A Certain Functional Equation

On a functional equation satisfied by certain Dirichlet series

by giving a representation of L(s) in terms of Hurwitz zeta functions. That representation allowed us to get some information about zeros and poles; nevertheless no functional equation could be deduced from it. In this paper following a classical argument we obtain for L(s) as above, under suitable hypothesis, a functional equation of Riemann’s type. More precisely, let us consider the Dirichle...

Analytic solution of certain second-order functional differential equation

We consider the existence of analytic solutions of a certain class of iterative second-order functional differential equation of the form x (x [r] (z)) = c 0 z 2 + c 1 (x(z)) 2 + (c 2 x [2] (z)) 2 + ··· + c m (x [m] (z)) 2 , m,r ≥ 0.

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.

On Hilbert Golab-Schinzel type functional equation

Let $X$ be a vector space over a field $K$ of real or complex numbers. We will prove the superstability of the following Go{l}c{a}b-Schinzel type equation$$f(x+g(x)y)=f(x)f(y), x,yin X,$$where $f,g:Xrightarrow K$ are unknown functions (satisfying some assumptions). Then we generalize the superstability result for this equation with values in the field of complex numbers to the case of an arbitr...

Hyers-Ulam Stability of Fibonacci Functional Equation