[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14317/jami.2020.483

A NEW THEOREM ON GENERALIZED ABSOLUTE CESÀRO SUMMABILITY FACTORS

BOR, HUSEYIN

Publication Information

Journal of applied mathematics & informatics / v.38, no.5_6, 2020 , pp. 483-487 More about this Journal

Abstract

In this paper, we have proved a new theorem dealing with 𝜑 - |C, 𝛼|_k summability factors of infinite series under weaker conditions. Also, some new and known results are obtained.

Keywords

$Ces{\grave{a}}ro$ mean; absolute summability; almost increasing sequence; quasi- ${\sigma}$ -power increasing sequence; infinite series; $H{\ddot{o}}lder^{\prime}s$ inequality; Minkowski's inequality;

Citations & Related Records

Reference

1	M. Balci, Absolute $\varphi$ -summability factors, Comm. Fac. Sci. Univ. Ankara, Ser. A1 29 (1980), 63-68.
2	N.K. Bari and S.B. Steckin, Best approximation and differential properties of two conjugate functions, Trudy. Moskov. Mat. Obsc. 5 (1956), 483-522.
3	H. Bor, Factors for generalized absolute Cesaro summability methods, Publ. Math. Debrecen 43 (1993), 297-302.
4	H. Bor, A new study on generalized absolute Cesaro summability methods, Quaest. Math. 43 (2020), (in press).
5	T.M. Flett, Some more theorems concerning the absolute summability of Fourier series, Proc. London Math. Soc. 8 (1958), 357-387.
6	L.S. Bosanquet, A mean value theorem, J. London Math. Soc. 16 (1941), 146-148. DOI
7	E. Cesaro, Sur la multiplication des series, Bull. Sci. Math. 14 (1890), 114-120.
8	T.M. Flett, On an extension of absolute summability and some theorems of Littlewood and Paley, Proc. London Math. Soc. 7 (1957), 113-141.
9	E. Kogbetliantz, Sur les series absolument sommables par la methode des moyennes arithmetiques, Bull. Sci. Math. 49 (1925), 234-256.
10	L. Leindler, A new application of quasi power increasing sequences, Publ. Math. Debrecen 58 (2001), 791-796.
11	S.M. Mazhar, Absolute summability factors of infinite series, Kyungpook Math. J. 39 (1999), 67-73.
12	T. Pati, The summability factors of infinite series, Duke Math. J. 21 (1954), 271-284. DOI