COMPOSITE DUAL SUMMABILITY METHODS OF THE NEW SORT

Following Altay and Ba¸sar [1], we define the duality relation of the new sort between a pair of infinite matrices. Our focus is to study the composite dual summability methods of the new sort and to give some inclusion theorems.

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  • B. Altay, F. Ba¸sar, Some paranormed Riesz sequence spaces of non-absolute type, Southeast Asian Bull. Math. 30(5)(2006), 591–608
  • S. Banach, Théorie des Operations Linéaries, Warsaw, 1932.
  • F. Ba¸sar, Matrix transformations between certain sequence spaces of Xpand `p, Soochow J. Math. 26(2)(2000), 191–204.
  • F. Ba¸sar, R. Çolak, Almost-conservative matrix transformations, Doµga Mat. 13(3)(1989), –100.
  • B. Kuttner, On dual summability methods, Proc. Camb. Phil. Soc. 71(1972), 67–73.
  • G.G. Lorentz, Über Limitierungsverfahren die von einem Stieltjes-Integral abhängen, Acta Math. 79(1947), 255–272.
  • G. G. Lorentz, A contribution to the theory of divergent sequences, Acta Math. 80(1948), –190.
  • G.G. Lorentz, K. Zeller, Summation of sequences and summation of series, Proc. Amer. Math. Soc. 15(1964), 743–746.
  • C. Orhan, E. Öztürk, On f-regular dual summability methods, Bull. Inst. Math. Acad. Sinica (1)(1986), 99–104.
  • E. Öztürk, On dual summability methods, Comm. Fac. Sci. Univ. Ank. Ser. A1 Math. Statist. (1)(1976), 1–19.
  • G.M. Petersen, Regular Matrix Transformations, McGraw-Hill Publishing Company Lim- ited, London, 1966.
  • Current address :Medine Ye¸silkayagil; Department of Mathematics, U¸sak University, 1 Eylül Campus, 64200–U¸sak, TURKEY , Feyzi Ba¸sar; Department of Mathematics, Fatih University, The Hadımköy Campus, Büyükçek- mece, 34500–·Istanbul, TURKEY
  • E-mail address : medine.yesilkayagil@usak.edu.tr, fbasar@fatih.edu.tr. URL: http://communications.science.ankara.edu.tr/index.php?series=A1
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics-Cover
  • ISSN: 1303-5991
  • Yayın Aralığı: Yılda 4 Sayı
  • Başlangıç: 1948
  • Yayıncı: Ankara Üniversitesi