d’Alembert functional equations in distributions

Functional Equations and Characterization of Probability Distributions

Functional Equations in Schwartz Distributions and Their Stabilities

Employing two methods we consider a class of n-dimensional functional equations in the space of Schwartz distributions. As the first approach, employing regularizing functions we reduce the equations in distributions to classical ones of smooth functions and find the solutions. Secondly, using differentiation in distributions, converting the functional equations to differential equations and fi...

Quadratic $alpha$-functional equations

In this paper, we solve the quadratic $alpha$-functional equations $2f(x) + 2f(y) = f(x + y) + alpha^{-2}f(alpha(x-y)); (0.1)$ where $alpha$ is a fixed non-Archimedean number with $alpha^{-2}neq 3$. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the quadratic $alpha$-functional equation (0.1) in non-Archimedean Banach spaces.

Infinite Systems of Functional Equations and Gaussian Limiting Distributions

Systems of functional equations for generating functions appear in many combinatorial enumeration problems, for example in tree enumeration problems or in the enumeration of planar graphs (and related problems), see Drmota (2009). Usually, these enumeration techniques can be extended to take several parameters into account: the number of vertices, the number of edges, the number of vertices of ...

Random fractional functional differential equations

In this paper, we prove the existence and uniqueness results to the random fractional functional differential equations under assumptions more general than the Lipschitz type condition. Moreover, the distance between exact solution and appropriate solution, and the existence extremal solution of the problem is also considered.