The extension of Montgomery identity via Fink identity with applications.
The Extremal Convex Functions.
The factorization of with monic and of degree .
In this paper we investigate the factorization of the polynomials in the special case where is a monic quadratic polynomial with negative discriminant. We also mention similar results in the case that is monic and linear.
The Feigenbaum functional equation and periodic points.
The Feigenbaum functional equation and periodic points. (Short Communication).
The foam drainage equation with time and space-fractional derivatives solved by the adomian method.
The fractal dimension of invariant subsets for piecewise monotonic maps on the interval.
The fundamental solutions for fractional evolution equations of parabolic type.
The fundamental solutions for fractional evolution equations of parabolic type.
The fundamental theorem for the -integral on more general sets and a corresponding divergence theorem with singularities
The fundamental theorem of calculus for Lebesgue integral.
The fundamental theorem of dynamical systems
We propose the title of The Fundamental Theorem of Dynamical Systems for a theorem of Charles Conley concerning the decomposition of spaces on which dynamical systems are defined. First, we briefly set the context and state the theorem. After some definitions and preliminary results, based both on Conley's work and modifications to it, we present a sketch of a proof of the result in the setting of the iteration of continuous functions on compact metric spaces. Finally, we claim that this theorem...
The generalization of the Du Bois-Reymond lemma for functions of two variables to the case of partial derivatives of any order
In the paper, the generalization of the Du Bois-Reymond lemma for functions of two variables to the case of partial derivatives of any order is proved. Some application of this theorem to the coercive Dirichlet problem is given.
The generalizations of Hilbert's inequality.
The generalized Heron mean and its dual form.
The generalized method of exhaustion.
The global existence of mild solutions for semilinear fractional Cauchy problems in the α-norm
We study the local and global existence of mild solutions to a class of semilinear fractional Cauchy problems in the α-norm assuming that the operator in the linear part is the generator of a compact analytic C₀-semigroup. A suitable notion of mild solution for this class of problems is also introduced. The results obtained are a generalization and continuation of some recent results on this issue.
The Hardy inequality with one negative parameter.
The Hardy-Landau-Littlewood inequalities with less smoothness.
The hardy-littlewood maximal function and derivation of integrals.