Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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RIESZ TRIPLE ALMOST LACUNARY χ3 SEQUENCE SPACES DEFINED BY A ORLICZ FUNCTION-I

  • SUBRAMANIAN, N. (Department of Mathematics, SASTRA Deemed to be University) ;
  • Esi, Ayhan (Department of Mathematics,Adiyaman University Adiyaman) ;
  • AIYUB, M. (Department of Mathematics,College of Science University of Bahrain)
  • 투고 : 2018.06.21
  • 심사 : 2018.10.29
  • 발행 : 2019.01.30
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초록

In this paper we introduce a new concept for Riesz almost lacunary ${\chi}^3$ sequence spaces strong P - convergent to zero with respect to an Orlicz function and examine some properties of the resulting sequence spaces. We introduce and study statistical convergence of Riesz almost lacunary ${\chi}^3$ sequence spaces and some inclusion theorems are discussed.

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참고문헌

  1. T. Apostol, Mathematical Analysis, Addison-Wesley London 1 , 978.
  2. A. Esi , On some triple almost lacunary sequence spaces defined by Orlicz functions, Research and Reviews:Discrete Mathematical Structures 1(2) (2014), 16-25.
  3. A. Esi and M. Necdet Catalbas, Almost convergence of triple sequences, Global Journal of Mathematical Analysis 2(1) (2014), 6-10.
  4. A. Esi and E. Savas, On lacunary statistically convergent triple sequences in probabilistic normed space,Appl.Math.and Inf.Sci. 9(5) (2015), 2529-2534.
  5. A. Esi , Statistical convergence of triple sequences in topological groups, Annals of the University of Craiova, Mathematics and Computer Science Series 40(1) (2013), 29-33.
  6. E. Savas and A. Esi, Statistical convergence of triple sequences on probabilistic normed space ,Annals of the University of Craiova, Mathematics and Computer Science Series 39(2) (2012), 226-236.
  7. G.H. Hardy, On the convergence of certain multiple series, Proc. Camb. Phil. Soc. 19 (1917), 86-95.
  8. A. Sahiner, M. Gurdal and F.K. Duden, Triple sequences and their statistical convergence, Selcuk J. Appl. Math.8(2) (2007), 49-55.
  9. Deepmala, N. Subramanian and Vishnu Narayan Misra, Double almost (${\lambda}_m{\nu}_n$) in ${\chi}^2$- Riesz space, Southeast Asian Bulletin of Mathematics 35 (2016), 1-11.
  10. N. Subramanian, B.C. Tripathy and C. Murugesan, The double sequence space of ${\Gamma}^2$, Fasciculi Math. 40 (2008), 91-103.
  11. N. Subramanian, B.C. Tripathy and C. Murugesan, The Cesaro of double entire sequences, International Mathematical Forum 4(2) (2009), 49-59.
  12. N. Subramanian and A. Esi, The generalized triple difference of ${\chi}^3$ sequence spaces , Global Journal of Mathematical Analysis 3(2) (2015), 54-60. https://doi.org/10.14419/gjma.v3i2.4412
  13. N. Subramanian and A. Esi, The study on ${\chi}^3$ sequence spaces, Songklanakarin Journal of Science and Technology 38(5) (2016), 581-590.
  14. N. Subramanian and A. Esi, Characterization of Triple $38^3$ sequence spaces , Mathematica Moravica 20(1) (2016), 105-114. https://doi.org/10.5937/MatMor1601105S
  15. N. Subramanian and A. Esi, Some New Semi-Normed Triple Sequence Spaces Defined By A Sequence Of Moduli, Journal of Analysis & Number Theory 3(2) (2015), 79-88. https://doi.org/10.18576/jant/030201
  16. T.V.G. Shri Prakash, M. Chandramouleeswaran and N. Subramanian , The Triple Almost Lacunary ${\Gamma}^3$ sequence spaces defined by a modulus function, International Journal of Applied Engineering Research 10(80) (2015), 94-99.
  17. T.V.G. Shri Prakash, M. Chandramouleeswaran and N. Subramanian , The triple entire sequence defined by Musielak Orlicz functions over p- metric space, Asian Journal of Mathematics and Computer Research,International Press 5(4) (2015), 196-203.
