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Abstrakty
In this paper, we present a Hyers–Ulam stability result for the approximately linear recurrence in Banach spaces. An example is given to show the results in more tangible form.
Wydawca
Czasopismo
Rocznik
Tom
Strony
81--85
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
- Department of Mathematics, Malayer Branch, Islamic Azad University, Malayer, Iran
autor
- Department of Computer Science, Paderborn University, Paderborn, Germany
autor
- Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195-363, Iran
Bibliografia
- [1] R. P. Agarwal, B. Xu and W. Zhang, Stability of functional equations in single variable, J. Math. Anal. Appl. 288 (2003), 852–869.
- [2] J. Brzdȩk, D. Popa and B. Xu, Note on the nonstability of the linear recurrence, Abh. Math. Semin. Univ. Hambg. 76 (2006), 183–189.
- [3] J. Brzdȩk, D. Popa and B. Xu, The Hyers–Ulam stability of the nonlinear recurrences, J. Math. Anal. Appl. 335 (2007), 443–449.
- [4] J. Brzdȩk, D. Popa and B. Xu, On nonstability of the linear recurrence of order one, J. Math. Anal. Appl. 367 (2010), 146–153.
- [5] S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, Singapore, 2002.
- [6] M. Eshaghi and S. Abbaszadeh, Approximate generalized derivations close to derivations in Lie C∗-algebras, J. Appl. Anal. 21 (2015), 37–43.
- [7] M. Eshaghi Gordji, Nearly involutions on Banach algebras: A fixed point approach, Fixed Point Theory 14 (2013), 117–123.
- [8] M. E. Gordji and S. Abbaszadeh, Intuitionistic fuzzy almost Cauchy–Jensen mappings, Demonstr. Math. 49 (2016), 18–25. Web of ScienceGoogle Scholar.
- [9] M. E. Gordji and S. Abbaszadeh, Theory of Approximate Functional Equations: In Banach Algebras, Inner Product Spaces and Amenable Groups, Elsevier, Amsterdam, 2016.
- [10] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. 27 (1941), 222–224.
- [11] D. H. Hyers, G. Isac and T. M. Rassias, Stability of Functional Equations in Several Variables, Progr. Nonlinear Differential Equations Appl. 34, Springer, Cham, 2012.
- [12] S. Jung, Hyers–Ulam–Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, 2001. Web of ScienceGoogle Scholar.
- [13] D. Popa, Hyers–Ulam–Rassias stability of a linear recurrence, J. Math. Anal. Appl. 309 (2005), 591–597.
- [14] D. Popa, Hyers–Ulam stability of the linear recurrence with constant coefficients, Adv. Difference Equ. 2005 (2005), 101–107.
- [15] T. M. Rassias, Functional Equations, Inequalities and Applications, Kluwer Academic, Dordrecht, 2003.
- [16] S. M. Ulam, Problems in Modern Mathematics, Wiley, New York, 1940.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
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