We propose certain Durrmeyer-type operators for Apostol-Genocchi polynomials in this research. We explore these operators' approximation attributes and measure the rate of convergence. In addition, we present a direct approximation theorem based on first and second-order modulus of continuity, local approximation findings for Lipschitz class functions and a direct theorem based on the typical modulus of continuity. Finally, we showed a graph illustrating the convergence of the suggested operators and an error table.
Citation: |
[1] |
U. Abel, V. Gupta and M. Ivan, Asymptotic approximation of functions and their derivatives by generalized Baskakov-Szász-Durrmeyer operators, Analysis in Theory and Applications, 21 (2005), 15-26.
doi: 10.1007/BF02835246.![]() ![]() ![]() |
[2] |
F. Altomare and M. Campiti, Korovkin-Type Approximation Theory and its Application, de Gruyter studies in Mathematics, 17, Walter de Gruyter & Co., Berlin, (1994).
doi: 10.1515/9783110884586.![]() ![]() ![]() |
[3] |
S. Araci, Novel identities involving Genocchi numbers and polynomials arising from applications of umbral calculus, Appl. Math. Comput., 233 (2014), 599-607.
doi: 10.1016/j.amc.2014.01.013.![]() ![]() ![]() |
[4] |
N. Deo, N. Bhardwaj and S. P. Singh, Simultaneous approximation on generalized Bernstein Durrmeyer operators, Afr. Mat., 24 (2013), 77-82.
doi: 10.1007/s13370-011-0041-y.![]() ![]() ![]() |
[5] |
N. Deo, M. Dhamija and D. Miclǎuş, New modified Baskakov operators based on the inverse Pólya-Eggenberger distribution, Filomat, 33 (2019), 3537-3550.
doi: 10.2298/FIL1911537D.![]() ![]() ![]() |
[6] |
R. A. DeVore and G. G. Lorentz, Constructive Approximation, Springer, Berlin, 1993.
![]() ![]() |
[7] |
M. Dhamija and N. Deo, Jain-Durrmeyer operators associated with the inverse Pólya-Eggenberger distribution, Appl. Math. Comput., 286 (2016), 15-22.
doi: 10.1016/j.amc.2016.03.015.![]() ![]() ![]() |
[8] |
A. Erençin, Durrmeyer type modification of generalized Baskakov operators, Applied Mathematics and Computation, 218 (2011), 4384-4390.
doi: 10.1016/j.amc.2011.10.014.![]() ![]() ![]() |
[9] |
V. Gupta and A. Aral, Convergence of the q analogue of Szász-Beta operators, Appl. Math. Comput., 216 (2010), 374-380.
doi: 10.1016/j.amc.2010.01.018.![]() ![]() ![]() |
[10] |
H. Jolany, H. Sharifi and R. E. Alikelaye, Some results for the Apostol-Genocchi polynomials of higher order, Bull. Malays. Math. Sci. Soc., 36 (2013), 465-479.
![]() ![]() |
[11] |
P. P. Korovkin, Convergence of linear positive operators in the spaces of continuous functions(Russian), Doklady Akad. Nauk. SSSR(N.N.), 90 (1953), 961-964.
![]() ![]() |
[12] |
Q.-M. Luo, q-Extensions for the Apostol-Genocchi Polynomials, General Mathematics, 17 (2009), 113-125.
![]() ![]() |
[13] |
Q.-M. Luo, Extensions of the Genocchi polynomials and their Fourier expansions and integral representations, Osaka J. Math., 48 (2011), 291-309.
![]() ![]() |
[14] |
Q.-M. Luo and H. M. Srivastava, Some generalizations of the Genocchi polynomials and the Stirling numbers of the second kind, Appl. Math. Comput., 217 (2011), 5702-5728.
doi: 10.1016/j.amc.2010.12.048.![]() ![]() ![]() |
[15] |
Neha and N. Deo, Integral modification of Apostol-Genocchi operators, Filomat, 35 (2021), 2533-2544.
doi: 10.2298/FIL2108533N.![]() ![]() ![]() |
[16] |
H. Ozden and Y. Simsek, Modification and unification of the Apostol-type numbers and polynomials and their applications, Appl. Math. Comput., 235 (2014), 338-351.
doi: 10.1016/j.amc.2014.03.004.![]() ![]() ![]() |
[17] |
C. Prakash, D. K. Verma and N. Deo, Approximation by a new sequence of operators involving Apostol-Genocchi polynomials, Mathematica Slovaca, 71 (2021), 1179-1188.
doi: 10.1515/ms-2021-0047.![]() ![]() ![]() |
[18] |
H. M. Srivastava, M. A. Özarslan and C. Kaanoğlu, Some generalized Lagrange-based Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials, Russ. J. Math. Phys., 20 (2013), 110-120.
doi: 10.1134/S106192081301010X.![]() ![]() ![]() |
[19] |
D. K. Verma, V. Gupta and P. N. Agrawal, Some approximation properties of Baskakov-Durrmeyer-Stancu operators, Appl. Math. Comput., 218 (2012), 6549-6556.
doi: 10.1016/j.amc.2011.12.031.![]() ![]() ![]() |
.....