STRONG $F_A$-SUMMABILITY

Authors

  • MURSALEEN Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India.
  • Q. A. KHAN Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India.

DOI:

https://doi.org/10.5556/j.tkjm.24.1993.4485

Keywords:

strong convergent sequences, strong F_A-summability, infinite matrix

Abstract

Let $A = (a_{nk})$ be an infinite matrix and $x =(x_k)$ an infinite sequence of complex numbers. A sequence $x$ is said to be $F_A$-summable to a number $\ell$ [ActaMath. 80(1948),167-190] if and only if $x$ is bounded and

\[\sum_{k=0}^\infty a_{nk}x_{k+p}\to \ell\]

as $n\to\infty$, uniformly for $p\ge 0$.
The object of this paper is to define strong $F_A$-summability which is a generalization of strong almost convergence due to I. J. Maddox [Math. Proc. Camb. Phil. Soc., 83 (1978), 61-64]. We also characterize the matrices which transform strong almost convergent sequences to strong $F_A$-summable sequences.

References

S. Banach, "Theorie des Operations Lineaires,, (Warszawa 1932).

G. G. Lorentz, "A contribution to the theory of divergent sequences", Acta Math., 80 (1948), 167-190.

I. J. Maddox, "Space of strongly summable sequences", Quart. J. Math. (Oxford), 18 (1967), 345-355.

I. J. Maddox, "A new type of convergence," Math. Proc. Camb. Phil. Soc., 83 (1978), 61-64.

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Published

1993-06-01

How to Cite

MURSALEEN, & KHAN, Q. A. (1993). STRONG $F_A$-SUMMABILITY. Tamkang Journal of Mathematics, 24(2), 153-159. https://doi.org/10.5556/j.tkjm.24.1993.4485

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Papers