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  • Research Article
  • Open Access

Some Geometric Inequalities in a New Banach Sequence Space

Journal of Inequalities and Applications20072007:086757

  • Received: 11 July 2007
  • Accepted: 18 November 2007
  • Published:


The difference sequence space , which is a generalization of the space introduced and studied by Sargent (1960), was defined by Çolak and Et (2005). In this paper we establish some geometric inequalities for this space.


  • Sequence Space
  • Difference Sequence
  • Geometric Inequality
  • Banach Sequence
  • Banach Sequence Space


Authors’ Affiliations

Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
Department of Mathematics, Firat University, Elazığ, 23119, Turkey


  1. Sargent WLC: Some sequence spaces related to the spaces. Journal of the London Mathematical Society 1960,35(2):161–171. 10.1112/jlms/s1-35.2.161MathSciNetView ArticleMATHGoogle Scholar
  2. Malkowsky E, Mursaleen M: Matrix transformations between FK-spaces and the sequence spaces and . Journal of Mathematical Analysis and Applications 1995,196(2):659–665. 10.1006/jmaa.1995.1432MathSciNetView ArticleMATHGoogle Scholar
  3. Mursaleen M: Some geometric properties of a sequence space related to. Bulletin of the Australian Mathematical Society 2003,67(2):343–347. 10.1017/S0004972700033803MathSciNetView ArticleMATHGoogle Scholar
  4. Tripathy BC, Sen M: On a new class of sequences related to the space. Tamkang Journal of Mathematics 2002,33(2):167–171.MathSciNetMATHGoogle Scholar
  5. Çolak R, Et M: On some difference sequence sets and their topological properties. Bulletin of the Malaysian Mathematical Sciences Society 2005,28(2):125–130.MathSciNetMATHGoogle Scholar
  6. Et M, Çolak R: On some generalized difference sequence spaces. Soochow Journal of Mathematics 1995,21(4):377–386.MathSciNetMATHGoogle Scholar
  7. Kı zmaz H: On certain sequence spaces. Canadian Mathematical Bulletin 1981,24(2):169–176. 10.4153/CMB-1981-027-5MathSciNetView ArticleGoogle Scholar
  8. Malkowsky E, Mursaleen M, Suantai S: The dual spaces of sets of difference sequences of orderand matrix transformations. Acta Mathematica Sinica 2007,23(3):521–532. 10.1007/s10114-005-0719-xMathSciNetView ArticleMATHGoogle Scholar
  9. Cui Y, Hudzik H: On the Banach-Saks and weak Banach-Saks properties of some Banach sequence spaces. Acta Scientiarum Mathematicarum 1999,65(1–2):179–187.MathSciNetMATHGoogle Scholar
  10. Gurariĭ VI: Differential properties of the convexity moduli of Banach spaces. Matematicheskie Issledovaniya 1967,2(1):141–148.MathSciNetGoogle Scholar
  11. Sánchez L, Ullán A: Some properties of Gurarii's modulus of convexity. Archiv der Mathematik 1998,71(5):399–406. 10.1007/s000130050283MathSciNetView ArticleMATHGoogle Scholar