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Year 2021, , 70 - 75, 30.06.2021
https://doi.org/10.32323/ujma.909885

Abstract

References

  • [1] R. G. Cooke, Infinite Matrices and Sequence Spaces, Macmillan, New York, 1950.
  • [2] J. Connor, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bul. 32(1989), 194-198.
  • [3] H. C¸ os¸kun, C. C¸ akan, Infinite matrices and s-core, Demonstratio Math., 34(2001), 825-830.
  • [4] H. C¸ os¸kun, C. C¸ akan, On some new inequalities related to the FB-convergence, Tamsui Oxford J. Math. Sci., 19(2)(2003), 131-140.
  • [5] H. C¸ os¸kun, C. C¸ akan, A class of matrices mapping s-core into A-statistical core, Tamsui Oxford Journal of Math. Sci., 20(1) (2004) 17-25.
  • [6] K. Demirci, A-statistical core of a sequence, Demonstratio Math., 160(2000), 43-51.
  • [7] H. Fast, Sur la convergence statisque, Colloq. Math., 2(1951), 241-244.
  • [8] A. R. Freedman, J. J. Sember, Densities and summability, Pasific J. Math., 95(1981), 293-305.
  • [9] J. A. Fridy, C. Orhan, Statistical core theorems, J. Math., Anal. Appl. 208(1997), 520-527.
  • [10] L. Leindler, Uber die de la Vall´ee-Pousinsche Summierbarkeit allgemeiner Orthogonalreihen, Acta Math. Acad. Sci. Hungar., 16(1965), 375-387.
  • [11] I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, Cambridge 1970.
  • [12] A. A. Shcherbakov, Kernels of sequences of complex numbers and their regular transformations, Math. Notes, 22(1977), 948-953.
  • [13] U. Ulusu, E. Dundar, Asymptotically I-Cesaro equivalence of sequences of sets, Universal Journal of Mathematics and Applications, 1(2) (2018), 101-105.
  • [14] R. Kama, Spaces of vector sequence defined by the f-statistical convergence and some characterizations of normed spaces, Revista de la Real Academia de Ciencias Exactas, 4(2) (2020), 1-9.
  • [15] C. Unal, Ergodic Theorem in Grand Variable Exponent Lebesgue Spaces, Mathematical Science and Applications E-notes, 8(2) (2020), 130-134.
  • [16] O. Talo, E. Yavuz, H. C¸ os¸kun, Tauberian Theorems for Statistical Logarithmic Summability of Strongly Measurable Fuzzy Valued Functions, Communications in Advanced Mathematical Sciences, 2 (2020), 91-100.
  • [17] V. Renukadevi, S. Vadakasi, On Various g-Topology in Statistical Metric Spaces, Universal Journal of Mathematics and Applications, 2(3) (2019), 107-115.

Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability

Year 2021, , 70 - 75, 30.06.2021
https://doi.org/10.32323/ujma.909885

Abstract

For a non-decreasing sequence of positive integers tending to
infinity $\lambda=(\lambda_m)$ such that $\lambda_{m+1}-\lambda_m\leq 1$, $\lambda_1=1$;
$(V,\lambda)$-summability has been defined as the limit of the generalized de la Val\'{e}e-Pousin of a sequence, [10]. In the present research, we will establish some Tauberian, Abelian and Core Theorems related to the $(V,\lambda)$-summability.

