Journal of Hebei University(Natural Science Edition) >

2022 , Vol. 42 >Issue 2: 118 - 123

DOI: https://doi.org/10.3969/j.issn.1000-1565.2022.02.002

Korovkin approximation theorem on fuzzy continuous functions of several variables

  • CHEN Yingwei ,
  • CHANG Zhikui ,
  • WANG Zhijun
Expand
  • College of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China

Received date: 2020-09-16

  Online published: 2022-04-12

Fold

Abstract

We prove the trigonometric Korovkin approximation theorem for fuzzy valued functions of several variables and verify the approximation via the fuzzy modulus of continuity. Some applications concerning Fejér operators of fuzzy valued functions are also given.

Key words： fuzzy valued continuous function; Korovkin approximation theorem; fuzzy set theory; Fejér operator

Cite this article

CHEN Yingwei , CHANG Zhikui , WANG Zhijun . Korovkin approximation theorem on fuzzy continuous functions of several variables[J]. Journal of Hebei University(Natural Science Edition), 2022 , 42(2) : 118 -123 . DOI: 10.3969/j.issn.1000-1565.2022.02.002

References

[1] ZADEH L A. Fuzzy sets[J]. Inf Control, 1965, 8(3): 338-353. DOI:10.1016/S0019-9958(65)90241-X.
[2] ANASTASSIOU G A. Fuzzy mathematics: Approximation theory[M]. Heidelberg: Springer, 2010.
[3] GOETSCHEL R, VOXMAN W. Elementary fuzzy calculus[J]. Fuzzy Sets Syst, 1986, 18(1): 31-43. DOI:10.1016/0165-0114(86)90026-6.
[4] DEMIRCI K, DIRIK F. Four-dimensional matrix transformation and rate of A-statistical convergence of periodic functions[J]. Math Comput Model, 2010, 52(9/10): 1858-1866. DOI:10.1016/j.mcm.2010.07.015.
[5] STOROZˇENKO È A. Approximation of functions of class Hp,0<p≤1[J]. Math USSR-Sb, 1978, 34(4): 527-545. DOI: 10.1070/SM1978v034n04ABEH001228.
[6] 陈英伟,王志军.四元数Hardy空间中的slice正则Jackson定理[J].河北大学学报(自然科学版), 2019, 39(3): 230-234. DOI: 10.3969/j.issn.1000 -1565.2019.03.002.
[7] ANASTASSIOU G A. Fuzzy approximation by fuzzy convolution type operators[J]. Comput Math Appl, 2004, 48(9): 1369-1386. DOI:10.1016/j.camwa.2004.10.027.
[8] TAS E, YURDAKADIM T, ATLIHAN O G. Korovkin type approximation theorems in weighted spaces via power series method[J]. Oper Matrices, 2018, 12(2): 529-535. DOI: 10.7153/oam-2018-12-32.
[9] AHIN P O, DIRIK F. A Korovkin-type theorem for double sequences of positive linear operators via power series method[J]. Positivity, 2018, 22(1): 209-218. DOI:10.1007/s11117-017-0508-7.
[10] DEVORE R A, LORENTZ G G. Construction approximation[M]. Berlin: Springer-Verlag, 1993.
[11] GARNETT J B. Bounded analytic functions[M]. New York: Academic Press, 1981. (
Options
Outlines

/

〈 〉