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

详细信息    查看全文

• 作者：Murat Candan ; Asuman Güne?
• 关键词：Paranormed sequence space ; Alpha ; beta ; and gamma ; duals ; Matrix mappings ; 46A45 ; 40C05
• 刊名：Proceedings of the National Academy of Sciences, India Section A: Physical Sciences
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：85
• 期：2
• 页码：269-276
• 全文大小：441 KB
• 参考文献：1.Ba?ar F (2012) Summability Theory and Its Applications, Bentham Science Publishers, e-books, Monographs, xi+405 pp., ?stanbul ISB:978-1-60805-252-3
  2.Maddox IJ (1968) Paranormed sequence spaces generated by infinite matrices. Proc Camb Philos Soc 64:335-40View Article ADS MathSciNet
  3.Maddox IJ (1967) Spaces of strongly summable sequences. Quart J Math Oxf 18(2):345-55View Article ADS MATH MathSciNet
  4.Simons S (1965) The sequence spaces \(\ell (p_v)\) and \(m(p_v)\) . Proc Lond Math Soc 15(3):422-36View Article MATH MathSciNet
  5.Nakano H (1951) Modulared sequence spaces. Proc Jpn Acad 27(2):508-12View Article MATH
  6.Ng PN, Lee PY (1978) Cesàro sequence spaces of non-absolute type. Comment Math Prace Mat 202:429-33MathSciNet
  7.Altay B, Ba?ar F (2002) On the paranormed Riesz sequence spaces of non-absolute type. Southeast Asian Bull Math 26:701-15
  8.Altay B, Ba?ar F, Mursaleen M (2006) On the Euler sequence spaces which include the spaces \(\ell _p\) and \(\ell _\infty \) I. Inf Sci 176(10):1450-462View Article MATH
  9.Mursaleen M, Ba?ar F, Altay B (2006) On the Euler sequence spaces which include the spaces \(\ell _p\) and \(\ell _\infty \) II. Nonlinear Anal 65(3):707-17View Article MATH MathSciNet
  10.Kara EE, ?ztürk M, Ba?ar?r M (2010) Some topological and geometric properties of generalized Euler sequence spaces. Math Slovaca 60(3):385-98View Article MATH MathSciNet
  11.Malkowsky E, Sava? E (2004) Matrix transformations between sequence spaces of generalized weighted means. Appl Math Comput 147:333-45View Article MATH MathSciNet
  12.Altay B, Ba?ar F (2007) Generalization of the sequence space \(\ell (p)\) derived by weighted mean. J Math Anal Appl 330:174-85View Article MATH MathSciNet
  13.Ayd?n C, Ba?ar F (2005) Some new sequence spaces which include the spaces \(\ell _p\) and \(\ell _\infty \) . Demonstr Math 38(3):641-56MATH
  14.Ayd?n C, Ba?ar F (2006) Some generalizations of the sequence spaces \(a^{r}_{p}\) . Iran J Sci Technol Trans A Sci 30(A2):175-90MathSciNet
  15.Malkowsky M, Rako?evi? V, ?ivkovi? S (2002) Matrix transformations between the sequence space \(bv^{p}\) and certain \(BK\) spaces. Bull Cl Sci Math Nat Sci Math 27:33-6View Article
  16.Ba?ar F, Altay B (2003) On the space of sequences of \(p\) -bounded variation and related matrix mappings. Ukranian Math J 55:136-47View Article
  17.Altay B, Ba?ar F (2006) Some paranormed sequence spaces of non-absolute type derived by weighted mean. J Math Anal Appl 319(2):494-08View Article MATH MathSciNet
  18.Choudhary B, Mishra SK (1993) On K?the-Toeplitz duals of certain sequence spaces and their matrix transformations. Indian J Pure Appl Math 24:291-01MATH MathSciNet
  19.Mursaleen M, Noman AK (2011) On some new sequence spaces of non-absolute type related to the spaces \(\ell _p\) and \(\ell _1\) I. Filomat 25(2):33-1View Article MATH MathSciNet
  20.Kiri??i M, Ba?ar F (2010) Some new sequence spaces derived by the domain of generalized difference matrix. Comput Math Appl 60(5):1299-309View Article MATH MathSciNet
  21.Candan M (2012) Domain of the double sequential band matrix in the classical sequence spaces. J Inequal Appl 281(1):1-5
  22.Ba?ar F, Kiri??i M (2011) Almost convergence and generalized difference matrix. Comput Math Appl 61(3):602-11View Article MATH MathSciNet
  23.Candan M (2014) Almost convergence and double sequential band matrix. Acta Math Sci 34B(2):354-66View Article MathSciNet
  24.Candan M (2014) A new sequence space isomorphic to the space \(\ell (p)\) and compact operators. J Math Comput Sci 4(2):306-34
  25.Candan M (2014) Domain of the double sequential band matrix in the spaces of convergent and null sequences. Adv Differ Edu 163(1):1-8
  26.Candan M (2014) Some new sequence spaces derived from the spaces of bounded, convergent and null sequences. Int J Mod Math Sci 12(2):74-7
  27.Kiri??i M (2013) On the spaces of Euler almost null and Euler almost convergent sequences. Commun Fac Sci Univ Ankara 2:85-00
  28.Kiri??i M (2012) Almost convergence and generalized weighted mean I. AIP Conf Proc 1470:191-94ADS
  29.Kiri??i M (2014) Almost convergence and generalized weighted mean II. J Inequal Appl ID 93(1):1-3
  30.Altay B, Ba?ar F (2006) Some paranormed sequence spaces derived by generalized weighted mean. J Math Anal Appl 319:494-08View Article MATH MathSciNet
  31.Polat H, Karakaya V, ?im?ek N (2011) Difference sequence spaces derived by generalized weighted mean. Appl Math Lett 24(5):608-14View Article MATH MathSciNet
  32.Ba?ar?r M (2010) On the generalized Riesz \(B\) -difference sequence spaces. Filomat 24(4):35-2View Article MATH MathSciNet
  33.Altay B, Ba?ar 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 18:3005-013
  34.Demiriz S, ?akan C Some topolojical and geometrical properties of a new difference sequence space, Abstr
• 作者单位：Murat Candan (1)
  Asuman Güne? (1)
  
  1. Department of Mathematics, Faculty of Arts and Sciences, Inonu University, Malatya, Turkey
  
• 刊物主题：Physics, general; Applied and Technical Physics; Atomic, Molecular, Optical and Plasma Physics; Quantum Physics;
• 出版者：Springer India
• ISSN：2250-1762

文摘

The present paper introduces the generalized Riesz difference sequence space \(r^{q}(B_{u}^{p})\) that consists of all sequences whose \(R_{u}^{q}B\)-transforms are in the space \(\ell (p)\), where B stands for generalized difference matrix. Some topological properties of the new brand sequence space have been investigated as well as \(\alpha \)- \(\beta \)- and \(\gamma \)-duals. In addition to this, we have also constructed the basis of \(r^{q}(B_{u}^{p})\). At the end of the article, we characterize a matrix class on the sequence space. These results are more general and more comprehensive than the corresponding results in the literature.