
تعداد نشریات | 26 |
تعداد شمارهها | 447 |
تعداد مقالات | 4,557 |
تعداد مشاهده مقاله | 5,380,001 |
تعداد دریافت فایل اصل مقاله | 3,580,066 |
The convexity of Chebyshev sets in normed spaces | ||
Journal of Mahani Mathematical Research | ||
دوره 10، شماره 1، مرداد 2021، صفحه 111-117 اصل مقاله (414.72 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22103/jmmrc.2021.14355.1097 | ||
نویسندگان | ||
H. Mazaheri* 1؛ Mohammad jafar Salehi2 | ||
1Yazd University | ||
2Payame Noore Shiraz | ||
چکیده | ||
In this paper, we consider “Nearest points” and “Farthest points” in inner product spaces and Hilbert spaces. The convexity of Chebyshev sets in Hilbert spacse is an open problem. In this paper we define sun sets and sunrise sets in normed spaces. | ||
کلیدواژهها | ||
Chebyshev centers؛ Uniquely remotal centers؛ Nearest points؛ Farthest points؛ Sun sets | ||
مراجع | ||
[1] E. Asplund, Chebyshsev sets in Hilbert spaces, Trans. Amer. Math. Soc. 144 (1969), 235240 [2] C. Franchetti, M. Furi, Some characteristic properties of real Hilbert spaces, Rev. Roumaine Math. Pures Appl. 17 (1972), 1045-1048. [3] R. C. Buck, Applications of duality in approximation theory, In Approximation of Func- tions (Proc. Sympos. General Motors Res. Lab., 1964), (1965), 27-42. [4] S. Elumalai and R. Vijayaragavan, Farthest points in normed linear spaces, General Mathematics 14 (3) (2006), 9-22. [5] C. Franchetti and I. Singer, Deviation and farthest points in normed linear spaces, Rev. Roum Math. Pures et appl, 24 (1979), 373-381. [6] O. Hadzic, A theorem on best approximations and applications, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat, 22 (1992), 47-55. [7] R. Khalil and Sh. Al-Sharif, Remotal sets in vector valued function spaces, Scientiae Mathematicae Japonicae. (3) (2006), 433-442. [8] H. V. Machado, A characterization of convex subsets of normed spaces, Kodai Math. Sem. Rep, 25 (1973), 307-320. [9] M. Marti'n and T. S. S. R. K. Rao, On remotality for convex sets in Banach spaces, J. Approx. Theory (162) (2010), 392-396. [10] M. Martin and T. S. S. R. K. Rao, On remotality for convex sets in Banach spaces, J. Approx. Theory, (162) (2010), 392-396. [11] H . Mazaheri, T. D. Narang and H. R. Khademzadeh, Nearest and Farthest points in normed spaces, In Press Yazd University, 2015. [12] H. Mazaheri, A characterization of weakly-Chebyshev subspaces of Banach spaces, J. Nat. Geom. 22 (2002), no. 1-2, 39{48. [13] H. Mohebi, On quasi-Chebyshev subspaces of Banach spaces, J. Approx. Theory 107 (2000), no. 1, 87{95. [14] T. D. Narang and Sangeeta, On singletonness of uniquely remotal sets, Bull. Belg. Soc. Simon. Stevin, 18 (2011), 113-120. Niknam, A., On uniquely remotal sets, Indian J. Pure Appl. Math., 15 (1984), 1079-1083. [15] A. Niknam, Continuity of the farthest point map, Indian J. Pure Appl. Math. 18 (1987), 630-632. [16] Sangeeta and T. D. Narang, On the farthest points in convex metric spaces and linear metric spaces, Publications de l'Institut Mathematique 95 (109) (2014), 229-238. [17] I. Singer, Best approximation in normed linear spaces by elements of linear subspaces, Springer-Verlag, New York-Berlin 1970. | ||
آمار تعداد مشاهده مقاله: 298 تعداد دریافت فایل اصل مقاله: 280 |