|
[1]
|
P. Appell, Sur une classe de polynômes, Ann. Sci. École Norm. Sup., 9 (1880), 119–144.
doi: 10.24033/asens.186.
|
|
[2]
|
T. Acar, M. Mursaleen and S. A. Mohiuddine, Stancu type $(p, q)$-Szász-Mirakyan-Baskakov operators, Commun. Fac. Sci. Univ. Ank. Series A1., 67 (2018), 116-128.
doi: 10.1501/Commua1_0000000835.
|
|
[3]
|
A. Alotaibi and M. Mursaleen, Approximation of Jakimovski-Leviatan-Beta type integral operators via $q$-calculus, AIMS Mathematics, 5 (2020), 3019-3034.
doi: 10.3934/math.2020196.
|
|
[4]
|
Ç. Atakut and İ. Büyükyazıcı, Approximation by modified integral type Jakimovski-Leviatan operators, Filomat, 30 (2016), 29-39.
doi: 10.2298/FIL1601029C.
|
|
[5]
|
A. Alotaibi, M. Nasiruzzaman and M. Mursaleen, A Dunkl type generalization of Szász operators via post-quantum calculus, J. Inequal. Appl., 2018 (2018), 287, 15 pp.
doi: 10.1186/s13660-018-1878-5.
|
|
[6]
|
A. Alotaibi, M. Nasiruzzaman and M. Mursaleen, Approximation by Phillips operators via q-Dunkl generalization based on a new parameter, Journal of King Saud University-Science, 33 (2021), 101413.
doi: 10.1016/j.jksus.2021.101413.
|
|
[7]
|
T. Acar, A. Aral and S. A. Mohiuddine, Approximation By Bivariate $(p, q)$-Bernstein Kantorovich operators, Iran. J. Sci. Technol. Trans. A Sci., 42 (2018), 655-662.
doi: 10.1007/s40995-016-0045-4.
|
|
[8]
|
T. Acar, S. A. Mohiuddine and M. Mursaleen, Approximation by $(p, q)$-Baskakov-Durrmeyer-Stancu operators, Comp. Anal. Op. Theory., 12 (2018), 1453-1468.
doi: 10.1007/s11785-016-0633-5.
|
|
[9]
|
Ç. Atakut and N. İspir, Approximation by modified Szá sz-Mirakjan operators on weighted spaces, Proc. Indian Acad. Sci. Math. Sci., 112 (2002), 571-578.
doi: 10.1007/BF02829690.
|
|
[10]
|
F. Altomare and M. Campiti, Korovkin-Type Approximation Theory and Its Applications, De Gruyter Studies in Mathematics, Vol. 17 Walter de Gruyter and Co., Berlin., 1994.
doi: 10.1515/9783110884586.
|
|
[11]
|
X. Guo, L. X. Li and Q. Wu, Modeling interactive components by coordinate kernel polynomial models, Mathematical Foundations of Computing, 3 (2020), 263-277.
doi: 10.3934/mfc.2020010.
|
|
[12]
|
Z.-C. Guo, D.-H. Xiang, X. Guo and D.-X. Zhou, Thresholded spectral algorithms for sparse approximations, Anal. Appl., 15 (2017), 433-455.
doi: 10.1142/S0219530517500026.
|
|
[13]
|
A. D. Gadžiev, Theorems of the Type of P.P. Korovkin's Theorems, Math. Notes., 20 (1976), 995-998.
|
|
[14]
|
A. Jakimovski and D. Leviatan, Generalized Szász operators for the approximation in the infinite interval, Mathematica (Cluj), 11 (1969), 97-103.
|
|
[15]
|
A. Kajla, S. A. Mohiuddine and A. Alotaibi, Blending-type approximation by Lupaş- Durrmeyer-type operators involving Pólya distribution, Math. Meth. Appl. Sci., 44 (2021), 9407-9418.
doi: 10.1002/mma.7368.
|
|
[16]
|
A. Kajla, S. A. Mohiuddine and A. Alotaibi, Durrmeyer-type generalization of $\mu$- Bernstein operators, Filomat, 36 (2022), 349-360.
doi: 10.2298/FIL2201349K.
|
|
[17]
|
P. P. Korovkin, Linear Operators and Approximation Theory, Russian Monographs and Texts on Advanced Mathematics and Physics, Vol. III Gordon and Breach Publishers, Inc., New York; Hindustan Publishing Corp. (India), Delhi, 1960.
|
|
[18]
|
B. Lenze, On Lipschitz type maximal functions and their smoothness spaces, Nederl. Akad. Indag. Math., 50 (1988), 53-63.
|
|
[19]
|
G. V. Milovanovic, M. Mursaleen and M. Nasiruzzaman, Modified Stancu type Dunkl generalization of Szász-Kantorovich operators, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. RACSAM, 112 (2018), 135-151.
doi: 10.1007/s13398-016-0369-0.
|
|
[20]
|
M. Mursaleen, M. Nasiruzzaman and A. Alotaibi, On Modified Dunkl generalization of Szász operators via $q$-calculus, J. Inequal. Appl., 2017 (2017), 38, 12 pp.
doi: 10.1186/s13660-017-1311-5.
|
|
[21]
|
M. Mursaleen, K. J. Ansari and A. Khan, Approximation by Kantorovich type $q$-Bernstein-Stancu operators, Complex Anal. Oper. Theory., 11 (2017), 85-107.
