In this paper, we establish the Pexiderized stability of coboundaries and cocycles and use them to investigate the Hyers–Ulam stability of some functional equations. We prove that for each Banach algebra A, Banach A-bimodule X and positive integer n,H(A,X) = 0 if and only if the n-th cohomology group approximately vanishes.

We investigate the stability of Pexiderized mappings in Banach modules over a unital Banach algebra. As a consequence, we establish the Hyers–Ulam stability of the orthogonal Cauchy functional equation of Pexider type f 1 (x + y) = f 2 (x) + f 3 (y), x ⊥ y in which ⊥ is the orthogonality in the sense of Rätz.

Using the integrating factor method, this paper deals with the Hyers-Ulam stability of a class of exact differential equations of second order. As a direct application of the main result, we also obtain the HyersUlam stability of a special class of Cauchy-Euler equations of second order. c ©2016 All rights reserved.

The generalized Hyers–Ulam–Rassias stability of adjointable mappings on Hilbert C∗-modules are investigated. As a result, we get a solution for stability of the equation f(x)∗y = xg(y)∗ in the context of C∗-algebras. ∗2000 Mathematics Subject Classification. Primary 39B82, secondary 46L08, 47B48, 39B52 46L05, 16Wxx.

In this paper, the nonlinear stability of a functional equation in the setting of non-Archimedean normed spaces is proved. Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean space, the and the theory of functional equations are also presented Key word: Hyers Ulam Rassias stability • cubic mappings • generalized normed space • Banach spac...

The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Using fixed point method, we prove the Hyers-Ulam stability of the functional equation

The generalized Hyers–Ulam–Rassias stability of adjointable mappings on Hilbert C∗-modules is investigated. As a corollary, we establish the stability of the equation f(x)∗y = xg(y)∗ in the context of C∗-algebras. We also prove that each approximately adjointable mapping is indeed adjointable.

Aoki,T. , (1950) "On stability of the linear transformation in Banach spaces," Journal of the Mathematical Society of Japan, 2,64-66 Chang, S. and Kim,H. M. , (2002), On the Hyer-Ulam stability of a quadratic functional equations, J. Ineq. Appl. Math. , 33, 1-12. Chang,S. , Lee,E. H. and Kim,H. M. , (2003)On the Hyer-Ulam Rassias stability of a quadratic functional equations, Math. In...

Aoki,T. , (1950) "On stability of the linear transformation in Banach spaces," Journal of the Mathematical Society of Japan, 2,64-66 Chang, S. and Kim,H. M. , (2002), On the Hyer-Ulam stability of a quadratic functional equations, J. Ineq. Appl. Math. , 33, 1-12. Chang,S. , Lee,E. H. and Kim,H. M. , (2003)On the Hyer-Ulam Rassias stability of a quadratic functional equations, Math. In...

Aoki,T. , (1950) "On stability of the linear transformation in Banach spaces," Journal of the Mathematical Society of Japan, 2,64-66 Chang, S. and Kim,H. M. , (2002), On the Hyer-Ulam stability of a quadratic functional equations, J. Ineq. Appl. Math. , 33, 1-12. Chang,S. , Lee,E. H. and Kim,H. M. , (2003)On the Hyer-Ulam Rassias stability of a quadratic functional equations, Math. In...