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T. Acar, \(\left ( p,q\right ) \)-Generalization of Szász-Mirakyan operators. Math. Methods Appl. Sci. 39(10), 2685–2695 (2016)
T. Acar, A. Aral, S.A. Mohiuddine, On Kantorovich modification of (p, q)-Baskakov operators. J. Inequal. Appl 2016, 98 (2016)
T. Acar, P.N. Agrawal, A.S. Kumar, On a modification of (p, q)-Szász-Mirakyan operators. Compl. Anal. Oper. Theory 12(1), 155–167 (2018)
A. Aral, V. Gupta, On the Durrmeyer type modification of the q Baskakov type operators. Nonlinear Anal. Theory Methods Appl. 72(3-4), 1171–1180 (2010)
A. Aral, V. Gupta, Generalized q Baskakov operators. Math. Slovaca 61(4), 619–634 (2011)
A. Aral, V. Gupta, (p, q)-type beta functions of second kind. Adv. Oper. Theory 1(1), 134–146 (2016)
A. Aral, V. Gupta, Applications of (p, q)-gamma function to Szász Durrmeyer operators. Publ. Inst. Math. 102(116), 211–220 (2017)
A. Aral, V. Gupta, R.P. Agarwal, Applications of q Calculus in Operator Theory (Springer, Cham, 2013)
M.-M. Derriennic, Modified Bernstein polynomials and Jacobi polynomials in q-calculus. Rendiconti Del Circolo Matematico Di Palermo, Serie II, Suppl. 76, 269–290 (2005)
R.A. DeVore, G.G. Lorentz, Constructive Approximation (Springer, Berlin, 1993)
T. Ernst, The history of q-calculus and a new method, U.U.D.M Report 2000, vol. 16. ISSN 1101-3591 (Department of Mathematics, Upsala University, 2000)
Z. Finta, Approximation properties of (p, q)-Bernstein type operators. Acta Univ. Sapientiae Math. 8(2), 222–232 (2016)
H. Gauchman, Integral inequalities in q-calculus. Comput. Math. Appl. 47, 281–300 (2004)
V. Gupta, Some approximation properties on q-Durrmeyer operators. Appl. Math. Comput. 197(1), 172–178 (2008)
V. Gupta, (p, q) genuine Bernstein Durrmeyer operators. Boll. Un. Matt. Ital. 9(3), 399–409 (2016)
V. Gupta, A. Aral, Bernstein Durrmeyer operators based on two parameters. Facta Univ. Ser. Math. Inform. 31(1), 79–95 (2016)
F.H. Jackson, On a q-definite integrals. Q. J. Pure Appl. Math. 41, 193–203 (1910)
V. Kac, P. Cheung, Quantum Calculus (Springer, New York, 2002)
A. Lupaş, A q-analogue of the Bernstein operator, in Seminar on Numerical and Statistical Calculus (Cluj-Napoca, 1987), pp. 85–92, Preprint 87–9 Univ. Babes-Bolyai, Cluj
S. Marinković, P. Rajković, M. Stanković, The inequalities for some type of q-integrals. Comput. Math. Appl. 56, 2490–2498 (2008)
G.V. Milovanović, M.Th. Rassias (eds.), Analytic Number Theory, Approximation Theory and Special Functions (Springer, New York, 2014)
G.V. Milovanovic, V. Gupta, N. Malik, (p, q)-beta functions and applications in approximation. Bol. Soc. Mat. Mex. 24(1), 219–237 (2018)
M. Mursaleen, K.J. Ansari, A. Khan, On (p, q)-analogue of Bernstein operators. Appl. Math. Comput. 266, 874–882 (2015)
M. Mursaleen, K.J. Ansari, A. Khan, Erratum to on (p, q)-analogue of Bernstein operators. Appl. Math. Comput. 266, 874–882 (2015), Appl. Math. Comput. 278, 70–71 (2016)
M. Mursaleen, K.J. Ansari, A. Khan, Some approximation results for Bernstein-Kantorovich operators based on (p, q)-calculus (15 Jan 2016). arXiv:1504.05887v4[math.CA]
S. Ostrovska, q-Bernstein polynomials and their iterates. J. Approx. Theory 123, 232–255 (2003)
S. Ostrovska, On the image of the limit q Bernstein operator. Math. Methods Appl. Sci. 32(15), 1964–1970 (2009)
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, 511–518 (1997)
P.N. Sadjang, On the fundamental theorem of (p, q)-calculus and some (p, q)-Taylor formulas. arXiv:1309.3934 [math.QA]
P.N. Sadjang, On the (p, q)-Gamma and the (p, q)-beta functions (22 Jun 2015). arXiv 1506.07394v1
V. Sahai, S. Yadav, Representations of two parameter quantum algebras and p, q-special functions. J. Math. Anal. Appl. 335, 268–279 (2007)
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Gupta, V., Rassias, T.M., Agrawal, P.N., Acu, A.M. (2018). Basics of Post-quantum Calculus. In: Recent Advances in Constructive Approximation Theory. Springer Optimization and Its Applications, vol 138. Springer, Cham. https://doi.org/10.1007/978-3-319-92165-5_3
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