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Article
Open AccessSome new refinements of the Young, Hölder, and Minkowski inequalities
We prove and discuss some new refined Hölder inequalities for any p > 1 ...
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Article
Open AccessRefinements of some classical inequalities via superquadraticity
Some new refined versions of the Jensen, Minkowski, and Hardy inequalities are stated and proved. In particular, these results both generalize and unify several results of this type. Some results are also new ...
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Article
Open Access\(M_{\varphi}M_{\psi}\) -convexity and separation theorems
A characterization of pairs of functions that can be separated by an M φ ...
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Article
Open AccessContinuous refinements of some Jensen-type inequalities via strong convexity with applications
In this paper we prove new continuous refinements of some Jensen type inequalities in both direct and reversed forms. As applications we also derive some continuous refinements of Hermite–Hadamard, Hölder, and...
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Article
Functionals Related to Gauss–Pólya Type Inequalities Involving Derivatives
We consider several functionals associated with inequalities which involve derivatives of functions. As a consequence of those results we get new refinements and improvements for the Gauss–Pólya inequalities.
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Article
Open AccessA new look at classical inequalities involving Banach lattice norms
Some classical inequalities are known also in a more general form of Banach lattice norms and/or in continuous forms (i.e., for ‘continuous’ many functions are involved instead of finite many as in the classic...
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Article
Continuous Forms of Classical Inequalities
The main aim of this paper is to focus on the question to develop classical inequalities to hold in a more general “continuous” form (involving infinitely many functions and/or spaces). First, we discuss such ...
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Article
Open AccessProperties of some functionals associated with h-concave and quasilinear functions with applications to inequalities
We consider quasilinearity of the functional ( h ∘ v ) ...
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Article
Open AccessOn some inequalities for functions with nondecreasing increments of higher order
We investigate a class of functions with nondecreasing increments of higher order. A generalization of Brunk’s theorem is proved for that class of functions. Also, we consider functions with nondecreasing incr...
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Article
Open AccessThe Beckenbach-Dresher inequality in the Ψ-direct sums of spaces and related results
Let ψ ...
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Article
Properties of Map**s Related to the Minkowski Inequality
In this paper we obtain properties of several map**s which are arisen from the Minkowski inequality. We investigate superadditivity (subadditivity) and monotonicity of those functions, and give some refineme...
