Related papers: A Fixed Points Approach to stability of the Pexide…

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…

We prove a new fixed - point result for the image Im(j) of any continuous function j from K to (K x K), where K is a compact convex subset of a Hausdorff locally convex space, provided that the projection of Im(j) to the first factor is…

By means of the recent $\psi$-Hilfer fractional derivative and of the Banach fixed-point theorem, we investigate stabilities of Ulam-Hyers, Ulam-Hyers-Rassias and semi-Ulam-Hyers-Rassias on closed intervals $[a,b]$ and $[a,\infty)$ for a…

In the present paper we establish a fixed point result of Krasnoselskii type for the sum $A+B$, where $A$ and $B$ are continuous maps acting on locally convex spaces. Our results extend previous ones. We apply such results to obtain strong…

We consider an $\alpha$-relaxed projection $P_A^\alpha:H\to H$ given by $P_A^\alpha(x)=\alpha P_A(x)+(1-\alpha)x$ where $\alpha\in[0,1]$ and $P_A$ is the projection onto a non-empty, convex and closed subset $A$ of the real Hilbert space…

In this paper, we study the generalized Hyers-Ulam stability of Euler-Lagrange type cubic functional equation of the form \begin{align*} 2mf(x + my) + 2f(mx - y) = (m^3 + m)[f(x+ y) + f(x - y)] + 2(m^4 - 1)f(y) \end{align*} for all $x,y \in…

In \cite{bbb} the authors obtained the Hyers-Ulam stability of the functional equation $$ \int_{K}\int_{G} f(xtk\cdot y)d\mu(t)dk=f(x)g(y), \; x, y \in G ,$$ where $G$ is a Hausdorff locally compact topological group, $K$ is a copmact…

In this paper, we obtain the general solution and investigate the generalized Hyers-Ulam-Rassias stability for the new mixed type additive and cubic functional equation $$3f(x+3y) - f(3x + y)=12[f(x+y)+f(x-y)]-16[f(x)+f(y)] + 12f(2y) -…

In this paper, we establish the conditional Hyers-Ulam-Rassias stability of the generalized Jensen functional equation $r f \left (\frac{sx+ty}{r}) = s g(x) + t h(y)$ on various restricted domains such as inside balls, outside balls, and…

In this paper we obtain a result on Hyers-Ulam stability of the linear functional equation in a single variable $f(\varphi(x)) = g(x) \cdot f(x)$ on a complete metric group.

The foundation of locally convex cone theory relies on order-theoretic concepts that induce specific topological frameworks. Within this structure, cones naturally possess three distinct topologies: lower, upper, and symmetric. In this…

In this paper, we establish the generalized Hyers--Ulam--Rassias stability of homomorphisms between ternary algebras associted to the generalized Jensen functional equation $r f(\frac{sx+ty}{r}) = s f(x) + t f(y)$.

In this work, we prove an existence theorem of the Hyers-Ulam stability for the nonlinear Volterra integral equations which improves and generalizes Castro-Ramos theorem by using some weak conditions.

In this paper we establish the stability of the functional equation $$f(x-y)=f(x)g(y)+g(x)f(y)+h(x)h(y)),\;\; x,y \in G, $$where $G$ is an abelian group.

By adopting the direct method and fixed point method, we prove that the Hyers-Ulam stability of the following additive-quadratic functional equation \begin{equation} f(x+y, z+w)+f(x-y, z-w)-2 f(x, z)-2 f(x, w)=0 \end{equation} in…

Since the main work on Ulam-Hyers dependable stabilities of differential equations to date, numerous significant and applicable papers have been published, both in the sense of integer order and fractional order differential equations.…

In this work, we determine the general solution of the quinquevigintic functional equation and also investigate its stability of this equation in the setting of matrix normed spaces and the framework of matrix non-Archimedean fuzzy normed…

In this paper, we examine the Hyers-Ulam and Hyers-Ulam-Rassias stability of solutions of a general class of nonlinear Volterra integral equations. By using a fixed point alternative and improving a technique commonly used in similar…

We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum methods.…

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