Kyungpook Mathematical Journal

  • 제64권2호
  • /
  • Pages.235-244
  • /
  • 2024
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지
DOI QR코드

DOI QR Code

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
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

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.

키워드

참고문헌

  1. A. Aizpuru, M. Listan-Garcia, and F. Rambla-Barreno, Density by moduli and statistical convergence, Quaest. Math., 37(4)(2014), 525-530.
  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.
  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.
  6. J. Connor, The statistical and strong p-cesaro convergence of sequences, Analysis, 8(1-2)(1988), 47-64.
  7. J. Connor, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bull., 32(2)(1989), 194-198.
  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.
  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.
  11. M. Et, On some generalized deferred Cesaro means of order β, Math. Method. Appl. Sci., 44(9)(2021), 7433-7441.
  12. H. Fast, Sur la convergence statistique, Colloq. Math., 2(3-4)(1951), 241-244.
  13. J. A. Fridy, On statistical convergence, Analysis, 5(4)(1985), 301-314.
  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.
  17. E. Kamber, Intuitionistic fuzzy I-convergent difference sequence spaces defined by modulus function, J. Inequal. Spec. Funct, 10(1)(2019), 93-100.
  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.
  19. I. J. Maddox, Inclusions between FK spaces and kuttner's theorem, Math. Proc. Cambridge Philos. Soc., 101(3)(1987), 523-527.
  20. I. J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Cambridge Philos. Soc., 100(1)(1986), 161-166.
  21. H. Nakano, Concave modulars, J. Math. Soc. Japan, 5(1)(1953), 29-49.
  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.
  24. B. Sarma, Some generalized sequence spaces operated by a modulus function, Invertis J. Sci. Tech., 11(1)(2018), 42-45.
  25. I. Schoenberg, The integrability of certain functions and related summability methods, Am. Math. Mon., 66(5)(1959), 361-375.
  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.
  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.
  29. A. Zygmund, Trigonometric series, Cambridge University Press, 1959.