پیوندهای مفید
آمار
| تعداد نشریات | 32 |
| تعداد شمارهها | 856 |
| تعداد مقالات | 8,310 |
| تعداد مشاهده مقاله | 52,844,402 |
| تعداد دریافت فایل اصل مقاله | 9,271,379 |
Taylor's formula for general quantum calculus | ||
| Journal of Mathematical Modeling | ||
| مقاله 6، دوره 11، شماره 3، دی 2023، صفحه 491-505 اصل مقاله (173.63 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2023.23936.2139 | ||
| نویسندگان | ||
| Svetlin G. Georgiev1؛ Sanket Tikare* 2 | ||
| 1Department of Mathematics, Sorbonne University, Paris, France | ||
| 2Department of Mathematics, Ramniranjan Jhunjhunwala College,\\ Mumbai, Maharashtra 400 086, India | ||
| چکیده | ||
| Let $I\subseteq\mathbb{R}$ be an interval and $\beta\colon I\to I$ a strictly increasing continuous function with a unique fixed point $s_0\in I$ satisfying $(t-s_0)(\beta(t)-t)\le 0$ for all $t\in I$. Hamza et al. introduced the general quantum difference operator $D_{\beta}$ by $D_{\beta}f(t):=\frac{f(\beta(t))-f(t)}{\beta(t)-t}$ if $t\ne s_0$ and $D_{\beta}f(t):=f'(s_0)$ if $t=s_0$. In this paper, we establish results concerning Taylor's formula associated with $D_{\beta}$. For this, we define two types of monomials and then present our main results. The obtained results are new in the literature and are useful for further research in the field. | ||
| کلیدواژهها | ||
| Quantum calculus؛ quantum difference operator؛ $\beta$-derivative؛ $\beta$-integral؛ Taylor's formula؛ monomials | ||
| مراجع | ||
|
[1] B. Ahmad, S.K. Ntouyas, J. Tariboon, Quantum Calculus: New Concepts, Impulsive IVPs and BVPs, Inequalities, World Scientific, Sinagpore, 2016. [2] R. Alvarez-Nodarse, On characterizations of classical polynomials, J. Comput. Appl. Math. 196 (2006) 320–337. [3] M.H. Annaby, A.E. Hamza, K.A. Aldwoah, Hahn difference operator and associated Jackson– Norlund integrals, J. Optim. Theory Appl. 154 (2012) 133–153. [4] M.H. Annaby, Z.S. Mansour, q-Taylor and interpolation series for Jackson q-difference operators, J. Math. Anal. Appl. 344 (2008) 472–483. [5] A.M.C. Brito da Cruz, Symmetric Quantum Calculus, Ph.D. Thesis, Universidade de Aveiro, Por- tugal, 2012. [6] A.M.C. Brito da Cruz, N. Martins, The q-symmetric variational calculus, Comput. Math. Appl. 64 (2012) 2241–2250. [7] A.M.C. Brito da Cruz, N. Martins, D.F.M. Torres, A symmetric quantum calculus, In Differential and Difference Equations with Applications: Contributions from the International Conference on Differential & Difference Equations and Applications (2013) 359–366. [8] A.M.C. Brito da Cruz, N. Martins, General quantum variational calculus, Stat. Optim. Inf. Comput. 6 (2018) 22–41. [9] J.L. Cardoso, Variations around a general quantum operator, Ramanujan J. 54 (2021) 555–569. [10] J.L. Cardoso, A β -Sturm–Liouville problem associated with the general quantum operator, J. Dif- fer. Equ. 27 (2021) 579–595. [11] R.S. Costas-Santos, F. Marcellan, Second structure relation for q-semiclassical polynomials of the Hahn Tableau, J. Math. Anal. Appl. 329 (2007) 206–228. [12] R.S. Costas-Santos, F. Marcellan, q-Classical orthogonal polynomials: A general difference calcu- lus approach, Acta Appl. Math. 111 (2020) 107–128. [13] A. Dobrogowska, A. Odzijewicz, Second order q-difference equations solvable by factorization method, Comput. Appl. Math. 193 (2006) 319–346. [14] S. Elaydi, An Introduction to Difference Equations, Third Edition, Springer International Publish- ing, New York, 2008. [15] T. Ernst, A Comprehensive Treatment of q-Calculus, Springer Science & Business Media, New York, 2012. [16] N. Faried, E.M. Shehata, R.M. El Zafarani, Theory of nth-order linear general quantum difference equations, Adv. Differ. Equ. 2018 (2018) 264 . [17] N. Faried, E.M. Shehata, R.M.El Zafarani, Quantum exponential functions in a Banach algebra, J. Fixed Point Theory Appl. 22 (2020) 22. [18] S. Goldberg, Introduction to Difference Equations: With Illustrative Examples from Economics, Psychology, and Sociology, Dover Publications, Inc., New York, 1986. [19] A.E. Hamza, AS.M. Sarhan, E.M. Shehata, K.A. Aldwoah, A general quantum difference calculus, Adv. Differ. Equ. 2015 (2015) 182 . [20] A.E. Hamza, E.M. Shehata, Some inequalities based on a general quantum difference operator, J. Inequal. Appl. 2015 (2015) 38. [21] A.E. Hamza, E.M. Shehata, Existence and uniqueness of solutions of general quantum difference equations, Adv. Dyn. Syst. Appl. 11 (2016) 45–58. [22] A.E. Hamza, E.M. Shehata, P. Agarwal, Leibnizs rule and Fubinis theorem associated with a gen- eral quantum difference operator, In Computational Mathematics and Variational Analysis, (121– 134). Cham: Springer International Publishing, 2020. [23] V.G. Kac, P. Cheung, Quantum Calculus, Springer, New York, 2002. [24] A.O. Karim, E.M. Shehata, J.L. Cardoso, The directional derivative in general quantum calculus, Symmetry 14 (2022) 1766. [25] W.G. Kelley, A.C. Peterson, Difference Equations: An Introduction with Applications, Academic press, San Diego, 2001. [26] H. Levy, F. Lessman, Finite Difference Equations, Dover Publications, Inc., New York, 1992. [27] A.B. Malinowska, D.F.M. Torres, Quantum Variational Calculus, Springer International Publish- ing, New York, 2014. [28] R.E. Mickens, Difference Equations: Theory, Applications and Advanced Topics, Third Edition, CRC Press, Boca Raton, 2015. [29] K. Oraby, A.E. Hamza, Taylor theory associated with Hahn difference operator, J. Inequal. Appl. 2020 124 (2020). [30] AS.M. Sarhan, E.M. Shehata, On the fixed points of certain types of functions for constructing associated calculi, J. Fixed Point Theory Appl. 20 (2018) 124. [31] E.M. Shehata, N. Faried, R.M. El Zafarani, A general quantum Laplace transform, Adv. Differ. Equ. 2020 (2020) 613. [32] E.M. Shehata, R.M. El Zafarani, A β -Convolution theorem associated with the general quantum difference operator, J. Funct. Spaces 2022 (2022) 1581362. [33] E.M. Shehata, N. Faried, R.M. El Zafarani, Stability of first order linear general quantum difference equations in a Banach algebra, Appl. Math. 16 (2022) 101–108. [34] L. Verde-Star, Characterization and construction of classical orthogonal polynomials using a ma- trix approach, Linear Algebra Appl. 438 (2013) 3635–3648. | ||
|
آمار تعداد مشاهده مقاله: 503 تعداد دریافت فایل اصل مقاله: 646 |
||