On certain Euler difference sequence spaces of fractional order and related dual properties
-
2199
Downloads
-
3954
Views
Authors
Ugur Kadak
- Department of Mathematics, Bozok University, 66100 Yozgat, Turkey.
P. Baliarsingh
- Department of Mathematics, School of Applied Sciences, KIIT University, India.
Abstract
The purpose of this paper is to generalize the Euler sequences of nonabsolute type by introducing a generalized
Euler mean difference operator \(E^r(\Delta^{(\tilde{\alpha})})\) of order \(\alpha\). We investigate their topological structures as
well as some interesting results concerning the operator \(E^r(\Delta^{(\tilde{\alpha})})\) for a proper fraction \(\tilde{\alpha}\). Also we obtain
the \(\alpha\)-, \(\beta\)- and
\(\gamma\)-duals of these sets.
Share and Cite
ISRP Style
Ugur Kadak, P. Baliarsingh, On certain Euler difference sequence spaces of fractional order and related dual properties, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 6, 997--1004
AMA Style
Kadak Ugur, Baliarsingh P., On certain Euler difference sequence spaces of fractional order and related dual properties. J. Nonlinear Sci. Appl. (2015); 8(6):997--1004
Chicago/Turabian Style
Kadak, Ugur, Baliarsingh, P.. "On certain Euler difference sequence spaces of fractional order and related dual properties." Journal of Nonlinear Sciences and Applications, 8, no. 6 (2015): 997--1004
Keywords
- Euler sequence spaces of nonabsolute type
- linear operator
- matrix transformations
- \(\alpha\)-
- \(\beta\)- and \(\gamma\)-duals.
MSC
References
-
[1]
Z. U. Ahmad, M. Mursaleen, Köthe-Toeplitz duals of some new sequence spaces and their matrix maps, Publ. Inst. Math. (Beograd), 42 (1987), 57-61.
-
[2]
B. Altay, F. Başar , On some Euler sequence spaces of non-absolute type, Ukrainian Math. J., 57 (2005), 1-17.
-
[3]
B. Altay, F. Başar, M. Mursaleen , On the Euler sequence spaces which include the spaces \(\ell_p\) and \(\ell_\infty\) , I. Inform. Sci., 76 (2006), 1450-1462.
-
[4]
B. Altay, H. Polat , On some new Euler difference sequence spaces, Southeast Asian Bull. Math., 30 (2006), 209-220.
-
[5]
C. Aydın, F. Başar , Some new difference sequence spaces, Appl. Math. Comput., 157 (3) (2004), 677-693.
-
[6]
P. Baliarsingh, S. Dutta , A unifying approach to the difference operators and their applications, Bol. Soc. Paran. Mat., 33 (2015), 49-57.
-
[7]
P. Baliarsingh, S. Dutta, On the classes of fractional order difference sequence spaces and their matrix transformations , Appl. Math. Comput., 250 (2015), 665-674.
-
[8]
P. Baliarsingh, Some new difference sequence spaces of fractional order and their dual spaces, Appl. Math. Comput., 219 (2013), 9737-9742.
-
[9]
P. Baliarsingh, S. Dutta, On an explicit formula for inverse of triangular matrices, J. Egypt. Math. Soc., 23 (2015), 297-302.
-
[10]
F. Başar, Summability Theory and Its Applications, Bentham Science Publishers, Istanbul (2012)
-
[11]
Ç . Bektas, M. Et, R. Çolak, Generalized difference sequence spaces and their dual spaces, J. Math. Anal. Appl., 292 (2004), 423-432.
-
[12]
S. Dutta, P. Baliarsingh , On some Toeplitz matrices and their inversion, J. Egypt. Math. Soc., 22 (2014), 420-423.
-
[13]
S. Dutta, P. Baliarsingh, A note on paranormed difference sequence spaces of fractional order and their matrix transformations, J. Egypt. Math. Soc., 22 (2014), 249-253.
-
[14]
M. Et, M. Basarir , On some new generalized difference sequence spaces, Periodica Math. Hungar., 35 (1997), 169-175.
-
[15]
M. Et, R. Çolak, On some generalized difference sequence spaces , Soochow J. Math., 21 (1995), 377-386.
-
[16]
U. Kadak, Generalized lacunary statistical difference sequence spaces of fractional order, Internat. J. Math. Math. Sci., (2015), in press
-
[17]
H. Kızmaz , On Certain Sequence spaces, Canad. Math. Bull. , 24 (1981), 169-176.
-
[18]
E. Malkowsky, M. Mursaleen, S. Suantai , The dual spaces of sets of difference sequences of order m and matrix transformations , Acta Math. Sin. (English Series), 23 (2007), 521-532.
-
[19]
M. Mursaleen, Generalized spaces of difference sequences , J. Math. Anal. Appl., 203 (1996), 738-745.
-
[20]
M. Mursaleen, A. K. Noman, On some new difference sequence spaces of non-absolute type, Math. Comput. Modelling, 52 (2010), 603-617.
-
[21]
H. Polat, F. Başar , Some Euler spaces of difference sequences of order m , Acta Math. Sci. Ser. B., Engl. Ed., 27 (2007), 254-266.
-
[22]
M. Stieglitz, H. Tietz, Matrix transformationen von Folgenraumen Eine Ergebnisubersict, Math. Z., 154 (1977), 1-16.
-
[23]
B. C. Tripathy, Y. Altin, M. Et, Generalized difference sequence spaces defined by Orlicz functions, Math Slovaca, 58 (2008), 315-324.