On reverse Hölder and Minkowski inequalities

2020 ◽  
Vol 70 (4) ◽  
pp. 821-828
Author(s):  
Chang-Jian Zhao ◽  
Wing Sum Cheung
Keyword(s):  
Integral Inequalities ◽  
Minkowski’S Inequality ◽  
Reverse Hölder ◽  
Special Case

AbstractIn the paper, we give new improvements of the reverse Hölder and Minkowski integral inequalities. These new results in special case yield the Pólya-Szegö’s inequality and reverse Minkowski’s inequality, respectively.

On Some Integral Inequalities Related to Hardy's

1977 ◽  
Vol 20 (3) ◽  
pp. 307-312 ◽  
Author(s):  
Christopher Olutunde Imoru
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Jensen’S Inequality ◽  
Integral Inequalities ◽  
Hardy’S Inequality ◽  
Jensen's Inequality ◽  
Hardy's Inequality ◽  
Special Case

AbstractWe obtain mainly by using Jensen's inequality for convex functions an integral inequality, which contains as a special case Shun's generalization of Hardy's inequality.

scholarly journals Hölder Type Inequalities for Sugeno Integrals under Usual Multiplication Operations

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Dug Hun Hong ◽  
Jae Duck Kim
Keyword(s):  
Lebesgue Measure ◽  
Upper Bound ◽  
Convex Functions ◽  
Hölder Inequality ◽  
Concave Functions ◽  
Lebesgue Integral ◽  
Reverse Hölder ◽  
Special Case

The classical Hölder inequality shows an interesting upper bound for Lebesgue integral of the product of two functions. This paper proposes Hölder type inequalities and reverse Hölder type inequalities for Sugeno integrals under usual multiplication operations for nonincreasing concave or convex functions. One of the interesting results is that the inequality, (S)∫01f(x)pdμ1/p(S)∫01g(x)qdμ1/q≤p-q/p-p-q+1∨q-p/q-q-p+1(S)∫01f(x)g(x)dμ, where 1<p<∞,1/p+1/q=1 and μ is the Lebesgue measure on R, holds if f and g are nonincreasing and concave functions. As a special case, we consider Cauchy-Schwarz type inequalities for Sugeno integrals involving nonincreasing concave or convex functions. Some examples are provided to illustrate the validity of the proposed inequalities.

More on reverses of Minkowski’s inequalities and Hardy’s integral inequalities

2018 ◽  
Vol 13 (03) ◽  
pp. 2050064
Author(s):  
Bouharket Benaissa
Keyword(s):  
Hardy Inequality ◽  
Integral Inequality ◽  
Minkowski Inequality ◽  
Integral Inequalities ◽  
Hardy’S Inequality ◽  
Minkowski’S Inequality ◽  
Hardy's Inequality ◽  
Hardy’S Inequalities

In 2012, Sulaiman [Reverses of Minkowski’s, Hölder’s, and Hardy’s integral inequalities, Int. J. Mod. Math. Sci. 1(1) (2012) 14–24] proved integral inequalities concerning reverses of Minkowski’s and Hardy’s inequalities. In 2013, Banyat Sroysang obtained a generalization of the reverse Minkowski’s inequality [More on reverses of Minkowski’s integral inequality, Math. Aeterna 3(7) (2013) 597–600] and the reverse Hardy’s integral inequality [A generalization of some integral inequalities similar to Hardy’s inequality, Math. Aeterna 3(7) (2013) 593–596]. In this article, two results are given. First one is further improvement of the reverse Minkowski inequality and second is further generalization of the integral Hardy inequality.

A note on a class of integral inequalities

1973 ◽  
Vol 74 (1) ◽  
pp. 127-131 ◽  
Author(s):  
Cornelius O. Horgan
Keyword(s):  
Variational Approach ◽  
Second Order ◽  
Integral Inequalities ◽  
Special Case

AbstractA unified variational approach to a class of second-order integral in-equalities is presented. A special case recently considered in a different manner by Anderson, Arthurs and Hall (1) is recovered.

scholarly journals Estimates of Mean-Type Fractional Inequalities For Differentiable Functions

2021 ◽  
Author(s):  
Muhammad Samraiz ◽  
Zahida Perveen ◽  
Sajid Iqbal ◽  
Saima Naheed ◽  
Thabet Abdeljawad
Keyword(s):  
Fractional Derivative ◽  
Convex Functions ◽  
Fractional Derivatives ◽  
Integral Inequalities ◽  
Hilfer Fractional Derivative ◽  
Caputo Fractional Derivatives ◽  
Differentiable Functions ◽  
Wide Range ◽  
Type Integral ◽  
Special Case

In this article, we established a wide range of fractional mean-type integral inequalities for notable Hilfer fractional derivative using twice differentiable convex and $s$-convex functions for $s\in(0,1]$ with related identities. Also the results for Caputo fractional derivatives are derived as a special case of our general results.