doi: 10.1007/s11785-016-0572-1.
|
|
[22]
|
S. A. Mohiuddine, B. Hazarika and M. A. Alghamdi, Ideal relatively uniform convergence with Korovkin and Voronovskaya types approximation theorems, Filomat, 33 (2019), 4549-4560.
doi: 10.2298/FIL1914549M.
|
|
[23]
|
S. A. Mohiuddine, A. Ahmad, F. Özger, A. Alotaibi and B. Hazarika, Approximation by the parametric generalization of Baskakov-Kantorovich operators linking with Stancu operators, Iran. J. Sci. Technol. Trans. Sci., 45 (2021), 593-605.
doi: 10.1007/s40995-020-01024-w.
|
|
[24]
|
S. A. Mohiuddine and U. Kadak, Generalized statistically almost convergence based on the difference operator which includes the $(p, q)$-gamma function and related approximation theorems, Results Math., 73 (2018), Paper No. 9, 31 pp.
doi: 10.1007/s00025-018-0789-6.
|
|
[25]
|
S. A. Mohiuddine, Approximation by bivariate generalized BernsteinSchurer operators and associated GBS operators, Adv. Difference Equ., 2020 (2020), Paper No. 676, 17 pp.
doi: 10.1186/s13662-020-03125-7.
|
|
[26]
|
S. A. Mohiuddine and F. Özger, Approximation of functions by Stancu variant of Bernstein-Kantorovich operators based on shape parameter $\alpha$, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. RACSAM, 114 (2020), 70, 17 pp.
doi: 10.1007/s13398-020-00802-w.
|
|
[27]
|
S. A. Mohiuddine, T. Acar and A. Alotaibi, Construction of a new family of Bernstein-Kantorovich operators, Math. Meth. Appl. Sci., 40 (2017), 7749-7759.
doi: 10.1002/mma.4559.
|
|
[28]
|
M. Nasiruzzaman and A. F. Aljohani, Approximation by Szász-Jakimovski-Leviatan type operators via aid of Appell polynomials, Journal of Functions Spaces, 2020 (2020), 9657489, 11 pp.
doi: 10.1155/2020/9657489.
|
|
[29]
|
M. Nasiruzzaman and A. F. Aljohani, Approximation by parametric extension of Szasz-Mirakjan-Kantorovich operators involving the Appell polynomials, Journal of functions spaces, 2020 (2020), 8863664, 11 pp.
doi: 10.1155/2020/8863664.
|
|
[30]
|
M. Nasiruzzaman, K. J. Ansari and M. Mursaleen, On the Parametric Approximation Results of Phillips Operators Involving the q-Appell Polynomials, Iran J. Sci. Technol Trans A Sci., 46 (2022), 251-263.
doi: 10.1007/s40995-021-01219-9.
|
|
[31]
|
F. Özger, On new Bézier bases with Schurer polynomials and corresponding results in approximation theory, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 69 (2020), 376-393.
doi: 10.31801/cfsuasmas.510382.
|
|
[32]
|
F. Özger, H. M. Srivastava and S. A. Mohiuddine, Approximation of functions by a new class of generalized Bernstein-Schurer operators, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. RACSAM, 114 (2020), 173, 21 pp.
doi: 10.1007/s13398-020-00903-6.
|
|
[33]
|
B. Wood, Generalized Szász operators for the approximation in the complex domain, SIAM J. Appl. Math., 17 (1969), 790-801.
doi: 10.1137/0117071.
|
|
[34]
|
O. Szász, Generalization of Bernstein's polynomials to the infinite interval, J. Res. Nat. Bur. Stds., 45 (1950), 239-245.
doi: 10.6028/jres.045.024.
|
|
[35]
|
M. A. Ozarslan and H. Aktuğlu, Local approximation for certain King type operators, Filomat, 27 (2013), 173-181.
doi: 10.2298/FIL1301173O.
|
|
[36]
|
N. Rao, A. Wafi and A. M. Acu, $q$ -Szász-Durrmeyer type operators based on Dunkl analogue, Complex Anal. Oper. Theory., 13 (2019), 915-934.
doi: 10.1007/s11785-018-0816-3.
|
|
[37]
|
N. Rao, M. Nasiruzzaman, M. Heshamuddin and M. Shadab, Approximation properties by modified Baskakov Durrmeyer operators based on shape parameter-$\alpha$, Iran. J. Sci. Technol. Trans. A Sci., 45 (2021), 1457-1465.
doi: 10.1007/s40995-021-01125-0.
|
|
[38]
|
M. Rosenblum, Generalized Hermite polynomials and the Bose-like oscillator calculus, Oper. Theory Adv. Appl., 73 (1994), 369-396.
|
|
[39]
|
S. Sucu, Dunkl analogue of Sz$\acute{a}$sz operators, Appl. Math. Comput., 244 (2014), 42-48.
doi: 10.1016/j.amc.2014.06.088.
|
|
[40]
|
O. Shisha and B. Bond, The degree of convergence of sequences of linear positive operators, Proc. Nat. Acad. Sci. U.S.A., 60 (1968), 1196-1200.
doi: 10.1073/pnas.60.4.1196.
|
|
[41]
|
D.X. Zhou, Deep distributed convolutional neural networks, Universality, Anal. Appl., 16 (2018), 895-919.
doi: 10.1142/S0219530518500124.
|
{{journal.titleEn}} 
DownLoad: