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

Year 2021, Volume: 4 Issue: 2, 70 - 75, 30.06.2021

Merve Temizer Ersoy

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

Cited By: 2

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.