Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering. In the present paper since the utilization of Zadeh's Extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct a fuzzy-valued function on a closed interval via related membership function. We de...

Abstract We define the $$L^r$$ L r -variational integral and we prove that it is equivalent to $$HK_r$$ H K -integral defined in 2004 by P. Musial Y. Sagher Studia Mathematica paper The $$L^...

We prove two existence theorems for the integrodifferential equation of mixed type: x′(t) = f (t,x(t), t0k1(t,s)g(s,x(s))ds, ∫ a 0k2(t,s)h(s,x(s))ds), x(0) = x0, where in the first part of this paper f , g, h, x are functions with values in a Banach space E and integrals are taken in the sense of Henstock-Kurzweil (HK). In the second part f , g, h, x are weakly-weakly sequentially continuous fu...