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In this article, first, we present an example of fuzzy normed space by means of the Mittag-Leffler function. Next, we extend the concept of fuzzy normed space to matrix valued fuzzy normed space and also we introduce a class of matrix valued fuzzy control functions to stabilize a nonlinear ϕ-Hadamard fractional Volterra integro-differential equation. In this sense, we investigate the Ulam–Hyers–Rassias stability for this kind of fractional equations in matrix valued fuzzy Banach space. Finally, as an application, we investigate the Ulam–Hyers–Rassias stability using matrix valued fuzzy control function obtained through the Mittag-Leffler function.

In this paper, we consider C ∗ $C^{*}$ -algebra valued fuzzy normed spaces. We study the random integral equation ( 1 2 c ) ∫ x − c d x + c d u ( γ , τ , d 0 ) d τ = u ( γ , x , d ) $(\frac{1}{2c})\int _{x-cd}^{x+cd}u(\gamma ,\tau ,d_{0})\,d\tau =u( \gamma ,x,d)$ which is related to the stochastic wave equation. In addition, using a C ∗ $C^{*}$ -algebra valued fuzzy controller function, we consider its C ∗ $C^{*}$ -algebra valued fuzzy Hyers–Ulam stability.

We consider a nonlinear Cauchy problem involving the Ψ-Hilfer stochastic fractional derivative with uncertainty, and we give a stability result. Using fixed point theory, we are able to provide a fuzzy Ulam–Hyers–Rassias stability for the considered nonlinear stochastic fractional differential equations.

We prove that approximations of derivations on random Banach ∗-algebras are exactly derivations by using a fixed point method. Furthermore, we show that approximations of quadratic ∗-derivations on random Banach ∗-algebras are exactly quadratic ∗-derivations. We, moreover, prove that approximations of derivations on random $C^{*}$ -ternary algebras are exactly derivations by using a fixed point method.

In this paper, we study the matrix equation X + A ⋆ X − 1 A + B ⋆ X − 1 B = Q , where A and B are square matrices, and Q is a positive definite matrix, and propose the iterative methods for finding positive definite solutions of the matrix equation. Also, general convergence results for the basic fixed point iteration for these equations are given. Some numerical examples are presented to show the usefulness of the iterations. MSC:65F10, 65F30, 65H10, 15A24.

Let X , Y be vector spaces. It is shown that if an odd mapping f : X → Y satisfies the functional equation j=1 ι(j)=l rf d j=1 (-1) ι(j) xj r

Park (J. Math. Phys. 47:103512, 2006) proved the Hyers-Ulam stability of homomorphisms in C ∗ -ternary algebras and of derivations on C ∗ -ternary algebras for the following generalized Cauchy-Jensen additive mapping: 2 f ( ∑ j = 1 p x j 2 + ∑ j = 1 d y j ) = ∑ j = 1 p f ( x j ) + 2 ∑ j = 1 d f ( y j ) . In this paper, we improve and generalize some results concerning this functional equation via the fixed-point method. MSC:39B52, 17A40, 46B03, 47Jxx.

Mustafa and Sims [Fixed Point Theory Appl. 2009, Article ID 917175, 10, (2009)] generalized a concept of a metric space and proved fixed point theorems for mappings satisfying different contractive conditions. In this article, we extend and generalize the results obtained by Mustafa and Sims and prove common fixed point theorems for three maps in these spaces. It is worth mentioning that our results do not rely on continuity and commutativity of any mappings involved therein. We also introduce the notation of a generalized probabilistic metric space and obtain common fixed point theorem in the frame work of such spaces. 2000 Mathematics Subject Classification: 47H10.

In this paper, we prove the generalized Hyers-Ulam stability of the following additive-cubic-quartic functional equation 1 1 f ( x + 2 y ) + 1 1 f ( x - 2 y ) = 4 4 f ( x + y ) + 4 4 f ( x - y ) + 1 2 f ( 3 y ) - 4 8 f ( 2 y ) + 6 0 f ( y ) - 6 6 f ( x ) in various complete lattictic random normed spaces. Mathematics Subject Classification (2000) Primary 54E40; Secondary 39B82, 46S50, 46S40.

Recently, Al-Fhaid and Mohiuddine (Adv. Differ. Equ. 2013:203, 2013) and Mohiuddine and Alghamdi (Adv. Differ. 2012:141, 2012) got some results in intuitionistic fuzzy normed spaces using ideas of intuitionistic fuzzy sets due to Atanassov and fuzzy normed spaces due to Saadati and Vaezpour. In this note, we show that the mentioned results follow directly from well-known theorems in fuzzy normed spaces.