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EN
In this paper, we establish fractional Ostrowski inequalities for functions whose modulus of the first derivatives are prequasi-invex. Midpoint inequalities are also derived.
2
Content available remote Fractional integral inequalities for composite and k-composite preinvex functions
EN
In this article we found some Ostrowski inequalities for composite and k-composite preinvex functions via fractional integrals. Also some special cases will be given.
EN
In the present paper, a new class of generalized (r; g, s, m, ϕ)-preinvex functions is introduced and some new integral inequalities for the left hand side of Gauss-Jacobi type quadrature formula involving generalized (r; g, s, m, ϕ)-preinvex functions are given. Moreover, some generalizations of Hermite-Hadamard type inequalities for generalized (r; g, s, m, ϕ)-preinvex functions via Riemann-Liouville fractional integrals are established. These results not only extend the results appeared in the literature (see [1],[2]), but also provide new estimates on these types.
4
EN
Some Ostrowski type inequalities for functions whose second derivatives in absolute value at certain powers are s-convex in the second sense are established. Two mistakes in a recently published paper are pointed out and corrected.
EN
For h : (0,∞) → R, the function h* (t) := th( 1/t ) is called (*)-conjugate to h. This conjugacy is related to the Hölder and Minkowski inequalities. Several properties of (*)-conjugacy are proved. If φ and φ* are bijections of (0,∞) then [formula]. Under some natural rate of growth conditions at 0 and ∞, if φ is increasing, convex, geometrically convex, then [formula] has the same properties. We show that the Young conjugate functions do not have this property. For a measure space (Ω,Σ,μ) denote by S = (Ω,Σ,μ) the space of all μ-integrable simple functions x : Ω → R, Given a bijection φ : (0,∞) → (0,∞) define [formula] by [formula] where Ω(x) is the support of x. Applying some properties of the (*) operation, we prove that if ƒ xy ≤ Pφ(x)Pψ (y) where [formula] and [formula] are conjugate, then φ and ψ are conjugate power functions. The existence of nonpower bijections φ and ψ with conjugate inverse functions [formula] such that Pφ and Pψ are subadditive and subhomogeneous is considered.
6
Content available remote Some new generalizations of Maroni inequality on time scales
EN
The aim of present paper is to establish some new integral inequalities on time scales involving several functions and their derivatives which in the special cases yield the well known Maroni inequality and some of its generalizations.
7
Content available remote On new multiple extension of Hilbert's integral inequality (2)
EN
Via laplace transformation some new generalization of Hardy-Hilbert's integral inequality is given.
8
Content available remote On new multiple extension of Hilbert's integral inequality
EN
This paper gives a new multiple extension of Hilbert’s integral inequality generalizing many known results.
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