We discuss operator inequalities associated with Hölder–McCarthy and Kantorovich inequalities. We give a complementary inequality of Hölder–McCarthy one as an extension of [2] and also we give an application to the order preserving power inequality.

A scale of Carlson type inequalities are proved and the best constants are found. Some multidimensional versions of these inequalities are also proved and it is pointed out that also a well-known inequality by Beurling–Kjellberg is included as an endpoint case.

A new method for minimizing a proper closed convex function is proposed and its convergence properties are studied. The convergence rate depends on both the growth speed off at minimizers and the choice of proximal parameters. An application of the method extends the corresponding results given by Kort and Bertsekas for proximal minimization algorithms to the case in which the ...

In our previous notes, we give a useful characterization of the chaotic order, i.e., for positive invertible operators and . In this note, we present a short proof to the characterization of the chaotic order and give an answer to a related problem on it. Moreover we consider the orders defined by as an interpolation between the chaotic order and the usual order via the Furuta ...

The analytic center of an -dimensional polytope with a nonempty interior is defined as the unique minimizer of the logarithmic potential function over . It is shown that one cycle of a conjugate direction method, applied to the potential function at any such that , generates a point such that .

We prove a multiplicity result of Ambrosetti–Prodi type problems of higher order. Proofs are based on upper and lower solutions method for higher order periodic boundary value problems and coincidence degree arguments.

Some inequalities related to the exponential function are solved and the stability of the functional equations and is studied.

We show that several of the classical Sobolev embedding theorems extend in the case of weighted Sobolev spaces to a class of quasibounded domains which properly include all bounded or finite measure domains when the weights have an arbitrarily weak singularity or degeneracy at the boundary. Sharper results are also shown to hold when the domain satisfies an integrability condition ...

We generalize the classical Gram determinant inequality. Our generalization follows from the boundedness of the antisymmetric tensor product operator. We use fermionic Fock space methods.

This note is concerned with a comparison of the approximation-theoretical behaviour of trigonometric convolution processes and their discrete analogues. To be more specific, for continuous functions it is a well-known fact that under suitable conditions the relevant uniform errors are indeed equivalent, apart from constants. It is the purpose of this note to extend the matter to ...

A new refinement of the classical arithmetic mean and geometric mean inequality is given. Moreover, a new interpretation of the classical mean is given and this refinement theorem is generalized.

We combine our previous method of multifunctions and differential inclusions with the technique of Carathéodory comparison equations and consider some partial differential inequalities of Haar type. In this way, certain new uniqueness criteria for global semiclassical solutions to weakly-coupled systems will be derived.

This paper is a first attempt to give numerical values for constants and , in classical estimates and where is an algebraic polynomial of degree at most and denotes the -metric on . The basic tools are Markov and Bernstein inequalities.

Sobolev inequalities in two-dimensional hyperbolic space are dealt with. Here is modeled on the upper Euclidean. half-plane equipped with the Poincaré–Bergman metric. Some borderline inequalities, where the leading exponent equals the dimension, are focused. The technique involves rearrangements of functions, and tools from calculus of variations and ordinary differential equations.

We shall obtain the best bound in Ozeki's inequality which estimates the difference of Cauchy's inequality. We also give an operator version of Ozeki's inequality which extends an inequality on the variance of an operator.

Let be the solution of the initial value problem for the dimensional heat equation. Then, for any and for any , an inequality about and is obtained.

We give an integral analogue of the Ostrowski inequality and several extensions, allowing in particular for multiple linear constraints.

A semilinear abstract differential-delay equation with a nonautonomous linear part is considered. Solution estimates are derived. They generalize Wazewski and Lozinskii inequalities. Conditions for global stability are established.

Let be any positive integer, and any positive real numbers. The inequality was conjectured for by T.J. Lyons, after he had proved it with an extra factor on the right, in a preprint (Imperial College of Science, Technology and Medicine, 1995). Many numerical trials confirmed the conjecture, and none disproved it. The present paper proves it, with strict inequality, for all a in ...

In this paper we introduce the mapping connected with the lower and upper semiinner products and , and study its monotonicity, boundedness, convexity and other properties. Applications to theory of inequalities in analysis are given including refinements of the Schwarz inequality.

The von Neumann–Jordan (NJ-) constant for Lebesgue–Bochner spaces is determined under some conditions on a Banach space . In particular the NJ-constant for as well as (the space of -Schatten class operators) is determined. For a general Banach space we estimate the NJ-constant of , which may be regarded as a sharpened result of a previous one concerning the uniform non-squareness ...

This paper is concerned with five integral inequalities considered as generalisations of an inequality first discovered by G.H. Hardy and J.E. Littlewood in 1932. Subsequently the inequality was considered in greater detail in the now classic text Inequalities of 1934, written by Hardy and Littlewood together with G. Pólya. All these inequalities involve Lebesgue square-integrable ...

We obtain several generalized variational inequalities from an equilibrium theorem due to the first author under more weaker hypothesis and in more general setting than known ones. Our new results extend, unify and improve many known Hartman–Stampacchia–Browder type variational inequalities for u.s.c. or monotone type multimaps. Our proofs are also much simpler than known ones.

A characterization of chaotic order is given by using generalized Furuta inequality and its application to related norm inequalities is given as a precise estimation of our previous paper [15]. Also parallel results related to generalized Furuta inequality are given by using nice characterization of chaotic order by Fujii et al. [7].

The notions of association and dependence of random variables, rearrangements, and heterogeneity via majorization ordering have proven to be most useful for deriving stochastic inequalities. In this survey article we first show that these notions are closely related to three basic inequalities in classical mathematical analysis: Chebyshev's inequality, the Hardy-Littlewood-Pólya ...