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A q-analogue of the multiplicative calculus: Q-multiplicative calculus
1. | Yildiz Technical University, Mathematical Engineering Department, Istanbul, Turkey, Turkey |
References:
[1] |
A. E. Bashirov, E. Kurpinar and A. Özyapici, Multiplicative calculus and its applications, J. Math. Anal. Appl., 337 (2008), 36-48.
doi: 10.1016/j.jmaa.2007.03.081. |
[2] |
A. E. Bashirov, E. Misirli, Y. Tandoğdu and A. Özyapici, On modeling with multiplicative differential equations, Appl. Math. J. Chinese Univ. Ser. B, 26 (2011), 425-438.
doi: 10.1007/s11766-011-2767-6. |
[3] |
T. Ernst, A New Notation for q-Calculus a New q-Taylor Formula, U. U. D. M. Report 1999:25, ISSN 1101-3591, Department of Mathematics, University, Uppsala, 1999. |
[4] |
D. A. Filip and C. Piatecki, A Non-Newtonian Examination of the Theory of Exogenous Economic Growth, CNCSIS - UEFISCSU(project number PNII IDEI 2366/2008) and LEO, 2010. |
[5] |
M. Grossman and R. Katz, Non-Newtonian Calculus, Lee Press, Pigeon Cove, MA, 1972. |
[6] |
F. H. Jackson, On q-definite integrals, Quart. J. Pure Appl. Math., 41 (1910), 193-203. |
[7] |
S.-C. Jing and H.-Y. Fan, q-Taylor's formula with its q-remainder, Commun. Theor. Phys., 23 (1995), 117-120.
doi: 10.1088/0253-6102/23/1/117. |
[8] |
V. Kac and P. Cheung, Quantum Calculus, Universitext, Springer-Verlag, New York, 2002.
doi: 10.1007/978-1-4613-0071-7. |
[9] |
R. Koekoek and R. F. Swarttouw, Askey-Scheme of Hypergeometric Orthogonal Polynomials and Its q-Analogue, Report No 98-17, Delft University of Technology, 1998. |
[10] |
E. Koelink, Eight lectures on quantum groups and q-special functions, Rev. Colombiana de Mat., 30 (1996), 93-180. |
[11] |
T. H. Koornwinder and R. F. Swarttouw, On q-analogues of the Fourier and Hankel transforms, Trans. Amer. Math. Soc., 333 (1992), 445-461.
doi: 10.2307/2154118. |
[12] |
P. M. Rajković, M. S. Stanković and S. D. Marinković, Mean value theorems in q-calculus, Mat. Vesnik, 54 (2002), 171-178. |
[13] |
F. Ryde, A Contribution to the Theory of Linear Homogeneous Geometric Difference Equations (q-Difference Equations), Dissertation, Lund, 1921. |
[14] |
D. Stanley, A multiplicative calculus, Primus, IX (1999), 310-326. |
show all references
References:
[1] |
A. E. Bashirov, E. Kurpinar and A. Özyapici, Multiplicative calculus and its applications, J. Math. Anal. Appl., 337 (2008), 36-48.
doi: 10.1016/j.jmaa.2007.03.081. |
[2] |
A. E. Bashirov, E. Misirli, Y. Tandoğdu and A. Özyapici, On modeling with multiplicative differential equations, Appl. Math. J. Chinese Univ. Ser. B, 26 (2011), 425-438.
doi: 10.1007/s11766-011-2767-6. |
[3] |
T. Ernst, A New Notation for q-Calculus a New q-Taylor Formula, U. U. D. M. Report 1999:25, ISSN 1101-3591, Department of Mathematics, University, Uppsala, 1999. |
[4] |
D. A. Filip and C. Piatecki, A Non-Newtonian Examination of the Theory of Exogenous Economic Growth, CNCSIS - UEFISCSU(project number PNII IDEI 2366/2008) and LEO, 2010. |
[5] |
M. Grossman and R. Katz, Non-Newtonian Calculus, Lee Press, Pigeon Cove, MA, 1972. |
[6] |
F. H. Jackson, On q-definite integrals, Quart. J. Pure Appl. Math., 41 (1910), 193-203. |
[7] |
S.-C. Jing and H.-Y. Fan, q-Taylor's formula with its q-remainder, Commun. Theor. Phys., 23 (1995), 117-120.
doi: 10.1088/0253-6102/23/1/117. |
[8] |
V. Kac and P. Cheung, Quantum Calculus, Universitext, Springer-Verlag, New York, 2002.
doi: 10.1007/978-1-4613-0071-7. |
[9] |
R. Koekoek and R. F. Swarttouw, Askey-Scheme of Hypergeometric Orthogonal Polynomials and Its q-Analogue, Report No 98-17, Delft University of Technology, 1998. |
[10] |
E. Koelink, Eight lectures on quantum groups and q-special functions, Rev. Colombiana de Mat., 30 (1996), 93-180. |
[11] |
T. H. Koornwinder and R. F. Swarttouw, On q-analogues of the Fourier and Hankel transforms, Trans. Amer. Math. Soc., 333 (1992), 445-461.
doi: 10.2307/2154118. |
[12] |
P. M. Rajković, M. S. Stanković and S. D. Marinković, Mean value theorems in q-calculus, Mat. Vesnik, 54 (2002), 171-178. |
[13] |
F. Ryde, A Contribution to the Theory of Linear Homogeneous Geometric Difference Equations (q-Difference Equations), Dissertation, Lund, 1921. |
[14] |
D. Stanley, A multiplicative calculus, Primus, IX (1999), 310-326. |
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