s, t, u)), where Q(r, s, t, u) is quadruple band matrix which generalizes the matrices Δ3, B(r, s, t), Δ2, B(r, s) and Δ, where Δ3, B(r, s, t), Δ2, B(r, s) and Δ are called third order difference, triple band, second order difference, double band and difference matrix, respectively. Also, we prove that these spaces are BK-spaces and are linearly isomorphic to the sequence spaces f, f0 and fs, respectively. Moreover, we give the Schauder basis and β, γ-duals of those spaces. Lastly, we characterize some matrix classes related to those spaces.


2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Ali Karaisa ◽  
Ümıt Karabıyık

By using , we introduce the sequence spaces , , and of normed space and -space and prove that , and are linearly isomorphic to the sequence spaces , , and , respectively. Further, we give some inclusion relations concerning the spaces , , and the nonexistence of Schauder basis of the spaces and is shown. Finally, we determine the - and -duals of the spaces and . Furthermore, the characterization of certain matrix classes on new almost convergent sequence and series spaces has exhaustively been examined.


2006 ◽  
Vol 02 (02) ◽  
pp. 115-121
Author(s):  
EKREM SAVAS

In this paper we define some almost convergent sequence spaces of fuzzy numbers by using the A-transforms and we also examine topological properties and some inclusion relations for these new sequence spaces.


2004 ◽  
Vol 35 (4) ◽  
pp. 313-320 ◽  
Author(s):  
Vatan Karakaya

In this paper we introduce $theta_sigma$ conservative and $theta_sigma$-regular matrices and also give matrices transformation from almost convergent sequence spaces into lacunary invariant convergent sequence spaces.


Author(s):  
Vakeel A. Khan ◽  
Umme Tuba ◽  
SK. Ashadul Rahama ◽  
Ayaz Ahmad

In 1990, Diamond [16] primarily established the base of fuzzy star–shaped sets, an extension of fuzzy sets and numerous of its properties. In this paper, we aim to generalize the convergence induced by an ideal defined on natural numbers ℕ , introduce new sequence spaces of fuzzy star–shaped numbers in ℝ n and examine various algebraic and topological properties of the new corresponding spaces as well. In support of our results, we provide several examples of these new resulting sequences.


2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Kuddusi Kayaduman ◽  
Mehmet Şengönül

We have discussed some important problems about the spacesV~σandV~0σof Cesàro sigma convergent and Cesàro null sequence.


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