scholarly journals Generalized Steffensen’s Inequality by Fink’s Identity

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 329
Author(s):  
Asfand Fahad ◽  
Saad Butt ◽  
Josip Pečarić
Keyword(s):  
Convex Functions ◽  
Type Inequality ◽  
Green Functions ◽  
Linear Functionals ◽  
Hardy Type Inequality ◽  
Steffensen’S Inequality ◽  
Hardy Type ◽  
Exponentially Convex Functions ◽  
Fink’S Identity

By using Fink’s Identity, Green functions, and Montgomery identities we prove some identities related to Steffensen’s inequality. Under the assumptions of n-convexity and n-concavity, we give new generalizations of Steffensen’s inequality and its reverse. Generalizations of some inequalities (and their reverse), which are related to Hardy-type inequality. New bounds of Gr u ¨ ss and Ostrowski-type inequalities have been proved. Moreover, we formulate generalized Steffensen’s-type linear functionals and prove their monotonicity for the generalized class of ( n + 1 ) -convex functions at a point. At the end, we present some applications of our study to the theory of exponentially convex functions. .

Refinements of the majorization-type inequalities via green and fink identities and related results

2018 ◽  
Vol 68 (4) ◽  
pp. 773-788 ◽  
Author(s):  
Sadia Khalid ◽  
Josip Pečarić ◽  
Ana Vukelić
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Convex Functions ◽  
Type Inequality ◽  
Cauchy Type ◽  
Linear Functionals ◽  
Ostrowski’S Inequality ◽  
New Family ◽  
Exponentially Convex Functions ◽  
The Difference

Abstract In this work, the Green’s function of order two is used together with Fink’s approach in Ostrowski’s inequality to represent the difference between the sides of the Sherman’s inequality. Čebyšev, Grüss and Ostrowski-type inequalities are used to obtain several bounds of the presented Sherman-type inequality. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking to the linear functionals associated with the obtained inequalities.

scholarly journals Stolarsky type means related to an extension of H ¨older-type inequality

2014 ◽  
Vol 23 (1) ◽  
pp. 107-114
Author(s):  
KSENIJA SMOLJAK ◽  
Keyword(s):  
Convex Functions ◽  
Type Inequality ◽  
Monotonicity Property ◽  
Linear Functionals ◽  
Exponential Convexity ◽  
Exponentially Convex Functions

In this paper linear functionals related to an extension of Holder-type inequality are defined and their n−exponential convexity is proved. Furthermore, new Stolarsky type means, using families of exponentially convex functions, are defined and their monotonicity property is proved.

scholarly journals Pseudo-monotonicity and degenerated or singular elliptic operators

1998 ◽  
Vol 58 (2) ◽  
pp. 213-221 ◽  
Author(s):  
P. Drábek ◽  
A. Kufner ◽  
V. Mustonen
Keyword(s):  
Sobolev Spaces ◽  
Differential Operators ◽  
Weighted Sobolev Spaces ◽  
Type Inequality ◽  
Elliptic Operators ◽  
Hardy Type Inequality ◽  
Hardy Type ◽  
Elliptic Differential Operators

Using the compactness of an imbedding for weighted Sobolev spaces (that is, a Hardy-type inequality), it is shown how the assumption of monotonicity can be weakened still guaranteeing the pseudo-monotonicity of certain nonlinear degenerated or singular elliptic differential operators. The result extends analogous assertions for elliptic operators.

scholarly journals Eigencurves of the p(·)-Biharmonic operator with a Hardy-type term

2020 ◽  
Vol 6 (2) ◽  
pp. 198-209
Author(s):  
Mohamed Laghzal ◽  
Abdelouahed El Khalil ◽  
My Driss Morchid Alaoui ◽  
Abdelfattah Touzani
Keyword(s):  
Dirichlet Problem ◽  
Variational Approach ◽  
Type Inequality ◽  
Biharmonic Operator ◽  
Nondecreasing Sequence ◽  
Hardy Type Inequality ◽  
Principal Curve ◽  
Hardy Type ◽  
Homogeneous Dirichlet Problem

AbstractThis paper is devoted to the study of the homogeneous Dirichlet problem for a singular nonlinear equation which involves the p(·)-biharmonic operator and a Hardy-type term that depend on the solution and with a parameter λ. By using a variational approach and min-max argument based on Ljusternik-Schnirelmann theory on C1-manifolds [13], we prove that the considered problem admits at least one nondecreasing sequence of positive eigencurves with a characterization of the principal curve μ1(λ) and also show that, the smallest curve μ1(λ) is positive for all 0 ≤ λ < CH, with CH is the optimal constant of Hardy type inequality.

Degenerate p-Laplacian Operators and Hardy Type Inequalities on H-Type Groups

2010 ◽  
Vol 62 (5) ◽  
pp. 1116-1130 ◽  
Author(s):  
Yongyang Jin ◽  
Genkai Zhang
Keyword(s):  
Vector Fields ◽  
Orthonormal Basis ◽  
Type Inequality ◽  
Laplacian Operator ◽  
Hardy Type Inequality ◽  
Invariant Vector ◽  
Hardy Type Inequalities ◽  
Hardy Type ◽  
Left Invariant Vector ◽  
Laplacian Operators

AbstractLet 𝔾 be a step-two nilpotent group of H-type with Lie algebra 𝔊 = V ⊕ t. We define a class of vector fields X = {Xj} on 𝔾 depending on a real parameter k ≥ 1, and we consider the corresponding p-Laplacian operator Lp,ku = divX(|∇Xu|p−2∇Xu). For k = 1 the vector fields X = {Xj} are the left invariant vector fields corresponding to an orthonormal basis of V; for 𝔾 being the Heisenberg group the vector fields are the Greiner fields. In this paper we obtain the fundamental solution for the operator Lp,k and as an application, we get a Hardy type inequality associated with X.

General Hardy type inequality for seminormed fuzzy integrals

2010 ◽  
Vol 216 (7) ◽  
pp. 1972-1977 ◽  
Author(s):  
Hamzeh Agahi ◽  
M.A. Yaghoobi
Keyword(s):  
Type Inequality ◽  
Hardy Type Inequality ◽  
Hardy Type

A weighted Hardy type inequality and its applications

2021 ◽  
Vol 166 ◽  
pp. 102937
Author(s):  
Emerson Abreu ◽  
Diego Dias Felix ◽  
Everaldo Medeiros
Keyword(s):  
Type Inequality ◽  
Hardy Type Inequality ◽  
Hardy Type
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