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

Merve Temizer Ersoy

doi:10.32323/ujma.909885

EN

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

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.

Keywords

$A$-statistically convergence , core theorems , matrix transformations

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.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Merve Temizer Ersoy ^*
Türkiye

Publication Date

June 30, 2021

Submission Date

April 5, 2021

Acceptance Date

June 4, 2021

Published in Issue

Year 2021 Volume: 4 Number: 2

DOI

https://doi.org/10.32323/ujma.909885

IZ

https://izlik.org/JA32XJ35PG

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

1.Temizer Ersoy M. Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability. Univ. J. Math. Appl. 2021;4(2):70-75. doi:10.32323/ujma.909885

Chicago

Temizer Ersoy, Merve. 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.

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

[1]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, June 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 1, 2021): 70-75. https://doi.org/10.32323/ujma.909885.

JAMA

1.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, June 2021, pp. 70-75, doi:10.32323/ujma.909885.

Vancouver

1.Merve Temizer Ersoy. Some Abelian, Tauberian and Core Theorems Related to the $(V,\lambda)$-Summability. Univ. J. Math. Appl. 2021 Jun. 1;4(2):70-5. doi:10.32323/ujma.909885