We construct Feigenbaum quadratic-like maps with a Julia set of positive Lebesgue measure. Indeed, in the quadratic family $P_c: z \mapsto z^2+c$ corresponding parameters $c$ is shown to have Hausdorff dimension. Our examples include renormalization fixed points, and polynomials their stable manifold are first known rational for which hyperbolic dimension different from set.

In this paper, we  present a version of Favard's inequality for special case and then generalize it for the Sugeno integral in fuzzy measure space $(X,Sigma,mu)$, where $mu$ is the Lebesgue measure. We consider two cases, when our function is concave and when is convex. In addition for illustration of theorems, several examples are given.

The �-dimensional Lebesgue space is the measurable space (E���(E�))— where E = [0 � 1) or E = R—endowed with the Lebesgue measure, and the “calculus of functions” on Lebesgue space is just “real and harmonic analysis.” The �-dimensional Gauss space is the same measure space (R���(R�)) as in the previous paragraph, but now we endow that space with the Gauss measure P� in place of the Lebesgue me...