  18. T.V.G. Shri Prakash, M. Chandramouleeswaran and N. Subramanian , The Random of Lacunary statistical on ${\Gamma}^3$ over metric spaces defined by Musielak Orlicz functions, Modern Applied Science 10(1) (2016), 171-183 .
  19. T.V.G. Shri Prakash, M. Chandramouleeswaran and N. Subramanian , The Triple ${\Gamma}^3$ of tensor products in Orlicz sequence spaces, Mathematical Sciences International Research Journal 4(2) (2015), 162-166.
  20. T.V.G. Shri Prakash, M. Chandramouleeswaran and N. Subramanian , The strongly generalized triple difference ${\Gamma}^3$ sequence spaces defined by a modulus , Mathematica Moravica ,in press.
  21. T.V.G. Shri Prakash, M. Chandramouleeswaran and N. Subramanian , Lacunary Triple sequence ${\Gamma}^3$ of Fibonacci numbers over probabilistic p- metric spaces , International Organization of Scientific Research 12(I-IV) (2016), 10-16.
  22. H. Nakano, Concave modulars, Journal of the Mathematical Society of Japan 5 (1953), 29-49. https://doi.org/10.2969/jmsj/00510029
  23. J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math. 10(1971), 379-390. https://doi.org/10.1007/BF02771656
  24. Y. Altin, M. Et and B.C. Tripathy, The sequence space ${\left}|N_p{\right}|$(M, r, q, s) on seminormed spaces, Applied Math.Comput. 154(2004), 423-430.
  25. M. Et, P.Y. Lee and B.C. Tripathy, Strongly almost (V, ${\lambda}$)(${\Delta}^r$)-summable sequences defined by Orlicz function, Hokkaido Math.Jour. 35(2006), 197-213. https://doi.org/10.14492/hokmj/1285766306
  26. A. Esi, N. Subramanian and A. Esi, Triple rough statistical convergence of sequence of Bernstein operators, Int. J. Adv. Appl. Sci. 4(2) (2017), 28-34. https://doi.org/10.21833/ijaas.2017.02.005
  27. A. Esi, N. Subramanian and A. Esi, The multi rough ideal convergence of difference strongly of ${\chi}^2$ in p-metric spaces defined by Orlicz functions, Turkish Journal of Analysis and Number Theory 5(3) (2017), 93-100.
  28. B.C. Tripathy and S. Mahanta, On a class of vector valued sequences associated with multiplier sequences, Acta Math.Applicata Sinica (Eng.Ser.) 20(3) (2004), 487-494. https://doi.org/10.1007/s10255-004-0186-7
  29. B.C. Tripathy and S. Mahanta, On a class of difference sequences related to the ${\lambda}^p$ space defined by Orlicz functions, Mathematica Slovaca 57(2) (2007), 171-178. https://doi.org/10.2478/s12175-007-0007-6
  30. B.C. Tripathy and H.Dutta, On some new paranormed difference sequence spaces defined by Orlicz functions, Kyungpook Mathematical Journal 50(1) (2010), 59-69. https://doi.org/10.5666/KMJ.2010.50.1.059
  31. B.C. Tripathy and H. Dutta, On some lacunary difference sequence spaces defined by a sequence of Orlicz functions and q-lacunary ${\Delta}_{m}^{n}$-statistical convergence, Analele Stiintifice ale Universitatii Ovidius, Seria Matematica 20(1) (2012), 417-430. https://doi.org/10.2478/v10309-012-0028-1
  32. B.C. Tripathy and R. Goswami, On triple difference sequences of real numbers in probabilistic normed spaces, Proyecciones Jour.Math. 33(2) (2014), 157-174. https://doi.org/10.4067/S0716-09172014000200003
  33. B.C. Tripathy and R. Goswami, Vector valued multiple sequences defined by Orlicz functions, Boletim de Sociedade Paranaense De Matematica 33(1) (2015), 67-79.
  34. B.C. Tripathy and R. Goswami, Multiple sequences in probabilistic normed spaces, Afrika Matematika 26(5-6) (2015), 753-760. https://doi.org/10.1007/s13370-014-0243-1
  35. B.C. Tripathy and R. Goswami, Statistically convergent multiple sequences in probabilistic normed spaces, U.P.B.Sci.Bull, Ser.A 78(4) (2016), 83-94.