Type Inequalities Research Articles

Refinement of Jensen Mercer and Hermite–Hadamard-Mercer type inequalities for generalized convex functions on co-ordinates with their computational analysis

In the current study, the Jensen-Mercer inequality is extended to co-ordinated h-convex functions. Additionally, a novel inequality is employed to derive Hermite–Hadamard-Mercer type inequalities for h-convex functions defined on the co-ordinates of a rectangle in the plane. These developments not only reinforce the core tenets of convex analysis but also expand the applicability of Hermite-Hadamard-Mercer type inequalities to generalized convex functions on co-ordinates. This provides valuable tools for data analysis and optimization problem-solving. The practical utility and efficacy of this generalized inequality in real-world scenarios involving co-ordinates are demonstrated through a computational study. Mathematics Subject Classification: 26D10, 26D15, 26A51, 34A08.

Correction: Hoffman–Wielandt type inequality for block companion matrices of certain matrix polynomials

Correction: Hoffman–Wielandt type inequality for block companion matrices of certain matrix polynomials

Hermite–Hadamard type inequality for non-convex functions employing the Caputo–Fabrizio fractional integral

Hermite–Hadamard type inequality for non-convex functions employing the Caputo–Fabrizio fractional integral

Inventive dynamic inequalities of Pachpatte type on time scales and applications

In this article, we report a set of unique dynamic inequalities for different time scales that are based on delta-derivatives. These proposed inequalities prove to be useful tools for investigating both qualitative and quantitative facets of a class of time-scale dynamic equations, in addition to enhancing and extending several inequalities found in the literature. The introduced inequalities aid in a more thorough comprehension of the features of these equations, which involve an unknown function and its associated delta derivatives. The endpoint of this article includes numerical illustrations to emphasize the practical significance of the developed results.

Some New Estimations of Left and Right Interval Fractional Pachpatte’s Type Integral Inequalities via Rectangle Plane

Inequalities involving fractional operators have been an active area of research, which is crucial in establishing bounds, estimates, and stability conditions for solutions to fractional integrals. In this paper, we initially presented a new class that is known as coordinated left and right ℏ-pre-invex interval-valued mappings (C·L·R-ℏ-pre-invex Ι·V-M), as well classical convex and nonconvex are also obtained. This newly defined class enabled us to derive novel inequalities, such as Hermite–Hadamard and Pachpatte’s type inequalities. Furthermore, the obtained results allowed us to recapture several special cases of known results for different parameter choices, which can be applications of the main results. Finally, we discussed the validity of the main outcomes.

A New Class of Coordinated Non-Convex Fuzzy-Number-Valued Mappings with Related Inequalities and Their Applications

Both theoretical and applied mathematics depend heavily on integral inequalities with generalized convexity. Because of its many applications, the theory of integral inequalities is currently one of the areas of mathematics that is evolving at the fastest pace. In this paper, based on fuzzy Aumann’s integral theory, the Hermite–Hadamard’s type inequalities are introduced for a newly defined class of nonconvex functions, which is known as U·D preinvex fuzzy number-valued mappings (U·D preinvex F·N·V·Ms) on coordinates. Some Pachpatte-type inequalities are also established for the product of two U·D preinvex F·N·V·Ms, and some Hermite–Hadamard–Fejér-type inequalities are also acquired via fuzzy Aumann’s integrals. Additionally, several new generalized inequalities are also obtained for the special situations of the parameters. Additionally, some of the interesting remarks are provided to acquire the classical and new exceptional cases that can be considered as applications of the main outcomes. Lastly, a few suggested uses for these inequalities in numerical integration are made.

Some Inequalities for Differentiable Functions on a Generalization of Hermite-Hadamard Inequality with Applications

The main identity of midpoint type inequalities is generalized and using this identity some composite midpoint type inequalities are estimated. Moreover, applications to some special means and some error estimates for the composite midpoint formula are discussed.

Better Approximations for Quasi-Convex Functions

In this paper, by using Hölder-İşcan, Hölder integral inequality and a general identity for differentiable functions we can get new estimates on generalization of Hadamard, Ostrowski and Simpson type integral inequalities for functions whose derivatives in absolute value at certain power are quasi-convex functions. It is proved that the result obtained Hölder-İşcan integral inequality is better than the result obtained Hölder inequality. Keywords: Hölder-İşcan scan inequality, Hermite-Hadamard inequality, Simpson and Ostrowski type inequality, midpoint and trapezoid type inequality, quasi-convex functions.

Ostrowski Type Inequalities Via ψ − (α, β, γ, δ)−Convex Function

In this paper, we are introducing very first time the class of ψ − (α, β, γ, δ)−convex function in mixed kind, which is the generalization of many classes of convex functions. We would like to state well-known Ostrowski inequality via Montgomery identity for ψ−(α, β, γ, δ)−convex function in mixed kind. In addition, we establish some Ostrowski type inequalities for the class of functions whose derivatives in absolute values at certain powers are ψ − (α, β, γ, δ)-convex functions in mixed kind by using different techniques including Hölder's inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, some applications in terms of special means would also be given. Keywords: Ostrowski inequality, Montgomery identity, convex functions, special means.

