Research Article
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On second-order q-difference operators

Year 2024, Volume: 73 Issue: 4, 1040 - 1049
https://doi.org/10.31801/cfsuasmas.1393825

Abstract

The minimal and maximal operators defined by second-order q-difference operator are discussed in this paper. Spectrum sets of these defined operators have been determined. In addition, two extensions of the minimal operator is also mentioned.

References

  • Ahmad, B., Alsaedi, A., Ntouyas, S. K., A study of second-order q-difference equations with boundary conditions, Adv. Differ. Equ. 1 (2012), 1–10. https://doi:10.1186/1687-1847-2012-35
  • Ahmad, B., Ntouyas, S. K., Boundary value problems for q-difference inclusions, Abstr. Appl. Abstr. Appl. Anal., Article ID 292860 (2011), 1–15. https://doi:10.1155/2011/292860
  • Allahverdiev, B. P., Tuna, H., Qualitative spectral analysis of singular q- Sturm–Liouville operators, Bull. Malays. Math. Sci. Soc., 43(2) (2020), 1391–1402. https://doi.org/10.1007/s40840-019-00747-3
  • Annaby, M. H., Mansour, Z. S., q-Fractional Calculus and Equations, Lecture Notes in Mathematics, vol. 2056, Springer, Heidelberg 2012. https://doi.org/10.1007/978-3-642-30898-7
  • Aral, A., A generalization of Szasz Mirakyan operators based on q-integers, Math. Comput. Modelling, 47(9-10) (2008), 1052–1062. https://doi.org/10.1016/j.mcm.2007.06.018
  • Bangerezako, G., An Introduction to q-Difference Equations, UCL, Institut de Mathematiques Pures and Appliquees, Seminaire de Mathematiques, Rapport n.354, Louvain, 2008.
  • Bromwich, T. J., I’A., An Introduction to the Theory of Infinite Series. 1st edn. Macmillan, London, 1908.
  • Euler, L., Introductio in Analysin Infinitorum, vol. 1. Lausanne, Switzerland, Bousquet, 1748 (in Latin).
  • Dobrogowska, A., Odzijewicz, A., Second order q-difference equations solvable by factorization method, J. Comput. Appl. Math., 193(1) (2006), 319–346. https://doi.org/10.1016/j.cam.2005.06.009
  • Phillips, G. M., Interpolation and Approximation by Polynomials, New York, Springer, 2003. https://doi.org/10.1007/b97417
  • Jackson, M., On a q-definite integrals, Quart. J. Pure and Appl. Math., 41 (1910), 193–203.
  • Jackson, F. H., On q-functions and a certain difference operator, Trans. Roy. Soc. Edinb., 46(2) (1909), 253–281. https://doi.org/10.1017/S0080456800002751
  • Naimark, M. A., Linear Differential Operators, Part II, Linear Differential Operators in Hilbert Space, Frederick Ungar, New York, 1968.
  • Stein, E. M., Shakarchi R. Complex Analysis. Princeton, NJ, USA, Princeton Univ. Press, 2003.
  • Yu, C., Wang, J., Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives, Adv. Differ. Equ., (2013), 1–11. https://doi:10.1186/1687-1847-2013-124
  • Ota, S., Some classes of q-deformed operators, J. Operator Theory, 48(1) (2002), 151–186.
  • Sertbaş, M., Saral, C., q-Difference operator and Its q-cohyponormality, Complex Anal. Oper. Theory, 14(8) (2020), 84. https://doi.org/10.1007/s11785-020-01043-w
Year 2024, Volume: 73 Issue: 4, 1040 - 1049
https://doi.org/10.31801/cfsuasmas.1393825

