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Order improvement for the sequence of $\alpha$-Bernstein-Paltanea operators | ||
International Journal of Nonlinear Analysis and Applications | ||
مقاله 3، دوره 14، شماره 9، آذر 2023، صفحه 47-64 اصل مقاله (663.74 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.28762.3982 | ||
نویسندگان | ||
Jaspreet Kaur؛ Meenu Goyal* | ||
Thapar Institute of Engineering and Technology, Patiala, 147004, India | ||
تاریخ دریافت: 28 مهر 1401، تاریخ بازنگری: 21 بهمن 1401، تاریخ پذیرش: 26 بهمن 1401 | ||
چکیده | ||
In the present paper, we give the modifications of $\alpha-$Bernstein-Paltanea operators with better approximation properties. We present three modifications of these operators having linear, quadratic and cubic order of approximation whereas the classical operators are of linear order. By increasing the order of approximation of these operators, the speed of the convergence will be increased. We establish some approximation results concerning the rate of convergence, error estimation and Voronovskaja type formulas for the new modifications. Also, we verify our analytical results with the help of MAPLE algorithms. | ||
کلیدواژهها | ||
Modulus of continuity؛ Convergence of series and sequences؛ Rate of convergence؛ Approximation by positive operators؛ Asymptotic approximations | ||
مراجع | ||
[1] T. Acar, A. Aral and V. Gupta, On approximation properties of a new type of Bernstein-Durrmeyer operators, Math. Slovaca 65(5) (2015), 1101–1122. [2] T. Acar, A.M. Acu and N. Manav, Approximation of functions by genuine Bernstein-Durrmeyer type operators, J. Math. Inequal. 12 (2018), no. 4, 975–987. [3] T. Acar, P.N. Agrawal and T. Neer, Bezier variant of the Bernstein-Durrmeyer type operators, Results Math. 72 (2017), 1341–1358. [4] T. Acar, A. Aral and I. Rasa, Positive linear operators preserving τ and τ2, CMA 2 (2019), no. 3, 98–102. [5] A.M. Acu, T. Acar and VA. Radu, Approximation of modified Uρn operators, RACSAM 113 (2019), 2715–2729. [6] A.M. Acu, V. Gupta and G. Tachev, Better numerical approximation by Durrmeyer type operators, Results Math. 74 (2019), no. 3, 1–24. [7] R.P. Agrawal and V. Gupta, On q analogue of a complex summation-integral type operators in compact disks, J. Inequal. Appl. 2012 (2012), 1–13. [8] K.J. Ansari, S. Rahman and M. Mursaleen, Approximation and error estimation by modified P˘alt˘anea operators associating Gould-Hopper polynomials, RACSAM 113 (2019), 2827–2851. [9] K.J. Ansari, M.A. Salman, M. Mursaleen and A.H.H. Al-Abied, On Jakimovski-Leviatan-P˘alt˘anea approximating operators involving Boas-Buck-type polynomials, J. King Saud. Univ. Sci. 32 (2020), 3018–3025. [10] K.J. Ansari and F. Usta, A generalization of Szasz-Mirakyan operators based on α non-negative parameter, Symmetry 14 (2022), no. 8, 1–19. [11] S.N. Bernstein, Demonstration du theoreme de Weierstrass fondee sur le calculdes probabilities, Commun. Soc. Math. Kharkov 13 (1913), 1–2. [12] P.L. Butzer, Linear combinations of Bernstein polynomials, Canad. J. Math. 5 (1953), no. 2, 559–567. [13] X. Chen, J. Tan, Z. Liu and J. Xie, Approximation of functions by a new family of generalized Bernstein operators, J. Math. Anal. Appl. 450 (2017), 244–261. [14] M.M. Derriennic, Sur l approximation des fonctions integrables par des polynomes de Bernstein modifies, J. Approx. Theory 31 (1981), 325–343. [15] J.L. Durrmeyer, Une formule d’inversion de la transformee de Laplace: Applications a La Theorie des Moments, These de 3e cycle, Faculte des Sciences de l’ Universite de Paris, 1967. [16] S.G. Gal and V. Gupta, Quantitative estimates for a new complex Durrmeyer operators in compact disks, Appl. Math. Comput. 218 (2011), 2944–2951. [17] H. Gonska, Quantitative Aussagen zur Approximation durch positive lineare operatoren, Ph.D. thesis, Universit at Duisburg, 1979. [18] V. Gupta, Some approximation properties of q−Durrmeyer operators, Appl. Math. Comput. 197 (2008), 172–178. [19] V. Gupta and MT. Rassias, Moments of linear positive operators and approximation, Springer New York, 2019. [20] V. Gupta, G. Tachev and A.M. Acu, Modified Kantorovich operators with better approximation properties, Numer. Algor. 81 (2019), 125–149. [21] A. Kajla and T. Acar, A new modification of Durrmeyer type mixed hybrid operators, Carpathian J. Math. 34 (2018), no. 1, 47–56. [22] A. Kajla and T. Acar, Blending type approximation by generalized Bernstein-Durrmeyer type operators, Miskolc. Math. Notes 19 (2018), no. 1, 319–336. [23] A. Kajla and T. Acar, Modified α-Bernstein operators with better approximation properties, Ann. Funct. Anal. 10 (2019), 570–582. [24] A. Kajla and M. Goyal, Generalized Bernstein-Durrmeyer operators of blending type, Afr. Mat. 30 (2019), 1103–1118. [25] H. Khosravian-Arab, M. Dehghan and M.R. Eslahchi, A new approach to improve the order of approximation of the Bernstein operators: Theory and applications, Numer. Algor. 77 (2018), no. 1, 111–150. [26] C.A. Micchelli, Saturation classes and iterates of operators, Ph. D. Thesis, Stanford University, 1969. [27] S.A. Mohiuddine, T. Acar and M.A. Alghamdi, Genuine modified Bernstein-Durrmeyer operators, J. Inequal. Appl. 2018 (2018), 1–13. [28] M. Mursaleen, A.H.H. Al-Abied and K.J. Ansari, Approximation by Jakimovski-Leviatan-P˘alt˘anea approximating operators involving Sheffer polynomials, RACSAM 113 (2019), 1251–1265. [29] D. Occorsio, MG. Russo and W. Themistoclakis, Some numerical applications of generalized Bernstein operators, CMA 4 (2021), no. 2, 186–214. [30] R. Paltanea, A class of Durrmeyer type operators preserving linear functions, Ann. Tiberiu Popoviciu Sem. Funct. Equat. Approxim. Convex. (Cluj-Napoca) 5 (2007), 109–117. [31] G.M. Phillips, Bernstein polynomials based on the q-integers, The heritage of P. L. Chebyshev: A Festschrift in honor of the 70th-birthday of professor T. J. Rivlin. Ann. Numer. Math. 4 (1997), 511–518. | ||
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