Title: An Application of δ-Quasi Monotone Sequence
Author(s): Hikmet Seyhan Özarslan
Pages: 134-139
Cite as:
Hikmet Seyhan Özarslan, An Application of δ-Quasi Monotone Sequence, Int. J. Anal. Appl., 14 (2) (2017), 134-139.

Abstract


In this paper, a known theorem dealing with $|A,p_{n}|_{k}$ summability method of infinite series has been generalized to $| A,p_{n};\delta|_{k}$ summability method. Also, some results have been obtained.

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References


  1. R. P. Boas, Quasi-positive sequences and trigonometric series, Proc. London Math. Soc. 14A (1965), 38-46.

  2. H. Bor, On two summability methods, Math. Proc. Cambridge Philos. Soc. 97 (1985), 147-149.

  3. H. Bor, On quasi-monotone sequences and their applications, Bull. Austral. Math. Soc. 43 (1991), 187-192.

  4. H. Bor, On local property of |¯N,p n ;δ | k summability of factored Fourier series, J. Math. Anal. Appl. 179 (1993), 646–649.

  5. G. H. Hardy, Divergent Series, Oxford University Press, Oxford, 1949.

  6. H. S. ¨ Ozarslan and H. N. Ogdük, Generalizations of two theorems on absolute summability methods, Aust. J. Math. Anal. Appl. 1 (1) (2004), Article 13, 7 pp.

  7. H. S. Ozarslan and M. O. S ¸akar, A new application of absolute matrix summability, Math. Sci. Appl. E-Notes 3 (2015), 36-43.

  8. W. T. Sulaiman, Inclusion theorems for absolute matrix summability methods of an infinite series. IV, Indian J. Pure Appl. Math. 34 (11) (2003), 1547-1557.

  9. N. Tanovi˘ c-Miller, On strong summability, Glas. Mat. Ser. III 14 (34) (1979), 87-97.