A generalization of variant of Wilson stype Hilbert space valued functional equations.

• Autores: Hajira Dimou, S. Kabbaj
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 36, Nº. 3, 2017, págs. 485-498
• Idioma: inglés
• DOI: 10.4067/s0716-09172017000300485
• Enlaces
  • Texto completo
• 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.

• Referencias bibliográficas
  • J. A. Baker,The stability of the Cosine Equation, Proc. Amer. Math. Soc. 80, 3, pp. 411-416, (1980).
  • A. Chahbi, B. Fadli, S. Kabbaj, A generalization of the symmetrized multiplicative Cauchy equation. Acta Math. Hung. 149 (1), pp. 170- 176,...
  • E. Elqorachi and A. Redouani, Solutions and stability of variant of Wil- son’s functional equation (14 May 2015), arXiv:1505.06512v1 [math....
  • H. Rezaei and M. Sharifzadeh, On the super-stability of exponential hilbert valued functional equations, J. Inequal. Appl. Article ID 114....
  • L. Szekelyhidi, D’Alembert’s functional equation on compact groups, Banach J. Math. Anal. 1, no. 2, pp. 221-226, (2007).
  • KH. Sabour, B. Fadli and S. Kabbaj, Wilson’s Functional equation on monoids with involutive automorphisms. Aequationes. Math. 90, no. 5, pp....
  • H. Stetkaer, D’Alembert’s and Wilson’s functional equations on step 2 nilpotent groups, Aequationes. Math. 67, No. 3, pp. 1001-1011, (2004).
  • H. Stetkaer, Functional Equations on Groups, World Scientific Publishing Co., Singapore, (2013).
  • H. Stetkaer, A link between Wilson’s functional and d’Alembert’s functional equations, Aequationes. Math. 90, No. 2, pp. 407-409, (2016).
  • W. H. Wilson, On a certain related functional equations, Proc. Amer. Math. Soc. 26, pp. 300-312, (1920).
  • 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).