ITERATED -FRACTIONAL VECTOR REPRESENTATION FORMULAE AND INEQUALITIES FOR BANACH SPACE VALUED FUNCTIONS

Here we present very general iterated fractional Bochner integral representation formulae for Banach space valued functions. Based on these we derive generalized and iterated left and right: fractional Poincar´e type inequalities, fractional Opial type inequalities and fractional Hilbert-Pachpatte inequalities. All these inequalities are very general having in their background Bochner type integrals

On Hardy-Hilbert-type inequalities with α-fractional derivatives

In the current manuscript, new alpha delta dynamic Hardy-Hilbert inequalities on time scales are discussed. These inequalities combine and expand a number of continuous inequalities and their corresponding discrete analogues in the literature. We shall illustrate our results using Hölder's inequality on time scales and a few algebraic inequalities

Inequalities Similar to Hilbert's Inequality

In the present paper, we establish some new inequalities similar to Hilbert’s type inequalities. Our results provide some new estimates to these types of inequalities

New fractional integral inequalities for preinvex functions involving Caputo-Fabrizio operator

It's undeniably true that fractional calculus has been the focus point for numerous researchers in recent couple of years. The writing of the Caputo-Fabrizio fractional operator has been on many demonstrating and real-life issues. The main objective of our article is to improve integral inequalities of Hermite-Hadamard and Pachpatte type incorporating the concept of preinvexity with the Caputo-Fabrizio fractional integral operator. To further enhance the recently presented notion, we establish a new fractional equality for differentiable preinvex functions. Then employing this as an auxiliary result, some refinements of the Hermite-Hadamard type inequality are presented. Also, some applications to special means of our main findings are presented

Lyapunov-type Inequalities for Partial Differential Equations

In this work we present a Lyapunov inequality for linear and quasilinear elliptic differential operators in $N-$dimensional domains $\Omega$. We also consider singular and degenerate elliptic problems with $A_p$ coefficients involving the $p-$Laplace operator with zero Dirichlet boundary condition. As an application of the inequalities obtained, we derive lower bounds for the first eigenvalue of the $p-$Laplacian, and compare them with the usual ones in the literature

On some Chebyshev type inequalities for the complex integral

Assume that f and g are continuous on γ, γ ⊂ C is a piecewisesmooth path parametrized by z (t) , t ∈ [a, b] from z (a) = u to z (b) = w withw 6= u, and the complex Chebyshev functional is defined bySean f y g funciones continuas sobre γ, siendo γ ⊂ C un caminosuave por partes parametrizado por z (t) , t ∈ [a, b] con z (a) = u y z (b) = w,w 6= u, y el funcional de Chebyshev complejo definido po