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1

A new factor theorem on absolute matrix summability method

Yıldız Şebnem

Journal of Applied Analysis

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2022

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Vol. 28, nr 1

83--89

EN

In this paper, we have a new matrix generalization with absolute matrix summability factor of an infinite series by using quasi-β-power increasing sequences. That theorem also includes some new and known results dealing with some basic summability methods.

2

Fractional integral inequalities for composite and k-composite preinvex functions

Kashuri A., Liko R., Iqbal S.

Fasciculi Mathematici

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2019

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nr 62

57--79

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.

3

Some new Hermite-Hadamard type inequalities via k-fractional integrals concerning differentiable generalized relative semi-(r; m, p, q, h1 , h2 ) -preinvex mappings

Kashuri A., Liko R.

Fasciculi Mathematici

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2018

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Nr 60

59--78

EN

In this article, we first presented a new identity concerning differentiable mappings defined on m-invex set via k-fractional integrals. By using the notion of generalized relative semi-(r; m,p, q, h1, h2 )-preinvexity and the obtained identity as an auxiliary result, some new estimates with respect to Hermite-Hadamard type inequalities via k-fractional integrals are established. It is pointed out that some new special cases can be deduced from main results of the article.

4

Hermite-Hadamard type fractional integral inequalities for generalized (r; g,s,m,φ)-preinvex functions

Kashuri A., Liko R.

Fasciculi Mathematici

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2017

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Nr 59

43--55

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.

5

Conjugate functions, lp-norm like functionals, the generalized Hölder inequality, Minkowski inequality and subhomogeneity

Matkowski J.

Opuscula Mathematica

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2014

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Vol. 34, no. 3

523-560

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.