A generalization of variant of Wilson stype Hilbert space valued functional equations
Resumen
In the present paper we characterize, in terms of characters, multi- plicative functions, the continuous solutions of some functional equa- tions for mappings defined on a monoid and taking their values in a complex Hilbert space with the Hadamard product. In addition, we investigate a superstability result for these equations.Citas
[1]J.A.Baker,The stability of the Cosine Equation, Proc. Amer. Math. Soc. 80, 3, pp. 411-416, (1980).
[2] A. Chahbi, B. Fadli, S. Kabbaj, A generalization of the symmetrized multiplicative Cauchy equation. Acta Math. Hung. 149 (1), pp. 170- 176, (2016).
[3] E. Elqorachi and A. Redouani, Solutions and stability of variant of Wil- son’s functional equation (14 May 2015), arXiv:1505.06512v1 [math. CA]. Demonstratio Math. (to appear).
[4] H. Rezaei and M. Sharifzadeh, On the super-stability of exponential hilbert valued functional equations, J. Inequal. Appl. Article ID 114. (2011).
[5] L. Szekelyhidi, D’Alembert’s functional equation on compact groups, Banach J.. Math. Anal. 1, no. 2, pp. 221-226, (2007).
[6] KH. Sabour, B. Fadli and S. Kabbaj, Wilson’s Functional equation on monoids with involutive automorphisms. Aequationes. Math. 90, no. 5, pp. 189-196, (2016).
[7] H. Stetkaer, D’Alembert’s and Wilson’s functional equations on step 2 nilpotent groups, Aequationes. Math. 67, No. 3, pp. 1001-1011, (2004).
[8] H. Stetkaer, Functional Equations on Groups, World Scientific Pub- lishing Co., Singapore, (2013).
[9] H. Stetkaer, A link between Wilson’s functional and d’Alembert’s func- tional equations, Aequationes. Math. 90, No. 2, pp. 407-409, (2016).
[10] W. H. Wilson, On a certain related functional equations, Proc. Amer. Math. Soc. 26, pp. 300-312, (1920).
[11] D. Zeglami, M. Tial and B. Fadli, Wilson’s type Hilbert space valued functional equations. Adv. Pure Appl. Math. 7 (3), pp. 189-196, (2016).
[2] A. Chahbi, B. Fadli, S. Kabbaj, A generalization of the symmetrized multiplicative Cauchy equation. Acta Math. Hung. 149 (1), pp. 170- 176, (2016).
[3] E. Elqorachi and A. Redouani, Solutions and stability of variant of Wil- son’s functional equation (14 May 2015), arXiv:1505.06512v1 [math. CA]. Demonstratio Math. (to appear).
[4] H. Rezaei and M. Sharifzadeh, On the super-stability of exponential hilbert valued functional equations, J. Inequal. Appl. Article ID 114. (2011).
[5] L. Szekelyhidi, D’Alembert’s functional equation on compact groups, Banach J.. Math. Anal. 1, no. 2, pp. 221-226, (2007).
[6] KH. Sabour, B. Fadli and S. Kabbaj, Wilson’s Functional equation on monoids with involutive automorphisms. Aequationes. Math. 90, no. 5, pp. 189-196, (2016).
[7] H. Stetkaer, D’Alembert’s and Wilson’s functional equations on step 2 nilpotent groups, Aequationes. Math. 67, No. 3, pp. 1001-1011, (2004).
[8] H. Stetkaer, Functional Equations on Groups, World Scientific Pub- lishing Co., Singapore, (2013).
[9] H. Stetkaer, A link between Wilson’s functional and d’Alembert’s func- tional equations, Aequationes. Math. 90, No. 2, pp. 407-409, (2016).
[10] W. H. Wilson, On a certain related functional equations, Proc. Amer. Math. Soc. 26, pp. 300-312, (1920).
[11] D. Zeglami, M. Tial and B. Fadli, Wilson’s type Hilbert space valued functional equations. Adv. Pure Appl. Math. 7 (3), pp. 189-196, (2016).
Publicado
2017-10-20
Cómo citar
Dimou, H., & Kabbaj, S. (2017). A generalization of variant of Wilson stype Hilbert space valued functional equations. Proyecciones. Journal of Mathematics, 36(3), 485-498. Recuperado a partir de http://www.revistaproyecciones.cl/article/view/2392
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