Series Solution of a Functional Equation

Neumann-Series Solution of Fractional Differential Equation

Functional Equation for Theta Series

In this short paper, we find the transformation formula for the theta series under the action of the Jacobi modular group on the Siegel-Jacobi space. This formula generalizes the formula (5.1) obtained by Mumford in [3, p. 189].

Power Series Solution of a Nonlinear Schrödinger Equation

A slightly modified variant of the cubic periodic one-dimensional nonlinear Schrödinger equation is shown to be well-posed, in a relatively weak sense, in certain function spaces wider than L. Solutions are constructed as sums of infinite series of multilinear operators applied to initial data, and these multilinear operators are analyzed directly.

Computing a Solution of Feigenbaum's Functional Equation in Polynomial Time

Lanford has shown in 1982 that Feigenbaum’s functional equation has an analytic solution. We show that this solution is a polynomial time computable function. This implies in particular that the so-called first Feigenbaum constant is a polynomial time computable real number.

Intuitionistic fuzzy stability of a quadratic and quartic functional equation

In this paper, we prove the generalized Hyers--Ulamstability of a quadratic and quartic functional equation inintuitionistic fuzzy Banach spaces.