Year 2024,
Volume: 6 Issue: 1, 18 - 28, 30.06.2024
Ecem Acar
,
Sevilay Kırcı Serenbay
,
Saleem Yaseen Majeed
References
- L.A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965) 338-353.
- K. Weierstrass, U¨ ber die analytische darstellbarkeit sogenannter willku¨richer 55 funktionen einer reellen
veranderlichen. Sitzungsberichte Der Akademie zu Berlin, 2(1)(1885) 633-639.
- V.A. Baskakov, An example of a sequence of linear positive operators in the space of continuous functions,
Dokl. Akad. Nauk SSSR 113 (1957, in Russian) 249–251.
- Z. Finta, Direct local and global approximation theorems for some linear positive operators, Anal. Theory
Appl. 20(4) (2004) 307–322.
- A. Lupas, Some properties of the linear positive operators, II. Mathematica (Cluj) 9(32) (1967) 295–298.
- B. Bede, L. Coroianu, S.G. Gal, Approximation by Max-Product Type Operators, Springer International
Publishing,Switzerland (2016).
- B. Bede, L. Coroianu, S.G. Gal, Approximation and Shape Preserving Properties of The Truncated
Baskakov Operator of Max-Product Kind, Revista De La Unio Mathematica Argentia, 52(1) (2011) 89-
107.
- S.G. Gal, Shape-Preserving Approximation by Real and Complex Polynomials, Birkhauser, Boston-Basel-
Berlin,(2008) 89-104.
- T. Popoviciu, Deux remarques sur les fonctions convexes, Bull. Soc. Sci. Acad. Roumaine, 220 (1938)
45-49.
- D. Dubois and H. Prade, Operations on fuzzy numbers, Int. J. Systems Sci., 9, 613-626, 1978.
- D. Dubois and H. Prade, Fuzzy sets and systems, Theory and Applications (Academic Press, New York),
(1980).
- L. Coroianu, Lipschitz functions and fuzzy number approximations, Fuzzy Sets and Systems, 200 (2012)
116-135.
- A.I. Ban, Trapezoidal and triangular approximations of fuzzy numbers-inadvertences and corrections, Fuzzy
Sets Syst. 160 (2009) 3048–3058.
- A.I. Ban, A. Brandas, L. Coroianu, C. Negrutiu, O. Nica, Approximations of fuzzy numbers by trapezoidal
fuzzy numbers preserving the ambiguity and value, Comput. Math. Appl. 61 (2011) 1379–1401.
- A.I. Ban, L. Coroianu, Continuity and linearity of the trapezoidal approximation preserving the expected
interval operator, in: International Fuzzy Systems Association World Congress, 20–24, July 2009, pp.
798–802.
P. Grzegorzewski, Nearest interval approximation of a fuzzy number, Fuzzy Sets Syst. 130 (2002) 321–330.
- P. Grzegorzewski, Trapezoidal approximations of fuzzy numbers preserving the expected interval-
Algorithms and properties, Fuzzy Sets Syst. 47 (2008) 1353–1354.
- P. Grzegorzewski, E. Mr´owka, Trapezoidal approximations of fuzzy numbers, Fuzzy Sets Syst. 153 (2005)
115–135.
- P. Grzegorzewski, E. Mr´owka, Trapezoidal approximations of fuzzy numbers-revisited, Fuzzy Sets Syst.
158 (2007) 757–768.
- P.P.Korovkin,Linear operators and approximation theory. HindustanPubl.Corp.,India,1960.
- F.Altomare,M.Campiti,Korovkin type approximation theory and its applications, Walterde-
Gruyter,Berlin,1994.
- W. Congxin and M. Ming, On embedding problem of fuzzy number space, Part I, Fuzzy Sets and Systems
44, 33-38, 1991.
