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In this paper we give the suffcient and necessary condition for the existence of any almost isometric operator from C(Ω) into C0(Ω0). As a corollary, we show that there is no ∈–isometry from any abstract M space with a strong unit into C0(Γ) if $$ 0 < \in < \frac{1} {9}. $$ [ABSTRACT FROM AUTHOR]

In this paper, the authors consider the existence of periodic solutions for a kind of second neutral functional differential equation as follows: in the critical case | c| = 1. By employing Mawhin's continuation theorem and some analysis techniques, some new results are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we determine the general solution of the functional equation f1(2 x + y) + f2(2 x − y) = f3( x + y) + f4( x − y) + f5( x) without assuming any regularity condition on the unknown functions f1, f2, f3, f4, f5 : ℝ → ℝ. The general solution of this equation is obtained by finding the general solution of the functional equations f(2 x + y) + f(2 x − y) = g( x + y) + g( x − y) + h( x) and f(2 x + y) + f(2 x − y) = g( x + y) + g( x − y). The method used for solving these functional equations is elementary but exploits an important result due to Hosszú. The solution of this functional equation can also be determined in certain type of groups using two important results due to Székelyhidi. [ABSTRACT FROM AUTHOR]

In this paper we present a mean value theorem derived from Flett’s mean value theorem. It turns out that cubic polynomials have the midpoint of the interval as their mean value point. To answer what class of functions have this property, we consider a functional equation associated with this mean value theorem. [ABSTRACT FROM AUTHOR]