Some weighted integral inequalities for differentiable h-preinvex functions

2018 ◽  
Vol 25 (3) ◽  
pp. 441-450 ◽  
Author(s):  
Muhammad Amer Latif ◽  
Sever Silvestru Dragomir ◽  
Ebrahim Momoniat
Keyword(s):  
Integral Inequality ◽  
Integral Inequalities ◽  
Real Numbers ◽  
Absolute Value ◽  
Type Integral ◽  
Weighted Integral ◽  
Preinvex Functions ◽  
Special Case

AbstractIn this paper, by using a weighted identity for functions defined on an open invex subset of the set of real numbers, by using the Hölder integral inequality and by using the notion of h-preinvexity, we present weighted integral inequalities of Hermite–Hadamard-type for functions whose derivatives in absolute value raised to certain powers are h-preinvex functions. Some new Hermite–Hadamard-type integral inequalities are obtained when h is super-additive. Inequalities of Hermite–Hadamard-type for s-preinvex functions are given as well as a special case of our results.

Chebyshev type inequality containing a fractional integral operator with a multi-index Mittag-Leffler function as a kernel

Analysis ◽  
2021 ◽  
Vol 41 (1) ◽  
pp. 61-67
Author(s):  
Kamlesh Jangid ◽  
S. D. Purohit ◽  
Kottakkaran Sooppy Nisar ◽  
Serkan Araci
Keyword(s):  
Integral Operator ◽  
Fractional Integral ◽  
Type Inequality ◽  
Integral Operators ◽  
Fractional Integral Operator ◽  
Integral Inequalities ◽  
Fractional Integral Operators ◽  
Multi Index ◽  
Type Integral ◽  
Special Case

Abstract In this paper, we derive certain Chebyshev type integral inequalities connected with a fractional integral operator in terms of the generalized Mittag-Leffler multi-index function as a kernel. Our key findings are general in nature and, as a special case, can give rise to integral inequalities of the Chebyshev form involving fractional integral operators present in the literature.

scholarly journals Properties of a Generalized Class of Weights Satisfying Reverse Hölder’s Inequality

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
S. H. Saker ◽  
S. S. Rabie ◽  
R. P. Agarwal
Keyword(s):  
Upper Bounds ◽  
Hölder Inequality ◽  
The Self ◽  
Power Mean ◽  
Lower And Upper Bounds ◽  
Real Numbers ◽  
Positive Real ◽  
Fundamental Properties ◽  
Reverse Hölder ◽  
Special Case

In this paper, we will prove some fundamental properties of the discrete power mean operator M p u n = 1 / n ∑ k = 1 n   u p k 1 / p , for   n ∈ I ⊆ ℤ + , of order p , where u is a nonnegative discrete weight defined on I ⊆ ℤ + the set of the nonnegative integers. We also establish some lower and upper bounds of the composition of different operators with different powers. Next, we will study the structure of the generalized discrete class B p q B of weights that satisfy the reverse Hölder inequality   M q u ≤ B M p u , for positive real numbers p , q , and B such that 0 < p < q and B > 1 . For applications, we will prove some self-improving properties of weights from B p q B and derive the self improving properties of the discrete Gehring weights as a special case. The paper ends by a conjecture with an illustrative sharp example.

Some inequalities for exponentially convex functions on time scales

2021 ◽  
Vol 71 (4) ◽  
pp. 925-940
Author(s):  
Svetlin G. Georgiev ◽  
Vahid Darvish ◽  
Tahere A. Roushan
Keyword(s):  
Time Scales ◽  
Convex Functions ◽  
Integral Inequalities ◽  
Double Inequality ◽  
Differentiable Functions ◽  
Classical Notion ◽  
Exponentially Convex Functions ◽  
Special Case ◽  
Class Of Functions

Abstract In this paper, we introduce the notion of exponentially convex functions on time scales and then we establish Hermite-Hadamard type inequalities for this class of functions. As special case, we derive this double inequality in the context of classical notion of exponentially convex functions and convex functions. Moreover, we prove some new integral inequalities for n-times continuously differentiable functions with exponentially convex first Δ-derivative.

Extreme self-sacrifice beyond fusion: Moral expansiveness and the special case of allyship

2018 ◽  
Vol 41 ◽  
Author(s):  
Daniel Crimston ◽  
Matthew J. Hornsey
Keyword(s):  
General Theory ◽  
Biological Markers ◽  
Natural Environment ◽  
Relevant Dimension ◽  
Special Case

AbstractAs a general theory of extreme self-sacrifice, Whitehouse's article misses one relevant dimension: people's willingness to fight and die in support of entities not bound by biological markers or ancestral kinship (allyship). We discuss research on moral expansiveness, which highlights individuals’ capacity to self-sacrifice for targets that lie outside traditional in-group markers, including racial out-groups, animals, and the natural environment.

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