Extension of Mazhar’s theorem on summability factors
Keywords:
Absolute Cesàro summability, absolute Riesz summability, bounded linear operators, matrix transformations, summability factors.Abstract
By (X; Y ) we denote the set of all sequences such thatPa nnis summable X wheneverPa n is summable Y , where X and Y are sum-mability methods. In this paper we characterize the set (jC; jk ;N; p n) fork > 1; >References
Bor, H. & B. Kuttner, B. 1989. On the necessary condition for absolute weighted arithmetic mean
summability factors. Acta Mathematica Hungarica 54: 57-61.
Bosanquet, L. S. & Das, G. 1979. Absolutely summability factors for Nörlund means. Proceedings
London Mathematical Society 838: 1-52.
Chow, H. C. 1954. Note on convergence and summability factors. Journal of the London Mathematical
Society 29: 459-476.
Flett, T. M. 1957. On an extension of absolute summability and some theorems of Littlewood and Paley.
Proceedings London Mathematical Society 7: 113-141.
Jakimovsky, A. & Russel, D. C. 1972. Matrix mapping between BK-spaces, Bulletin London
Mathematical Society 4: 345-353.
Mazhar, S. M. 1971. On the Absolute summability factors of infinite series. Tohoku Mathematical Journal
: 433-451.
Mehdi, M. R. 1960. Summability factors for generalized absolute summability I. Proceedings London
Mathematical Society. 10: 180-200.
Peyerimhoff, A. 1954. Summierbarkeitsfactoren für absolut Cesàro summierbareReihen. Mathematische
Zeitschrift 59: 417-424.
Rhoades, B. E. & Savas, E. 2004. A characterization of absolute summability factors. Taiwanese Journal
of Mathematics 8: 453-465.
Sarigol, M. A. 1993a. On two absolute Riesz summability factors of infinite series. Proceedings of the
American Mathematical Society 118: 485-488.
Sarigol, M. A. 1993b. A note on summability. Studia Scientiarum Mathematicarum Hungarica 28; 395-
Sarigol, M. A. & Bor, H. 1995. Characterization of absolute summability factors. Journal of Mathematical
Analysis and Applications 195: 537-545.
Sarigol, M. A. 2011a. Matrix transformations on fields of absolute weighted mean summability. Studia
Scientiarum Mathematicarum Hungarica 48; 331-341.
Sarigol, M. A. 2011b. Characterization of general summability factors and applications, Computers and
Mathematics with Applications 62: 2665-2670.
Stieglitz, M. & Tietz, H. 1977. Matrixtransformationen von Folgenraumen Eine Ergebnisübersicht.
Mathematische Zeitschrift 154: 1-16.
Sulaiman, W. T. 1992. On summability factors of infinite series. Proceedings of the American Mathematical
Society 115: 313-317.