References

  • [1] R. G. Cooke, Infinite Matrices and Sequence Spaces, Macmillan, New York, 1950.
  • [2] J. Connor, On strong matrix summability with respect to a modulus and statistical convergence, Canad. Math. Bul. 32(1989), 194-198.
  • [3] H. C¸ os¸kun, C. C¸ akan, Infinite matrices and s-core, Demonstratio Math., 34(2001), 825-830.
  • [4] H. C¸ os¸kun, C. C¸ akan, On some new inequalities related to the FB-convergence, Tamsui Oxford J. Math. Sci., 19(2)(2003), 131-140.
  • [5] H. C¸ os¸kun, C. C¸ akan, A class of matrices mapping s-core into A-statistical core, Tamsui Oxford Journal of Math. Sci., 20(1) (2004) 17-25.
  • [6] K. Demirci, A-statistical core of a sequence, Demonstratio Math., 160(2000), 43-51.
  • [7] H. Fast, Sur la convergence statisque, Colloq. Math., 2(1951), 241-244.
  • [8] A. R. Freedman, J. J. Sember, Densities and summability, Pasific J. Math., 95(1981), 293-305.
  • [9] J. A. Fridy, C. Orhan, Statistical core theorems, J. Math., Anal. Appl. 208(1997), 520-527.
  • [10] L. Leindler, Uber die de la Vall´ee-Pousinsche Summierbarkeit allgemeiner Orthogonalreihen, Acta Math. Acad. Sci. Hungar., 16(1965), 375-387.
  • [11] I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, Cambridge 1970.
  • [12] A. A. Shcherbakov, Kernels of sequences of complex numbers and their regular transformations, Math. Notes, 22(1977), 948-953.
  • [13] U. Ulusu, E. Dundar, Asymptotically I-Cesaro equivalence of sequences of sets, Universal Journal of Mathematics and Applications, 1(2) (2018), 101-105.
  • [14] R. Kama, Spaces of vector sequence defined by the f-statistical convergence and some characterizations of normed spaces, Revista de la Real Academia de Ciencias Exactas, 4(2) (2020), 1-9.
  • [15] C. Unal, Ergodic Theorem in Grand Variable Exponent Lebesgue Spaces, Mathematical Science and Applications E-notes, 8(2) (2020), 130-134.
  • [16] O. Talo, E. Yavuz, H. C¸ os¸kun, Tauberian Theorems for Statistical Logarithmic Summability of Strongly Measurable Fuzzy Valued Functions, Communications in Advanced Mathematical Sciences, 2 (2020), 91-100.
  • [17] V. Renukadevi, S. Vadakasi, On Various g-Topology in Statistical Metric Spaces, Universal Journal of Mathematics and Applications, 2(3) (2019), 107-115.
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Merve Temizer Ersoy

Publication Date June 30, 2021
Submission Date April 5, 2021
Acceptance Date June 4, 2021
Published in Issue Year 2021

Cite

APA Temizer Ersoy, M. (2021). Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability. Universal Journal of Mathematics and Applications, 4(2), 70-75. https://doi.org/10.32323/ujma.909885
AMA Temizer Ersoy M. Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability. Univ. J. Math. Appl. June 2021;4(2):70-75. doi:10.32323/ujma.909885
Chicago Temizer Ersoy, Merve. “Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability”. Universal Journal of Mathematics and Applications 4, no. 2 (June 2021): 70-75. https://doi.org/10.32323/ujma.909885.
EndNote Temizer Ersoy M (June 1, 2021) Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability. Universal Journal of Mathematics and Applications 4 2 70–75.
IEEE M. Temizer Ersoy, “Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability”, Univ. J. Math. Appl., vol. 4, no. 2, pp. 70–75, 2021, doi: 10.32323/ujma.909885.
ISNAD Temizer Ersoy, Merve. “Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability”. Universal Journal of Mathematics and Applications 4/2 (June 2021), 70-75. https://doi.org/10.32323/ujma.909885.
JAMA Temizer Ersoy M. Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability. Univ. J. Math. Appl. 2021;4:70–75.
MLA Temizer Ersoy, Merve. “Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability”. Universal Journal of Mathematics and Applications, vol. 4, no. 2, 2021, pp. 70-75, doi:10.32323/ujma.909885.
Vancouver Temizer Ersoy M. Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability. Univ. J. Math. Appl. 2021;4(2):70-5.

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