Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
권호 표지
DOI QR코드

DOI QR Code

IDENTICAL THEOREM OF APPROXIMATION UNBOUNDED FUNCTIONS BY LINEAR OPERATORS

  • ALAA ADNAN AUAD (Department of Mathematics, Faculity of Education for Pure Sciences, University Of Anbar) ;
  • FAISAL AL-SHARQI (Department of Mathematics, Faculity of Education for Pure Sciences, University Of Anbar)
  • Received : 2022.10.04
  • Accepted : 2022.12.27
  • Published : 2023.07.30
Download PDF
⟨ Previous Next ⟩

Abstract

The aim of this paper, investigated of weighted space which contained the unbounded functions which is to be approximated by linear operators in terms some Well-known approximation tools such as the modulus of smoothness and K-functional. The characteristics of the identical theorem between modulus of smoothness and K-functional are consider. In addition to the establish the direct, converse and identical theorem by using some linear operators in terms modulus Ditzian-Totik.

Keywords

Acknowledgement

This work was supported by Faculity of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq.

References

  1. V. Gupta, A.M. Acu, and H.M. Srivastava, Difference of Some Positive Linear Approximation Operators for Higher-Order Derivatives, Symmetry 12 (2020), 915.
  2. K. Krishna, P. Johnson, and R. Mohapatra, Multipliers for operator-valued besse sequences and generalized hilbert-schmidt classes, Journal of applied mathematics and informatics 40 (2022), 153-171. https://doi.org/10.14317/JAMI.2022.153
  3. H.J. Rhee, The operators π G of best approximations and continuous metric projections, Journal of applied mathematics and informatics 40 (2022), 669-674. https://doi.org/10.14317/JAMI.2022.669
  4. M.M. Abed, A.F. Al-Jumaili and F.G. Al-Sharqi, Some mathematical structures in a topological group, J. Algab. Appl. Math. 16 (2018), 99-117.
  5. F.G. Al-Sharqi, M.M. Abed and A.A. Mhassin, On Polish Groups and their Applications, Journal of Engineering and Applied Sciences 13 (2018), 7533-7536.
  6. V. Gupt and M.N. Noor, On simultaneous approximation for certain Baskakov Durmeyer type operators, Journal of inequalities in pure and applied Mathematics 7 (2006), 1-33.
  7. P.N. Agrawl and K.J. THamer, Approximation of unbounded functions by new sequences of linear positive operators, Journal Mathematics analysis and applied 225 (1998), 600-672.
  8. Z. Finta, Direct approximation theorems for discrete type operators, Journal of inequities in pure and applied Mathematics 125 (2006), 1-21.
  9. V. Guta, Global approximation by modified Baskakov type operators, Publications Mahatma 39 (1995), 263-271. https://doi.org/10.5565/PUBLMAT_39295_04
  10. A. Aral and H. Erbay, Parametric generalization of Baskakov operators, Mathematical Communications 24 (2019), 119-131.
  11. A. Kilicman, M.A. Mursaleen and A.A. Al-Abied, Stancu type Baskakov- Durmeyer operators and approximation properties, Mathematics 8 (2020), 1-13. https://doi.org/10.3390/math8071164
  12. M. Goyal and P.N. Agrawal, Bezier variant of the generalized Baskakov Kantorvich operators, Bollettino dell unione Mathematica Italiona 8 (2016), 229-238. https://doi.org/10.1007/s40574-015-0040-2
  13. A. Kajla, S.A. Mohiuddine, Approximation by Baskakov- Durrmeyer type hybrid operators, Iranian journal of science and technology, Transactions 44 (2020), 1111-1118. https://doi.org/10.1007/s40995-020-00914-3
  14. Z. Ditzain and V. Totik, Moduli of smoothness, springer-verlag, New-York, 1987.
  15. L. Aharouch, J. Khursheed, Approximation by Bezier variant of Baskakov- Durrmeyer-type hybrid operators, Journal of Functions Space 2021 (2021), 1-9. https://doi.org/10.1155/2021/6673663
  16. V. Naragan, K. Khartri, Some approximation properties of q- Baskakov- Beta- Stancu type operations, Journal of Variation 2013 (2013), art. 814824, 1-8.
  17. W.N. Rao and A. wafi, Stancu of generalized Baskakov operators, Filomat 13 (2017), 2625-2632. https://doi.org/10.2298/FIL1709625R
  18. I. Gadjev, Approximation of functions by Baskakov- Kanntorovich operators, Results in Math. 70 (2016), 385-400. https://doi.org/10.1007/s00025-016-0554-7
  19. G. Wu and L. Han, Strong converse inequality of weighted simultaneous approximation for gamma operators in Orlicz spaces, Application Mathematics Journal 31 (2016), 366-378.
  20. A.A. Auad and A.A. Hussein, Best Approximation In Linear K-Normed Spaces, Turkish Journal of Computer and Mathematics Education 12 (2021), 2910-2914.
  21. F. Al-Sharqi, A. Al-Quran, A.G. Ahmad and S. Broumi, Interval-valued complex neutrosophic soft set and its applications in decision-making, Neutrosophic Sets Syst. 40 (2021), 149-168.
  22. F. Al-Sharqi, A.G. Ahmad and A. Al-Quran, Interval-Valued Neutrosophic Soft Expert Set from Real Space to Complex Space, CMES-Comp. Model. Eng. Sci. 132 (2022), 267-293.
  23. F. Al-Sharqi, A.G. Ahmad and A. Al-Quran, Interval complex neutrosophic soft relations and their application in decision-making, J. Intell. Fuzzy Syst. 43 (2022), 745-771. https://doi.org/10.3233/JIFS-212422
  24. F. Al-Sharqi, A.G. Ahmad and A. Al-Quran, Similarity Measures on Interval-Complex Neutrosophic Soft Sets with Applications to Decision Making and Medical Diagnosis under Uncertainty, Neutrosophic Sets Syst. 51 (2022), 495-515.
  25. H. Qoqazeh, Y. Al-qudah, M. Almousa and A. Jaradat, On d-compact topological spaces, Journal of Applied Mathematics and Informatics 39 (2021), 883-894. https://doi.org/10.14317/JAMI.2021.883
  26. M.M. Abed, N. Hassan and F. Al-Sharqi, On Neutrosophic Multiplication Module, Neutrosophic Sets Syst. 49 (2022), 198-208.
  27. A.F. Al-Jumaili, M.M. Abed and F. Al-Sharqi, Other new types of Mappings with Strongly Closed Graphs in Topological spaces via e-θ and δ-β-θ-open sets, J. Phys. Conf. Ser. 1234 (2019), 012101.