Research Article
BibTex RIS Cite
Year 2024, Volume: 6 Issue: 1, 18 - 28, 30.06.2024
https://doi.org/10.47086/pims.1362142

Abstract

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
https://doi.org/10.47086/pims.1362142

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.
There are 21 citations in total.

Details

Primary Language English
Subjects Approximation Theory and Asymptotic Methods
Journal Section Articles
Authors

Ecem Acar 0000-0002-2517-5849

Sevilay Kırcı Serenbay 0000-0001-5819-9997

Saleem Yaseen Majeed 0000-0002-4998-7681

Early Pub Date July 1, 2024
Publication Date June 30, 2024
Acceptance Date March 25, 2024
Published in Issue Year 2024 Volume: 6 Issue: 1

Cite

Creative Commons License
The published articles in PIMS are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.