Paranormed Sequence Space of Non-absolute Type Founded Using Generalized Difference Matrix

Murat Candan1, Asuman Güneş1
1Department of Mathematics, Faculty of Arts and Sciences, Inonu University, Malatya, Turkey

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Başar F (2012) Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monographs, xi+405 pp., İstanbul ISB:978-1-60805-252-3

Maddox IJ (1968) Paranormed sequence spaces generated by infinite matrices. Proc Camb Philos Soc 64:335–340

Maddox IJ (1967) Spaces of strongly summable sequences. Quart J Math Oxf 18(2):345–355

Simons S (1965) The sequence spaces $$\ell (p_v)$$ ℓ ( p v ) and $$m(p_v)$$ m ( p v ) . Proc Lond Math Soc 15(3):422–436

Nakano H (1951) Modulared sequence spaces. Proc Jpn Acad 27(2):508–512

Ng PN, Lee PY (1978) Cesàro sequence spaces of non-absolute type. Comment Math Prace Mat 202:429–433

Altay B, Başar F (2002) On the paranormed Riesz sequence spaces of non-absolute type. Southeast Asian Bull Math 26:701–715

Altay B, Başar F, Mursaleen M (2006) On the Euler sequence spaces which include the spaces $$\ell _p$$ ℓ p and $$\ell _\infty $$ ℓ ∞ I. Inf Sci 176(10):1450–1462

Mursaleen M, Başar F, Altay B (2006) On the Euler sequence spaces which include the spaces $$\ell _p$$ ℓ p and $$\ell _\infty $$ ℓ ∞ II. Nonlinear Anal 65(3):707–717

Kara EE, Öztürk M, Başarır M (2010) Some topological and geometric properties of generalized Euler sequence spaces. Math Slovaca 60(3):385–398

Malkowsky E, Savaş E (2004) Matrix transformations between sequence spaces of generalized weighted means. Appl Math Comput 147:333–345

Altay B, Başar F (2007) Generalization of the sequence space $$\ell (p)$$ ℓ ( p ) derived by weighted mean. J Math Anal Appl 330:174–185

Aydın C, Başar F (2005) Some new sequence spaces which include the spaces $$\ell _p$$ ℓ p and $$\ell _\infty $$ ℓ ∞ . Demonstr Math 38(3):641–656

Aydın C, Başar F (2006) Some generalizations of the sequence spaces $$a^{r}_{p}$$ a p r . Iran J Sci Technol Trans A Sci 30(A2):175–190

Malkowsky M, Rakočević V, Źivković S (2002) Matrix transformations between the sequence space $$bv^{p}$$ b v p and certain $$BK$$ B K spaces. Bull Cl Sci Math Nat Sci Math 27:33–46

Başar F, Altay B (2003) On the space of sequences of $$p$$ p -bounded variation and related matrix mappings. Ukranian Math J 55:136–147

Altay B, Başar F (2006) Some paranormed sequence spaces of non-absolute type derived by weighted mean. J Math Anal Appl 319(2):494–508

Choudhary B, Mishra SK (1993) On Köthe-Toeplitz duals of certain sequence spaces and their matrix transformations. Indian J Pure Appl Math 24:291–301

Mursaleen M, Noman AK (2011) On some new sequence spaces of non-absolute type related to the spaces $$\ell _p$$ ℓ p and $$\ell _1$$ ℓ 1 I. Filomat 25(2):33–51

Kirişçi M, Başar F (2010) Some new sequence spaces derived by the domain of generalized difference matrix. Comput Math Appl 60(5):1299–1309

Candan M (2012) Domain of the double sequential band matrix in the classical sequence spaces. J Inequal Appl 281(1):1–15

Başar F, Kirişçi M (2011) Almost convergence and generalized difference matrix. Comput Math Appl 61(3):602–611

Candan M (2014) Almost convergence and double sequential band matrix. Acta Math Sci 34B(2):354–366

Candan M (2014) A new sequence space isomorphic to the space $$\ell (p)$$ ℓ ( p ) and compact operators. J Math Comput Sci 4(2):306–334

Candan M (2014) Domain of the double sequential band matrix in the spaces of convergent and null sequences. Adv Differ Edu 163(1):1–18

Candan M (2014) Some new sequence spaces derived from the spaces of bounded, convergent and null sequences. Int J Mod Math Sci 12(2):74–87

Kirişçi M (2013) On the spaces of Euler almost null and Euler almost convergent sequences. Commun Fac Sci Univ Ankara 2:85–100

Kirişçi M (2012) Almost convergence and generalized weighted mean I. AIP Conf Proc 1470:191–194

Kirişçi M (2014) Almost convergence and generalized weighted mean II. J Inequal Appl ID 93(1):1–13

