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Lacunary arithmetic convergence

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In this article we introduce and study the lacunary arithmetic convergent sequence space ACθ. Using the idea of strong Cesaro summable sequence and arithmetic convergence we define ACσ₁and study the relations between ACθ and ACσ₁. Finally using modulus function we define ACθ(f) and study some interesting results.

Abstract

In this article we introduce and study the lacunary arithmetic convergent sequence space ACθ. Using the idea of strong Cesaro summable sequence and arithmetic convergence we define ACσ₁and study the relations between ACθ and ACσ₁. Finally using modulus function we define ACθ(f) and study some interesting results.

참고문헌 (16)

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  10. S. Pehlivan, "On Some Sequence Space", lndian J. Pure Appl., 25(10), pp.1067~1071 (1994)
  11. W. H. Ruckle, "Arithmetical Summability", J. Math. Anal. Appl., 396, pp.741~748 (2012)[DOI]
  12. W. H. Ruckle, "FK spaces in which the sequence of coordinate vectors is bounded", Canad. J. Math., 25, pp.973~978 (1973)[DOI]
  13. Taja Yaying, "On arithmetical summability and multiplier sequences", National Academy Sci. Letters, 40(1), pp.43~46 (2017)[DOI]
  14. Taja Yaying, "On arithmetic continuity", Bol. Soc. Parana. Mat., 35(1), pp.139~145 (2017)[DOI]
  15. Taja Yaying, "Bipan Hazarika and Huseyin Cakalli, New results in quasi cone metric spaces", J. Math. Comput. Sci., 16(3), pp.435~444 (2016)[DOI]
  16. B. C. Tripathy, "On generalized difference lacunary statistical convergence", Studia Univ. Babes-Bolyai Math., 50(1), pp.119~130 (2005)

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