In this paper, we establish the general solution of the functional equation f(nx+ y) + f(nx− y) = nf(x+ y) + nf(x− y) + 2(f(nx)− nf(x))− 2(n − 1)f(y) for fixed integers n with n 6= 0,±1 and investigate the generalized Hyers-Ulam-Rassias stability of this equation in quasi-Banach spaces.

In the current manuscript, we study uniqueness and Ulam-stability of solutions for sequential fractionalpantograph differential equations with nonlocal boundary conditions. The is es-tablished by Banach's fixed point theorem. We also define Ulam-Hyers stability theUlam-Hyers-Rassias mentioned problem. An example presented to illustrate main results.

In this paper, we investigate the generalized Hyers-Ulam-Rassias and the Isac and Rassias-type stability of the conditional of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras. As a consequence of this, we prove the hyperstability of orthogonally ring $*$-$n$-derivation and orthogonally ring $*$-$n$-homomorphism on $C^*$-algebras.

The question concerning the stability of group homomorphisms was posed by Ulam 1 . Hyers 2 solved the case of approximately additive mappings on Banach spaces. Aoki 3 provided a generalization of the Hyers’ theorem for additive mappings. In 4 , Rassias generalized the result of Hyers for linear mappings by allowing the Cauchy difference to be unbounded see also 5 . The result of Rassias has bee...

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...

In this paper, we study the existence of solutions for fractional differential equations with Caputo-Hadamard derivative order 2 (1, 2]. The uniqueness result is proved via Banach’s contraction mapping principle and results are established by using Schauder’s fixed point theorem. Furthermore, Ulam-Hyers Ulam-Hyers-Rassias stability proposed equation employed. Some examples given to illustrate r...

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation f(2x+ y) + f(2x− y) = 4(f(x+ y) + f(x− y))− 3 7 (f(2y)− 2f(y)) + 2f(2x) − 8f(x).

Using fixed point methods, we prove the generalized Hyers–Ulam–Rassias stability of ternary homomorphisms, and ternary multipliers in ternary Banach algebras for the Jensen–type functional equation f( x+ y + z 3 ) + f( x− 2y + z 3 ) + f( x+ y − 2z 3 ) = f(x) .