NOTE ON APPROXIMATION OF TRUNCATED BASKAKOV OPERATORS
Year 2024,
Volume: 6 Issue: 1, 18 - 28, 30.06.2024
Ecem Acar
,
Sevilay Kırcı Serenbay
,
Saleem Yaseen Majeed
Abstract
In this paper, we firstly introduce nonlinear truncated Baskakov operators on compact intervals and obtain some direct theorems. Also, we give the approximation of fuzzy numbers by truncated nonlinear Baskakov operators.
References
- L.A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965) 338-353.
- K. Weierstrass, U¨ ber die analytische darstellbarkeit sogenannter willku¨richer 55 funktionen einer reellen
veranderlichen. Sitzungsberichte Der Akademie zu Berlin, 2(1)(1885) 633-639.
- V.A. Baskakov, An example of a sequence of linear positive operators in the space of continuous functions,
Dokl. Akad. Nauk SSSR 113 (1957, in Russian) 249–251.
- Z. Finta, Direct local and global approximation theorems for some linear positive operators, Anal. Theory
Appl. 20(4) (2004) 307–322.
- A. Lupas, Some properties of the linear positive operators, II. Mathematica (Cluj) 9(32) (1967) 295–298.
- B. Bede, L. Coroianu, S.G. Gal, Approximation by Max-Product Type Operators, Springer International
Publishing,Switzerland (2016).
- B. Bede, L. Coroianu, S.G. Gal, Approximation and Shape Preserving Properties of The Truncated
Baskakov Operator of Max-Product Kind, Revista De La Unio Mathematica Argentia, 52(1) (2011) 89-
107.
- S.G. Gal, Shape-Preserving Approximation by Real and Complex Polynomials, Birkhauser, Boston-Basel-
Berlin,(2008) 89-104.
- T. Popoviciu, Deux remarques sur les fonctions convexes, Bull. Soc. Sci. Acad. Roumaine, 220 (1938)
45-49.
- D. Dubois and H. Prade, Operations on fuzzy numbers, Int. J. Systems Sci., 9, 613-626, 1978.
- D. Dubois and H. Prade, Fuzzy sets and systems, Theory and Applications (Academic Press, New York),
(1980).
- L. Coroianu, Lipschitz functions and fuzzy number approximations, Fuzzy Sets and Systems, 200 (2012)
116-135.
- A.I. Ban, Trapezoidal and triangular approximations of fuzzy numbers-inadvertences and corrections, Fuzzy
Sets Syst. 160 (2009) 3048–3058.
- A.I. Ban, A. Brandas, L. Coroianu, C. Negrutiu, O. Nica, Approximations of fuzzy numbers by trapezoidal
fuzzy numbers preserving the ambiguity and value, Comput. Math. Appl. 61 (2011) 1379–1401.
- A.I. Ban, L. Coroianu, Continuity and linearity of the trapezoidal approximation preserving the expected
interval operator, in: International Fuzzy Systems Association World Congress, 20–24, July 2009, pp.
798–802.
P. Grzegorzewski, Nearest interval approximation of a fuzzy number, Fuzzy Sets Syst. 130 (2002) 321–330.
- P. Grzegorzewski, Trapezoidal approximations of fuzzy numbers preserving the expected interval-
Algorithms and properties, Fuzzy Sets Syst. 47 (2008) 1353–1354.
- P. Grzegorzewski, E. Mr´owka, Trapezoidal approximations of fuzzy numbers, Fuzzy Sets Syst. 153 (2005)
115–135.
- P. Grzegorzewski, E. Mr´owka, Trapezoidal approximations of fuzzy numbers-revisited, Fuzzy Sets Syst.
158 (2007) 757–768.
- P.P.Korovkin,Linear operators and approximation theory. HindustanPubl.Corp.,India,1960.
- F.Altomare,M.Campiti,Korovkin type approximation theory and its applications, Walterde-
Gruyter,Berlin,1994.
- W. Congxin and M. Ming, On embedding problem of fuzzy number space, Part I, Fuzzy Sets and Systems
44, 33-38, 1991.