Global burden of type 1 diabetes in adults aged 65 years and older, 1990-2019: population based study

ObjectivesTo estimate the burden, trends, and inequalities of type 1 diabetes mellitus (T1DM) among older adults at global, regional, and national level from 1990 to 2019.DesignPopulation based study.PopulationAdults aged ≥65...

Weak monotonicity property of Korevaar-Schoen norms on nested fractals

In this paper, we study the weak monotonicity property of Korevaar-Schoen (p-energy) norms on nested fractals for 1<p<∞. Such property has many important applications on fractals and other metric measure spaces, such as constructing p-energies (when p=2 this is basically a Dirichlet form), generalizing the classical Sobolev type inequalities and the celebrated Bourgain-Brezis-Mironescu convergence.

Tensorial Simpson 1/8 Type Inequalities for Convex Functions of Selfadjoint Operators in Hilbert Space

Several Simpson 1 8 tensorial type inequalities for selfadjoint operators have been obtained with variation depending on the conditions imposed on the function f||1/8[f(A)⊗1 + 6f(A⊗1 + 1⊗B/2) + 1⊗f(B)] − ∫01f(λ1⊗B + (1−λ)A⊗1)dλ|| ≤ 5||1⊗B − A⊗1||/32 ||f’||I,+∞.

On Reverse and Generalized of Bellman Type Inequality

On Reverse and Generalized of Bellman Type Inequality

Schwarz-Pick type inequalities from an operator theoretical point of view

We use (versions of) the von Neumann inequality for Hilbert space contractions to prove several Schwarz-Pick type inequalities. Specifically, we derive an alternate proof for a multi-point Schwarz-Pick inequality by Beardon and Minda, along with a generalized version for operators. Connections with model spaces and Peschl's invariant derivatives are established. Finally, Schwarz-Pick inequalities for analytic functions on polydisks and for higher order derivatives are discussed. An enhanced version of the Schwarz-Pick lemma, using the notion of distinguished variety, is obtained for the bidisk.

On some extensions of the Hua determinant inequality and a question of Poon

In this note, we give simple proofs of two recent extensions of the Hua determinant inequality. We also answer a question of Poon affirmatively on a Young type inequality, which appears in his investigation of inequalities on eigenvalues arising from the Hua determinant inequality.

Some new clique inequalities in four-index hub location models

Hub location problems can be modeled in several ways, one of which is the path-based family of models that make use of four-index variables. Clique inequalities are frequently used to describe solution characteristics for optimization problems with binary variables. In this study, new valid inequalities of the clique type are introduced for the path-based family of hub location models. Some of their properties and corresponding lifting are discussed, and a separation heuristic algorithm is proposed. We also report a set of computational experiments to evaluate the usefulness of the proposals when embedded in a commercial solver.

J-selfadjoint matrix means and their indefinite inequalities

AbstractLet J be a non trivial involutive Hermitian matrix. Consider $${\mathbb {C}}^n$$ C n equipped with the indefinite inner product induced by J, $$[x,y]=y^*J x$$ [ x , y ] = y ∗ J x for all $$x,y\in {{\mathbb {C}}}^n,$$ x , y ∈ C n , which endows the matrix algebra $${\mathbb {C}}^{n\times n}$$ C n × n with a partial order relation $$\le ^J$$ ≤ J between J-selfadjoint matrices. Inde-finite inequalities are given in this setup, involving the J-selfadjoint $$\alpha $$ α -weighted geometric matrix mean. In particular, an indefinite version of Ando–Hiai inequality is proved to be equivalent to Furuta inequality of indefinite type.

Hermite –Hadamard and Hermaite –Hadamard Fejer inequality for new f-divergence measure via conformable fractional integrals

In information geometry, a divergence measure is a type of statistical distance and a binary function which established the separation from one probability distribution to another on a statistical numerous. The basic use of divergence measure is statistical data processing, information storage, decision making etc. The most famous inequality regarding the integral mean of a convex function is HermiteâHadamard's inequality and the weighted version of this is called the Hermite-Hadamard-Fejér inequality. Purpose of this paper is to find Hermaite-Hadamard and Hermite-Hadamard Fejer type inequalities for new f-divergence measure with the help of conformable fractional integrals. Hermaite-Hadamard inequality gives us necessary and sufficient condition for a function must be convex. Here we consider the new f-divergence measure, it has the property of convexity. In this research article we drive some inequalities for t-convex function which gives us the extensions of the previous work for convex and t-convex function and also obtains some fractional midpoint type inequalities. The main purpose of this paper is to establish conformal fractional approximation of Hermaite-Hadamard and Hermite-Hadamard Fejer type inequalities for new f-divergence measure which close the fractional integral and the Riemann-Liouville integrable into single form,also gives us some new results for -Riemann-Liouville integral as special cases of main results. This article gives us most useful link between convexity and symmetry.

Hardy type inequalities with mixed weights in cones

Hardy type inequalities with mixed weights in cones

Weighted Alexandrov–Fenchel type inequalities for hypersurfaces in Rn$\mathbb {R}^n$

AbstractIn this paper, we prove the following geometric inequalities in the Euclidean space , which are weighted Alexandrov–Fenchel type inequalities, provided that is a star‐shaped and ‐convex hypersurface. Equality holds if and only if is a coordinate sphere in . As an application, by letting in the above inequality, we obtain a lower bound for the outer radius in terms of the curvature integrals for star‐shaped and ‐convex hypersurfaces.