Linear functional equations and their solutions in generalized Orlicz spaces

Multiple solutions for Kirchhoff elliptic equations in Orlicz-Sobolev spaces

Generalized Maxwell Equations and Their Solutions

The generalized Maxwell equations are considered which include an additional gradient term. Such equations describe massless particles possessing spins one and zero. We find and investigate the matrix formulation of the first order of equations under consideration. All the linearly independent solutions of the equations for a free particle are obtained in terms of the projection matrix-dyads (d...

On Approximate Solutions of the Generalized Radical Cubic Functional Equation in Quasi-$beta$-Banach Spaces

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of the generalized radical cubic functional equation[    fleft( sqrt[3]{ax^3 + by^3}right)=af(x) + bf(y),]    where $a,b in mathbb{R}_+$ are fixed positive real numbers, by using direct method in quasi-$beta$-Banach spaces. Moreover, we use subadditive functions to investigate stability of the generaliz...

Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces

We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in [Formula: see text]. We also make an effort to prove that every symmetric normalized block Orlicz-Garling sequen...

On two functional equations and their solutions

The present work aims to determine the solution f : R2 → R of the equation f(ux − vy, uy − vx) = f(x, y) + f(u, v) + f(x, y) f(u, v) for all x, y, u, v ∈ R without any regularity assumption. The solution of the functional equation f(ux+ vy, uy− vx) = f(x, y) + f(u, v) + f(x, y) f(u, v) is also determined. The methods of solution of these equations are simple and elementary. These two equations ...