On the Hyers-Ulam-Rassias stability of a pexiderized quadratic inequality

Abstract

Abstract. In this paper we prove the stability of the Pexiderized quadratic inequalityϕ(x, y) in the spirit of D. H. Hyers, S. M. Ulam, Th. M. Rassias and P. Gȃvruta. (2000): Primary 39B72, 47H15. Mathematics subject classification

Hyers-Ulam-Rassias of Orthogonal Pexiderized Quadratic Functional Equation

“…K.W. Jun and Y. H. Lee [13] proved the stability of quadratic equation of Pexider type. The stability problem of the quadratic equation has been extensively investigated by some mathematicians [17], [5], [6].…”

Generalized Hyers-Ulam Stability for a General Mixed Functional Equation in Quasi-β-normed Spaces

“…Rassias [27]- [30] treated the Ulam-Gavruta-Rassias stability on linear and nonlinear mappings and generalized Hyers result. During the last two decades, a number of papers and research monographs have been published on various generalizations and applications of the generalized Hyers-Ulam stability to a number of functional equations and mappings (see [9]- [13], [18]- [26], [33]- [35]). We also refer the readers to the books: P. Czerwik [7] and D.H. Hyers, G. Isac and Th.M.…”

Hyers–Ulam–Rassias Stability of a Quadratic and Additive Functional Equation in Quasi-Banach Spaces

“…Grabiec [9] give a generalization of the results mentioned above. Jun and Lee [12] proved the Hyers-Ulam-Rassias stability of the pexiderized quadratic equation (1.1). Moslehian investigated the orthogonal stability of the pexiderized quadratic equation (1.1) in [15].…”