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Hyers stability of lattice derivations | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 13، شماره 1، خرداد 2022، صفحه 3239-3248 اصل مقاله (332.7 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.24090.2668 | ||
| نویسندگان | ||
| Ehsan Movahednia1؛ Choonkil Park2؛ Jung Rye Lee* 3 | ||
| 1Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Iran. | ||
| 2Department of Mathematics, Hanyang University, Seoul, 133-791, South Korea | ||
| 3Department of Data Science, Daejin University, Kyunggi 11159, South Korea | ||
| تاریخ دریافت: 06 مرداد 1400، تاریخ بازنگری: 12 مرداد 1400، تاریخ پذیرش: 30 آبان 1400 | ||
| چکیده | ||
| In this paper, lattice derivations are introduced and studied and the Ulam stability of lattice derivations is investigated by using the direct method and the fixed point method. | ||
| کلیدواژهها | ||
| Banach lattice؛ Ulam stability؛ functional equation؛ f-algebra؛ lattice derivation | ||
| مراجع | ||
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[1] N. K. Agbeko, Stability of maximum preserving functional equations on Banach lattices, Miskolc Math. Notes, 13(2012) 187-196. [2] C. D. Aliprantis and O. Burkinshaw, Positive operators, Springer Science and Business Media, 2006. [3] L. Cadariu and V. Radu, On the stability of the Cauchy functional equation: a fixed point approach, Grazer Mathematische Berichte, 2004. [4] L. Cadariu and V. Radu, Fixed points and the stability of Jensen’s functional equation, J. Inequal. Pure Appl. Math, 4(2003) 1–4. [5] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. U.S.A., 27(1941) 222. [6] Peter Meyer-Nieberg, Banach lattices, Springer Science and Business Media, 2012. [7] A. K. Mirmostafaee and M. S. Moslehian, Fuzzy almost quadratic functions, Results Math., 52(2008) 161-177. [8] M. Mirzavaziri and M. S. Moslehian, A fixed point approach to stability of a quadratic equation, Bull. Braz. Math. Soc., 37(2006) 361-376. [9] S. M. S. Modarres Mosadegh and E. Movahednia, Stability of preserving lattice cubic functional equation in Menger probabilistic normed Riesz spaces, J. Fixed Point Theory Appl. 20 (2018) 34. [10] E. Movahednia, Y. Cho, C. Park and S. Paokanta, On approximate solution of lattice functional equations in Banach f-algebras, AIMS Math., 5(2020) 5458-5469. [11] E. Movahednia, C. Park and D. Y. Shin, Approximation of involution in multi-Banach algebras: Fixed point technique, AIMS Math., 6(2021) 5851-5868. [12] M. R. Velayati and N. SalehiStability of maximum preserving functional equation on multi-Banach lattice by fixed point method, Fixed Point Theory, 21(2020) 363-374. [13] P. LoeLoe, E. Movahednia and Manuel De la Sen, Hyers Stability and Multi-Fuzzy Banach Algebra, Mathematics, 10(2022) 106. [14] V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory, 4(2003) 91-96. [15] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Am. Math. Soc., 72(1978) 297-300. [16] F. Riesz, Sur la d´ecomposition des op´erations fonctionnelles lin´eaires, In Atti del Congresso Internazionale dei Matematici, 3(1928) 143-148. [17] H. H. Schaefer, In Banach Lattices and Positive Operators, Springer, 1974. [18] S. M. Ulam, Problems in modern mathematics, Courier Corporation, 2004. [19] A. C. Zaanen, Introduction to operator theory in Riesz spaces, Springer Science and Business Media, 2012. | ||
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