In this paper, we obtain the general solution and investigate the Hyers-Ulam-Rassias stability of the functional equation f(ax− y)± af(x± y) = (a± 1)[af(x)± f(y)] in non-Archimedean -fuzzy normed spaces. Mathematics Subject Classification: 39B55, 39B52, 39B82

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...

Abstract In this paper, we investigate the existence and uniqueness of a solution for class ψ -Hilfer implicit fractional integro-differential equations with mixed nonlocal conditions. The arguments are based on Banach’s, Schaefer’s, Krasnosellskii’s fixed point theorems. Further, applying techniques nonlinear functional analysis, establish various kinds Ulam stability results analyzed problem,...

In this paper we establish Hyers-Ulam-Rassias stability of a generalized functional equation in fuzzy Banach spaces. The concept originated from Th. M. Rassias theorem that appeared his paper: On the linear mapping spaces, Proc. Amer. Math. Soc. 72 (1978), 297-30.

The generalized Hyers-Ulam-Rassias stability proposition in respect of the quadratic functional equation namely f(x+y+z)+f(x−y)+f(x−z) = f(x−y−z)+f(x+y)+f(x+z) is what is taken into account to be dealt with in this paper.

The fixed point alternative methods are implemented to give generalized Hyers-Ulam-Rassias stability for the Pexiderized quadratic functional equation in the fuzzy version. This method introduces a metrical context and shows that the stability is related to some fixed point of a suitable operator.

In this paper, we obtain the general solution and the generalized Hyers-Ulam Rassias stability of the functional equation 3(f(x+ 2y) + f(x− 2y)) = 12(f(x + y) + f(x− y)) + 4f(3y)− 18f(2y) + 36f(y)− 18f(x).