Mathematical Inequalities & Applications 

About: Mathematical Inequalities & Applications is an academic journal published by University of Zagreb. The journal publishes majorly in the area(s): Mathematics Subject Classification & Mathematics. It has an ISSN identifier of 1331-4343. It is also open access. Over the lifetime, 1841 publications have been published receiving 18366 citations. The journal is also known as: Mathematical inequalities end applications & MIA.

On ψ- interpolation spaces

Abstract: In this paper the sequence Banach space ψ (Z) is defined for a class of convex functions ψ , and properties of the Kand Jinterpolation spaces (E0,E1)θ ,ψ,K and (E0,E1)θ ,ψ,J for a Banach couple E = (E0,E1) and θ ∈ (0,1) are studied. Mathematics subject classification (2000): 46B70.

Maximal function on generalized Lebesgue spaces $L^{p(\cdot)}$

Abstract: We prove the boundedness of the Hardy–Littlewood maximal function on the generalized Lebesgue space Lp(·)(Rd) under a continuity assumption on p that is weaker than uniform Holder continuity. We deduce continuity of mollifying sequences and density of C∞(Ω) in W1,p(·)(Ω) . Mathematics subject classification (2000): 42B25, 46E30.

Inequalities on Time Scales: A Survey

Abstract: The study of dynamic equations on time scales, which goes back to its founder Stefan Hilger (1988), is an area of mathematics which is currently receiving considerable attention. Although the basic aim of this is to unify the study of differential and difference equations, it also extends these classical cases to cases “in between”. In this paper we present time scales versions of the inequalities: Holder, Cauchy-Schwarz, Minkowski, Jensen, Gronwall, Bernoulli, Bihari, Opial, Wirtinger, and Lyapunov. 1. Unifying Continuous and Discrete Analysis In 1988, Stefan Hilger [13] introduced the calculus on time scales which unifies continuous and discrete analysis. A time scale is a closed subset of the real numbers. We denote a time scale by the symbol T . For functions y defined on T , we introduce a so-called delta derivative y∆ . This delta derivative is equal to y (the usual derivative) if T = R is the set of all real numbers, and it is equal to ∆y (the usual forward difference) if T = Z is the set of all integers. Then we study dynamic equations f (t; y; y∆; y∆ 2 ; : : : ; y∆ n ) = 0; which may involve higher order derivatives as indicated. Along with such dynamic equations we consider initial values and boundary conditions. We remark that these dynamic equations are differential equations when T = R and difference equations when T = Z . Other kinds of equations are covered by them as well, such as q difference equations, where T = q := fqkj k 2 Zg[ f0g for some q > 1 and difference equations with constant step size, where T = hZ := fhkj k 2 Zg for some h > 0: Particularly useful for the discretization purpose are time scales of the form T = ftkj k 2 Zg where tk 2 R; tk < tk+1 for all k 2 Z: Mathematics subject classification (2000): 34A40, 39A13.

Convexity according to the geometric mean

Abstract: We develop a parallel theory to the classical theory of convex functions, based on a change of variable formula, by replacing the arithmetic mean by the geometric one. It is shown that many interesting functions such as exp sinh cosh sec csc arc sin Γ etc illustrate the multiplicative version of convexity when restricted to appropriate subintervals of 0 .A s a consequence, we are not only able to improve on a number of classical elementary inequalities but also to discover new ones.