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http://dx.doi.org/10.14477/jhm.2017.30.6.353

On the Summability of Infinite Series and Hüseyin Bor  

Lee, Jung Oh (Dept. of Liberal Arts, Chosun College of Science and Technology)
Publication Information
Journal for History of Mathematics / v.30, no.6, 2017 , pp. 353-365 More about this Journal
Abstract
In general, there is summability among the mathematical tools that are the criterion for the convergence of infinite series. Many authors have studied on the summability of infinite series, the summability of Fourier series and the summability factors. Especially, $H{\ddot{u}}seyin$ Bor had published his important results on these topics from the beginning of 1980 to the end of 1990. In this paper, we investigate the minor academic genealogy of teachers and pupils from Fourier to $H{\ddot{u}}seyin$ Bor in section 2. We introduce the $H{\ddot{u}}seyin$ Bor's major results of the summability for infinite series from 1983 to 1997 in section 3. In conclusion, we summarize his research characteristics and significance on the summability of infinite series. Also, we present the diagrams of $H{\ddot{u}}seyin$ Bor's minor academic genealogy from Fourier to $H{\ddot{u}}seyin$ Bor and minor research lineage on the summability of infinite series.
Keywords
Summability of infinite series; summability of Fourier series; summability factor; absolute summability;
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1 Huseyin BOR, Local property of ${\mid}{\bar{N}},p{_n}{\mid}{_k}$ summability of factored Fourier series, Bull. Inst. Math. Acad. Sinica 17 (1989), 165-170.
2 Huseyin BOR, Multipliers for ${\mid}{\bar{N}},p{_n}{\mid}{_k}$ summability of Fourier series, Bull. Inst. Math. Acad.Sinica 17 (1989), 285-290.
3 Huseyin BOR, On absolute Cesaro summability factors of infinite series and Fourier series, Bull.Inst.Math. Acad. Sinica 26 (1998), 195-203.
4 Huseyin BOR, On absolute summability factors of infinite series, Proc. Indian Acad. Sci. (Math. Sci.) 104(2) (1994), 367-372.   DOI
5 Huseyin BOR, On absolute summability factors, Proc. Amer. Math. Soc. 118(1) (1993), 71-75.   DOI
6 Huseyin BOR, On ${\mid}{\bar{N}},p{_n}{\mid}{_k}$ summability factors, Kuwait J. Sci. Engng. 23 (1996), 1-5.
7 Huseyin BOR, On ${\mid}{\bar{N}},p{_n};{\delta}{\mid}{_k}$ summability factors of infinite series, Taiwanese J. Math. 1(3) (1997), 327-332.   DOI
8 Huseyin BOR, On ${\mid}{\bar{N}},p{_n}{\mid}{_k}$ summability factors, Proc. Amer. Math. Soc. 94(3) (1985), 419-422.   DOI
9 Huseyin BOR, On the local property of factored Fourier series, Z. Anal. Anwendungen 16 (1997), 769-773.   DOI
10 Huseyin BOR, On the relative strength of two absolute summability methods, Proc. Amer. Math. Soc. 113(4) (1991), 1009-1012.   DOI
11 Huseyin BOR, On the ${\mid}{\bar{N}},p{_n}{\mid}$ summability factors of infinite series, Proc. Indian Acad. Sci.(Math.Sci.) 98(1) (1988), 53-57.   DOI
12 Huseyin BOR, On two summability methods, Math. Proc. Cambridge Philos. Soc. 97 (1985), 147-149.   DOI
13 Huseyin BOR, The absolute summability factors of infinite series, Pure Appl. Math. Sci. 18 (1983), 75-79.
14 Huseyin BOR, Factors for ${\mid}{\bar{N}},p{_n}{\mid}{_k}$ summability of infinite series, Annales Academiae Scientiarum Fennicae Series A. I. Mathematica Volumen 16 (1991), 151-154.   DOI
15 Huseyin BOR, A note on ${\mid}{\bar{N}},p{_n}{\mid}{_k}$ summability factors for infinite series, Jour. Math. Sci. 16 (1983), 70-73.
16 Huseyin BOR, A note on two summability methods, Proc. Amer. Math. Soc. 98(1) (1986), 81-84.   DOI
17 Huseyin BOR and M. A. SARIGOL, Characterization of absolute summability factors, J. Math. Anal.Appl. 195 (1995), 537-545.   DOI