Abstract

References

  • Ahmad, B., Alsaedi, A., Ntouyas, S. K., A study of second-order q-difference equations with boundary conditions, Adv. Differ. Equ. 1 (2012), 1–10. https://doi:10.1186/1687-1847-2012-35
  • Ahmad, B., Ntouyas, S. K., Boundary value problems for q-difference inclusions, Abstr. Appl. Abstr. Appl. Anal., Article ID 292860 (2011), 1–15. https://doi:10.1155/2011/292860
  • Allahverdiev, B. P., Tuna, H., Qualitative spectral analysis of singular q- Sturm–Liouville operators, Bull. Malays. Math. Sci. Soc., 43(2) (2020), 1391–1402. https://doi.org/10.1007/s40840-019-00747-3
  • Annaby, M. H., Mansour, Z. S., q-Fractional Calculus and Equations, Lecture Notes in Mathematics, vol. 2056, Springer, Heidelberg 2012. https://doi.org/10.1007/978-3-642-30898-7
  • Aral, A., A generalization of Szasz Mirakyan operators based on q-integers, Math. Comput. Modelling, 47(9-10) (2008), 1052–1062. https://doi.org/10.1016/j.mcm.2007.06.018
  • Bangerezako, G., An Introduction to q-Difference Equations, UCL, Institut de Mathematiques Pures and Appliquees, Seminaire de Mathematiques, Rapport n.354, Louvain, 2008.
  • Bromwich, T. J., I’A., An Introduction to the Theory of Infinite Series. 1st edn. Macmillan, London, 1908.
  • Euler, L., Introductio in Analysin Infinitorum, vol. 1. Lausanne, Switzerland, Bousquet, 1748 (in Latin).
  • Dobrogowska, A., Odzijewicz, A., Second order q-difference equations solvable by factorization method, J. Comput. Appl. Math., 193(1) (2006), 319–346. https://doi.org/10.1016/j.cam.2005.06.009
  • Phillips, G. M., Interpolation and Approximation by Polynomials, New York, Springer, 2003. https://doi.org/10.1007/b97417
  • Jackson, M., On a q-definite integrals, Quart. J. Pure and Appl. Math., 41 (1910), 193–203.
  • Jackson, F. H., On q-functions and a certain difference operator, Trans. Roy. Soc. Edinb., 46(2) (1909), 253–281. https://doi.org/10.1017/S0080456800002751
  • Naimark, M. A., Linear Differential Operators, Part II, Linear Differential Operators in Hilbert Space, Frederick Ungar, New York, 1968.
  • Stein, E. M., Shakarchi R. Complex Analysis. Princeton, NJ, USA, Princeton Univ. Press, 2003.
  • Yu, C., Wang, J., Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives, Adv. Differ. Equ., (2013), 1–11. https://doi:10.1186/1687-1847-2013-124
  • Ota, S., Some classes of q-deformed operators, J. Operator Theory, 48(1) (2002), 151–186.
  • Sertbaş, M., Saral, C., q-Difference operator and Its q-cohyponormality, Complex Anal. Oper. Theory, 14(8) (2020), 84. https://doi.org/10.1007/s11785-020-01043-w
There are 17 citations in total.

Details

Primary Language English
Subjects Ordinary Differential Equations, Difference Equations and Dynamical Systems, Operator Algebras and Functional Analysis
Journal Section Research Articles
Authors

Meltem Sertbaş 0000-0001-9606-951X

Publication Date
Submission Date November 21, 2023
Acceptance Date July 23, 2024
Published in Issue Year 2024 Volume: 73 Issue: 4

Cite

APA Sertbaş, M. (n.d.). On second-order q-difference operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 73(4), 1040-1049. https://doi.org/10.31801/cfsuasmas.1393825
AMA Sertbaş M. On second-order q-difference operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 73(4):1040-1049. doi:10.31801/cfsuasmas.1393825
Chicago Sertbaş, Meltem. “On Second-Order Q-Difference Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73, no. 4 n.d.: 1040-49. https://doi.org/10.31801/cfsuasmas.1393825.
EndNote Sertbaş M On second-order q-difference operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73 4 1040–1049.
IEEE M. Sertbaş, “On second-order q-difference operators”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 73, no. 4, pp. 1040–1049, doi: 10.31801/cfsuasmas.1393825.
ISNAD Sertbaş, Meltem. “On Second-Order Q-Difference Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 73/4 (n.d.), 1040-1049. https://doi.org/10.31801/cfsuasmas.1393825.
JAMA Sertbaş M. On second-order q-difference operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.;73:1040–1049.
MLA Sertbaş, Meltem. “On Second-Order Q-Difference Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 73, no. 4, pp. 1040-9, doi:10.31801/cfsuasmas.1393825.
Vancouver Sertbaş M. On second-order q-difference operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 73(4):1040-9.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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