Kyungpook Mathematical Journal

  • 제64권2호
  • /
  • Pages.235-244
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  • 2024
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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On The Sets of f-Strongly Cesàro Summable Sequences

  • Ibrahim Sulaiman Ibrahim (University of Zakho, College of Education, Department of Mathematics) ;
  • Rifat Colak (Firat University, Faculty of Science, Department of Mathematics)
  • 투고 : 2023.08.15
  • 심사 : 2024.01.20
  • 발행 : 2024.06.30
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초록

In this paper, we establish relations between the sets of strongly Cesàro summable sequences of complex numbers for modulus functions f and g satisfying various conditions. Furthermore, for some special modulus functions, we obtain relations between the sets of strongly Cesàro summable and statistically convergent sequences of complex numbers.

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참고문헌

  1. A. Aizpuru, M. Listan-Garcia, and F. Rambla-Barreno, Density by moduli and statistical convergence, Quaest. Math., 37(4)(2014), 525-530. https://doi.org/10.2989/16073606.2014.981683
  2. Y. Altin and M. Et, Generalized difference sequence spaces defined by a modulus function in a locally convex space, Soochow J. Math, 31(2)(2005), 233-243.
  3. V. K. Bhardwaj and S. Dhawan, f-Statistical convergence of order α and strong Cesaro summability of order α with respect to a modulus, J. Inequal. Appl., 67(4)(2015), 1-14. https://doi.org/10.1186/s13660-015-0850-x
  4. V. K. Bhardwaj, S. Dhawan, and S. Gupta, Density by moduli and statistical boundedness, Abstr. Appl. Anal., 2016(2016), 1-6.
  5. B. Bilalov and T. Nazarova, On statistical convergence in metric spaces, J. Math. Res., 7(1)(2015), 37-43. https://doi.org/10.5539/jmr.v1n1p37
  6. J. Connor, The statistical and strong p-cesaro convergence of sequences, Analysis, 8(1-2)(1988), 47-64. https://doi.org/10.1524/anly.1988.8.12.47
  7. J. Connor, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull., 32(2)(1989), 194-198. https://doi.org/10.4153/CMB-1989-029-3
  8. R. C olak and E. Kayan, df-Statistical convergence of order α and df-strong Cesaro summability of order α in accordance to a modulus in metric spaces, Thai J. Math., 20(2)(2022), 861-875.
  9. O. Duman, Generalized Cesaro summability of fourier series and its applications, Constr. Math. Anal., 4(2)(2021), 135-144. https://doi.org/10.33205/cma.838606
  10. M. Et and H. Sengul, Some Cesaro-type summability spaces of order α and lacunary statistical convergence of order α, Filomat, 28(8)(2014), 1593-1602. https://doi.org/10.2298/FIL1408593E
  11. M. Et, On some generalized deferred Cesaro means of order β, Math. Method. Appl. Sci., 44(9)(2021), 7433-7441. https://doi.org/10.1002/mma.6243
  12. H. Fast, Sur la convergence statistique, Colloq. Math., 2(3-4)(1951), 241-244. https://doi.org/10.4064/cm-2-3-4-241-244
  13. J. A. Fridy, On statistical convergence, Analysis, 5(4)(1985), 301-314. https://doi.org/10.1524/anly.1985.5.4.301
  14. D. Ghosh and P. Srivastava, On some vector valued sequence space using orlicz function, Glas. Mat. Ser. III, 34(2)(1999), 253-261.
  15. C. Granados and A. Dhital, Statistical convergence of double sequences in neutrosophic normed spaces, Neutrosophic Sets Syst., 42(2021), 333-344.
  16. I. S. Ibrahim and R. Colak, On strong lacunary summability of order α with respect to modulus functions. An. Univ. Craiova Ser. Mat. Inform., 48(1)(2021), 127-136. https://doi.org/10.52846/ami.v48i1.1399
  17. E. Kamber, Intuitionistic fuzzy I-convergent difference sequence spaces defined by modulus function, J. Inequal. Spec. Funct, 10(1)(2019), 93-100. https://doi.org/10.1186/s13660-019-2152-1
  18. F. Leon-Saavedra, M. D. Listan-Garcia, and M. D. Romero de la Rosa, On statistical convergence and strong Cesaro convergence by moduli for double sequences, J. Inequal. Appl., 2022(1)(2022), 1-13. https://doi.org/10.1186/s13660-021-02735-3
  19. I. J. Maddox, Inclusions between FK spaces and kuttner's theorem, Math. Proc. Cambridge Philos. Soc., 101(3)(1987), 523-527. https://doi.org/10.1017/S0305004100066883
  20. I. J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Cambridge Philos. Soc., 100(1)(1986), 161-166. https://doi.org/10.1017/S0305004100065968
  21. H. Nakano, Concave modulars, J. Math. Soc. Japan, 5(1)(1953), 29-49. https://doi.org/10.2969/jmsj/00510029
  22. D. Rath and B. Tripathy, On statistically convergent and statistically cauchy sequences, Indian J. Pure Appl. Math., 25(1994), 381-381.
  23. W. H. Ruckle, FK spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math., 25(5)(1973), 973-978. https://doi.org/10.4153/CJM-1973-102-9
  24. B. Sarma, Some generalized sequence spaces operated by a modulus function, Invertis J. Sci. Tech., 11(1)(2018), 42-45. https://doi.org/10.5958/2454-762X.2018.00006.9
  25. I. Schoenberg, The integrability of certain functions and related summability methods, Am. Math. Mon., 66(5)(1959), 361-375. https://doi.org/10.1080/00029890.1959.11989303
  26. H. M. Srivastava, B. B. Jena, and S. K. Paikray, Deferred cesaro statistical convergence of martingale sequence and korovkin-type approximation theorems, Miskolc Math. Notes, 23(1)(2022), 443-456. https://doi.org/10.18514/MMN.2022.3624
  27. T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, 30(2)(1980), 139-150.
  28. F. Weisz, Cesaro summability and Lebesgue points of higher dimensional Fourier series, Math. Found. Comput., 5(3)(2022), 241-257. https://doi.org/10.3934/mfc.2021033
  29. A. Zygmund, Trigonometric series, Cambridge University Press, 1959.