Christensen measurability and some functional equation

Superstability of Some Pexider-Type Functional Equation

Hyperstability of some functional equation on restricted domain‎: direct and fixed point methods

The study of stability problems of functional equations was motivated by a question of S.M. Ulam asked in 1940. The first result giving answer to this question is due to D.H. Hyers. Subsequently, his result was extended and generalized in several ways.We prove some hyperstability results for the equation g(ax+by)+g(cx+dy)=Ag(x)+Bg(y)on restricted domain. Namely, we show, under some weak natural...

The Measurability of Complex-Valued Functional Sequences

In this article, we formalized the measurability of complexvalued functional sequences. First, we proved the measurability of the limits of real-valued functional sequences. Next, we defined complex-valued functional sequences dividing real part into imaginary part. Then using the former theorems, we proved the measurability of each part. Lastly, we proved the measurability of the limits of com...

Some Remarks on the Measurability of Certain Sets

The present note contains some elementary remarks on sets defined by simple geometric properties. Our main tool will be the Lebesgue density theorem. First we introduce a few notations : d(a, b) denotes the distance from a to b and Six, r) the open sphere of center x and radius r. A point x of a set A is said to be of metric density 1 if to every e there exists a ô such that AC\S{x, r) , r < 5,...

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.