On Manifold Jain-Beta Operators
DOI:
https://doi.org/10.29304/jqcm.2020.12.4.721Keywords:
Beta operators, Jain operators, Approximation theorem, Voronovskaja Theorem,, Korovkinʼs Theorem, Modulus of ContinuityAbstract
The aim of this paper is to construct a new sequence of linear and positive operators which called Jain-Beta operators based on a parameter . We investigated some properties of these operators when applied the approximation theorems. Moreover, we estimated the rate of convergence relying on concept the modulus of continuity. Finally, established a Voronoviskaja- type asymptotic formula.
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References
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[8] Vishnu Narayan Mishra, Prashant kumar Patel, “Some Approximation of new Families of Positive Linear Operators”, Hindawi Publishing Corporation Journal of Calculus of Variations, Article ID 489249, 8 pages, http://dx.doi.org/10.1155/2013/489249, vol. 2013 (2013), pp 1-8.
[9] Gulen Bascanbaz –Tunca, Murat Bodur, Dilek Soylemez, “On Lupas – Jain Operators.”, Stud. Univ. Babes-Bolyai Math., Doi: 10.24193/subbmath.2018.4.08, vol. 63 No.4 (2018), pp 525-537.
[10] Haneen J. Sadiq, “Approximation of Bounded Functions by Positive Linear Operators in C_p”, Basrah Journal of Science, vol. 37(3) (2019), pp 412-429.
[11] Voronovskaja E, “Détermination de la forme asymptotiqued’ ápproximation des functions par les polynômes de S. N. Bernstein.”, C. R. Acad. Sci. USSR (1932), pp 79-85.
[12] Serhan Varma, Fatma Taşdelen “Százs Type Operators Involving Charlier Polynomials”, Mathematical and Computer Moduling, Journal homepage: www.elsevier.com/locate/mcm. Doi: 10. 1016/j.mcm.2011.12.017, vol. 56 (2012) pp 118-122.
[13] Haneen J. Sadiq, “Some Approximation properties of New Family of Baskakov – Type Operators”, IOP Conference Series: Materials Science and Engineering, 2nd International Scientific Conference of Al-Ayen University (ISCAU-2020). vol. 928 (2020), pp 1-13.
[2] Vijay Gupta, G. S. Srivastava and A. Sahai, “On simultaneous approximation
by Szãsz-Beta Operators”, Soochow J. Math, vol. 21(1995), pp 1-11.
[3] Ali J. Mohammad, Ansam A. Abdul-Rahman, “Rate of converges for new family of summation- Integral Beta operators”, Iraqi Journal of Statistical Science, The Fourth Scientific Conference of the College of Computer Science & Mathematics, vol. 20 (2011), pp 83-92.
[4] Ali J. Mohammad, Hanadi A. AbdulSattar, Haneen J. Sadiq, “On Truncated of Classical Beta operators”, Journal of Basrah researches ((Sciences)), vol. 41 No. 3, A(2015), pp 15-23.
[5] P. P. Korovkin, “Linear Operators and Approximation Theory”, Hindustan Publ. Corp. Delhi, 1960 (Translated from Russian Edition) (1960).
[6] O. Dogru, R. N. Mohapatra, M. Orkcu, “Approximation Properties of Generalized Jain Operators”, published by University of Nis, Serbia, Faculty of Sciences and Mathematics. Doi 10.2298/FIL1609359D, Filomat, vol. 30 No. 9 (2016), pp 2359-2366.
[7] Prashantkumar Patel, “Some Approximation of new Families of Positive Linear Operators”, Hindawi Publishing Corporation Journal of Calculus of Variations, Article ID 489249, 8 pages, http://dx.doi.org/10.1155/2013/489249, vol. 2013 (2013), pp 1-8.
[8] Vishnu Narayan Mishra, Prashant kumar Patel, “Some Approximation of new Families of Positive Linear Operators”, Hindawi Publishing Corporation Journal of Calculus of Variations, Article ID 489249, 8 pages, http://dx.doi.org/10.1155/2013/489249, vol. 2013 (2013), pp 1-8.
[9] Gulen Bascanbaz –Tunca, Murat Bodur, Dilek Soylemez, “On Lupas – Jain Operators.”, Stud. Univ. Babes-Bolyai Math., Doi: 10.24193/subbmath.2018.4.08, vol. 63 No.4 (2018), pp 525-537.
[10] Haneen J. Sadiq, “Approximation of Bounded Functions by Positive Linear Operators in C_p”, Basrah Journal of Science, vol. 37(3) (2019), pp 412-429.
[11] Voronovskaja E, “Détermination de la forme asymptotiqued’ ápproximation des functions par les polynômes de S. N. Bernstein.”, C. R. Acad. Sci. USSR (1932), pp 79-85.
[12] Serhan Varma, Fatma Taşdelen “Százs Type Operators Involving Charlier Polynomials”, Mathematical and Computer Moduling, Journal homepage: www.elsevier.com/locate/mcm. Doi: 10. 1016/j.mcm.2011.12.017, vol. 56 (2012) pp 118-122.
[13] Haneen J. Sadiq, “Some Approximation properties of New Family of Baskakov – Type Operators”, IOP Conference Series: Materials Science and Engineering, 2nd International Scientific Conference of Al-Ayen University (ISCAU-2020). vol. 928 (2020), pp 1-13.
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Published
2020-12-27
How to Cite
Sadiq, H. J. (2020). On Manifold Jain-Beta Operators. Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(4), Math Page 39– 48. https://doi.org/10.29304/jqcm.2020.12.4.721
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Math Articles