Altay B, Başar F (2006) Some paranormed sequence spaces derived by generalized weighted mean. J Math Anal Appl 319:494–508

Polat H, Karakaya V, Şimşek N (2011) Difference sequence spaces derived by generalized weighted mean. Appl Math Lett 24(5):608–314

Başarır M (2010) On the generalized Riesz $$B$$ B -difference sequence spaces. Filomat 24(4):35–52

Altay B, Başar F (2008) On the fine spectrum of the generalized difference operator B(r, s) over the sequence c 0 and c. Int J Math Sci 18:3005–3013

Demiriz S, Çakan C Some topolojical and geometrical properties of a new difference sequence space, Abstr Appl Anal doi: 10.1155/2011/213878 , p 14

Başarır M, Öztürk M (2008) On the Riesz diference sequence space. Rend Circ Mat Palermo 57:377–389

Başarır M (1991) Paranormed Cesàro difference sequence space and related matrix transformation. Doğa Tr J Math 15:14–19

Et M, Işık M (2012) On pa-dual spaces of generalized difference sequence spaces. Appl Math Lett 25(10):1486–1489

Et M (2013) Generalized Cesàro difference sequence spaces of non-absolute type involving lacunary sequence spaces. Appl Math Comput 219(17):9372–9376

Başarır M, Kara EE (2013) On the mth order difference sequence space of generalized weighted mean and compact operator. Acta Math Sci 33B(3):1–18

Başarır M, Kara EE (2012) On the B-difference sequence space derived by generalized weighted mean and compact operators. J Math Anal Appl 391:67–81

Başarır M, Kayıkçı M (2009) On the generalized Bth Riesz difference sequence space and beta-property. J Inequal Appl ID 1:1–18

Başarır M, Kara EE (2011) On some difference sequence spaces of weighted means and compact operators. Ann Funct Anal 2(2):116–131

Başarır M, Kara EE (2011) On compact operators on the Riesz B m -difference sequence space. Iran J Sci Technol Trans 35A(4):279–285

Başarır M, Kara EE (2012) On compact operators on the Riesz B m -difference sequence space-II. Iran J Sci Technol Trans 36A(3):371–376

Başarır M, Öztürk M (2011) On some generalized B m - difference Riesz sequence spaces and uniform opial property. J Inequal Appl 1:1–17

Konca Ş, Başarır M (2013) Generalized difference sequence spaces associated with a multiplier sequence on a real n-normed space. J Inequal Appl 335:1–12

Konca Ş, Başarır M (2014) On some spaces of almost lacunary convergent sequences derived by Riesz mean and weighted almost lacunary statistical convergence in a real n-normedspace. J Inequal Appl 811:1–11

Kızmaz H (1981) On certain sequence spaces. Canad Math Bull 24(2):169–176

Altay B, Başar F (2007) The matrix domain and the fine spectrum of the difference operator $$\Delta $$ Δ on the sequence space $$\ell _p$$ ℓ p $$(0<p<1)$$ ( 0 < p < 1 ) . Commun Math Anal 2(2):1–11

Başar F, Altay B (2003) On the space of sequences of p-bounded variation and related matrix mappings. Ukrainian Math J 55(1):136–147

Çolak R, Et M, Malkowsky E (2004) Some topics of sequence spaces, lecture notes in mathematics, Fırat Univ Elâzığ, Turkey Fırat Univ Press, pp 1–63 ISBN: 975-394-038-6

Çolak R, Et M (1997) On some generalized difference sequence spaces and related matrix transformations. Hokkaido Math J 26(3):483–492

Malkowsky E, Parashar SD (1997) Matrix transformations in space of bounded and convergent difference sequence of order m. Analysis 17:87–97

Polat H, Başar F (2007) Some Euler spaces of difference sequences of order m. Acta Math Sci 27B(2):254–266

Altay B (2006) On the space of $$p$$ p -summable difference sequences of order $$m\,(1\le p < \infty )$$ m ( 1 ≤ p < ∞ ) . Stud Sci Math Hungar 43(4):387–402

Sheikh NA, Ganie AH (2012) A new paranormed sequence space and some matrix transformations. Acta Math Acad Paedago Nyregy 28:47–58

Ganie AH, Sheikh NA (2013) New type of paranormed sequence space of non-absolute type and a matrix transformation. Int J of Mod Math Sci 8(2):196–211

Grosse-Erdmann KG (1993) Matrix transformations between the sequence spaces of Maddox. J Math Anal Appl 180:223–238

Lascarides CG, Maddox IJ (1970) Matrix transformations between some classes of sequences. Proc Camb Philos Soc 68:99–104