zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Matrix transformations on some sequence spaces related to strong Cesàro summability and boundedness. (English) Zbl 1171.40002
Recently {\it C. Adydin} and {\it F. Başar} [Appl. Math. Comput. 157, No. 3, 677--693 (2004; Zbl 1072.46007)] studied the matrix domain of a triangular matrix in the sets of sequences that are (i) summable to zero, (ii) summable and (iii) bounded by the Cesàro method of order one. {\it I. J. Maddox} [J. Lond. Math. Soc. 43, 285-290 (1968; Zbl 0155.38802)] introduced and studied the above-mentioned class of sequences by the strong Cesàro method of order 1 with index $p$, $p\geq 1$. Here the authors discuss the class of sequences studied by C. Adydin and F. Basar for the strong Cesàro method of order 1 with index $p$, $p\geq 1$. They also determine the $\beta$-duals of the spaces studied and characterize matrix transformations on them into the sets of bounded, convergent and null sequences.

40C05Matrix methods in summability
40H05Functional analytic methods in summability
Full Text: DOI
[1] Altay, B.: On the space of p-summable difference sequences of order m,(1&les;$p<\infty $), Stud. sci. Math. hungar. 43, No. 4, 387-402 (2006) · Zbl 1121.46005
[2] Altay, B.; Başar, F.: On the paranormed Riesz sequence spaces of non-absolute type, Southeast asian bull. Math. 26, No. 5, 701-715 (2002) · Zbl 1058.46002
[3] Altay, B.; Başar, F.: Some Euler sequence spaces of non-absolute type, Ukrainian math. J. 57, No. 1, 1-17 (2005) · Zbl 1096.46011 · doi:10.1007/s11253-005-0168-9
[4] Altay, B.; Başar, F.; Mursaleen, M.: On the Euler sequence spaces which include the spaces $\ell p$ and $\ell \infty $ I, Inform. sci. 176, 1450-1464 (2006) · Zbl 1101.46015 · doi:10.1016/j.ins.2005.05.008
[5] Aydın, C.; Başar, F.: On the new sequence spaces which include the spaces c0 and c, Hokkaido math. J. 33, No. 2, 383-398 (2004) · Zbl 1085.46002
[6] Aydın, C.; Başar, F.: Some new difference sequence spaces, Appl. math. Comput. 157, No. 3, 677-693 (2004) · Zbl 1072.46007 · doi:10.1016/j.amc.2003.08.055
[7] Başar, F.; Altay, B.: On the space of sequences of p-bounded variation and related matrix mappings, Ukrainian math. J. 55, No. 1, 136-147 (2003) · Zbl 1040.46022 · doi:10.1023/A:1025080820961
[8] Başar, F.; Malkowsky, E.; Altay, B.: Matrix transformations on the matrix domains of triangles in the spaces of strongly C1-summable and bounded sequences, Publ. math. 73, No. 1 -- 2, 193-213 (2008) · Zbl 1164.46003
[9] &ccedil, R.; Olak; Et, M.: On some generalized difference sequence spaces and related matrix transformations, Hokkaido math. J. 26, No. 3, 483-492 (1997) · Zbl 0888.40002
[10] &ccedil, R.; Olak; M.; ; Malkowsky, E.: Some topics of sequence spaces, Lecture notes in mathematics, fırat univ. Elâzı&gbreve;, Turkey, 2004 (2004)
[11] Et, M.: On some difference sequence spaces, Turkish J. Math. 17, 18-24 (1993) · Zbl 0826.40001
[12] M.; ; Başarır, M.: On some new generalized difference sequence spaces, Period. math. Hung. 35, No. 3, 169-175 (1997) · Zbl 0922.40003 · doi:10.1023/A:1004597132128
[13] M.; ; &ccedil, R.; Olak: On some generalized difference sequence spaces, Soochow J. Math. 21, No. 4, 377-386 (1995)
[14] Jarrah, A. M.; Malkowsky, E.: Ordinary, absolute and strong summability and matrix transformations, Filomat 17, 59-78 (2003) · Zbl 1274.40001
[15] Maddox, I. J.: On kuttner’s theorem, J. London math. Soc. 43, 285-290 (1968) · Zbl 0155.38802 · doi:10.1112/jlms/s1-43.1.285
[16] Malkowsky, E.; Mursaleen; Suantai, S.: The dual spaces of sets of difference sequences of order m and matrix transformations, Acta math. Sinica eng. Ser. 23, No. 3, 521-532 (2007) · Zbl 1123.46007 · doi:10.1007/s10114-005-0719-x
[17] Malkowsky, E.; Parashar, S. D.: Matrix transformations in space of bounded and convergent difference sequence of order m, Analysis 17, 87-97 (1997) · Zbl 0872.40002
[18] Malkowsky, E.; Rakočević, V.: An introduction into the theory of sequence spaces and measure of noncompactness, Zb. rad. Beogr. 9, No. 17, 143-274 (2000) · Zbl 0996.46006
[19] Malkowsky, E.; Savaş, E.: Matrix transformations between sequence spaces of generalized weighted means, Appl. math. Comput. 147, 333-345 (2004) · Zbl 1036.46001 · doi:10.1016/S0096-3003(02)00670-7
[20] Mursaleen, M.: Generalized spaces of difference sequences, J. math. Anal. appl. 203, No. 3, 738-745 (1996) · Zbl 0873.46014 · doi:10.1006/jmaa.1996.0409
[21] Mursaleen, M.; Başar, F.; Altay, B.: On the Euler sequence spaces which include the spaces $\ell p$ and $\ell \infty $ II, Nonlinear anal. 65, 707-717 (2006) · Zbl 1108.46019 · doi:10.1016/j.na.2005.09.038
[22] Ng, P. -N.; Lee, P. -Y.: Cesàro sequence spaces of non-absolute type, Comm. math. Prac. mat. 20, No. 2, 429-433 (1978) · Zbl 0408.46012
[23] Polat, H.; Başar, F.: Some Euler spaces of difference sequences of order m, Acta math. Sci. 27B, No. 2, 254-266 (2007) · Zbl 1246.46007
[24] &scedil, M.; Engönül; Başar, F.: Some new Cesàro sequence spaces of non-absolute type which include the spaces c0 and c, Soochow J. Math. 31, No. 1, 107-119 (2005)
[25] Wang, C. -S.: On nörlund sequence spaces, Tamkang J. Math. 9, 269-279 (1978)
[26] A. Wilansky, Summability through Functional Analysis, vol. 85, North-Holland Mathematics Studies, Amsterdam -- New York -- Oxford, 1984. · Zbl 0531.40008