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.

In this paper, we introduced the notion of a generalized multivalued (α,φ)-almost contractions and establish the existence of fixed point theorems for this class of mapping. The results presented in this paper generalize and extend some recent results in multivalued almost contraction. Also, we show its applications in the Ulam-Hyers stability of fixed point problems for multivalued operators.

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).

In this paper, we prove the generalized Hyers–Ulam stability of the following additive-quadratic-cubic-quartic functional equation f(x + 2y) + f(x− 2y) = 4f(x + y) + 4f(x− y)− 6f(x) + f(2y) + f(−2y)− 4f(y)− 4f(−y) in non-Archimedean Banach spaces.

In this paper, we obtain the general solution and the generalized Hyers-Ulam stability for quadratic functional equations f(2x+ y)+ f(2x− y) = f(x+ y)+ f(x− y)+6f(x) and f(2x + y) + f(x + 2y) = 4f(x + y) + f(x) + f(y).

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces:begin{equation} sum_{ j = 1}^{n}fBig(-2 x_{j} + sum_{ i = 1, ineq j}^{n} x_{i}Big) =(n-6) fBig(sum_{ i = 1}^{n} x_{i}Big) + 9 sum_{ i = 1}^{n}f(x_{i}).end{equation}

A boundary-value problem for a couple of scalar nonlinear differential equations with delay and several generalized proportional Caputo fractional derivatives is studied. Ulam-type stability the given investigated. Sufficient conditions existence an arbitrary parameter are obtained. In study stability, this was chosen to depend on solution corresponding inequality. We provide sufficient Ulam–Hy...