General Inequalities 5

The Fifth International Conference on General Inequalities was held from May 4 to May 10, 1986, at the Mathematisches Forschungsinstitut Oberwolfach (Black Forest, Germany). The organizing committee consisted of W.N. Everitt (Birmingham), L. Losonczi (Debrecen) and W. Walter (Karlsruhe). Dr. A. Kovacec served efficiently an'd enthusiastically as secretary to the con­ ference. The meeting was attended by 50 participants from 16 countries. In his opening address, W. Walter had to report on the death of five colleagues who had been active in the area of inequali­ ties and who had served the mathematical community: P.R. Beesack, G. Polya, D.K. Ross, R. Bellman, G. Szegö. He made special mention of G. Polya, who had been the last surviving author of the book InequaZities (Cambridge University Press, 1934), who died at the age of 97 years and whose many and manifold contributions to mathematics will be recorded elsewhere, in due course. Inequalities continue to play an important and significant role in nearly all areas of mathematics. The interests of the participants to this conference reflected the many different fields in which both classical and modern inequalities continue to influence developments in mathematics. In addition to the established fields, the lectures clearly indicated the importance of inequalities in functional analysis, eigenvalue theory, con­ vexi ty., number theory, approximation theory, probability theory, mathematical prograrnrning and economics.

The Bieberbach Conjecture. - De Branges proof of the Bieberbach conjecture. - Inequalities for Sums, Series and Integrals. - Tauberian theorems, convolutions and some results of D. C. Russell. - On a Hardy-Littlewood type integral inequality with a monotonic weight function. - Contributions to inequalities II. - On some discrete quadratic inequalities. - Some inequalities for geometric means. - Estimation of an integral. - Tauberian-type results for convolution of sequences. - Inequalities in Analysis and Approximation. - Weighted inequalities for maximal functions in spaces of homogeneous type with applications to non-isotropic fractional integrals. - Some inequalities concerning convolutions of kernel functions. - Inequalities for some special functions and their zeros. - Uniqueness inequality and best harmonic L1-approximation. - On the structure of (s, t)-convex functions. - Moments of convex and monotone functions. - An even order search problem. - Inequalities of Functional Analysis. - Positivity in absolute summability. - Fourier inequalities with Ap-weights. - Experimenting with operator inequalities using APL. - p-estimates for ultraproducts of Banach lattices. - Functional Equations and Inequalities. - On the stability of a functional equation arising in probabilistic normed spaces. - Some iterative functionsl inequalities and Schroder s equation. - On an inequality of P. W. Cholewa. - Subadditive multifunctions and Hyers-Ulam stability. - Bemerkungen zu einem Existenz- und Eindeutigkeitsproblem von W. Walter aus dem Gebiet der Differenzengleichungen. - Inequalities for Differential Operators. - Linear and nonlinear discrete inequalities in n independent variables. - Extremal problems for eigenvalues of the Sturm-Liouville type. - The HELP inequality in the regular case. - On estimatingeigenvalues of a second order linear differential operator. - Landau s inequality for the differential and difference operators. - Ein Existenzsatz für gewöhnliche Differentialgleichungen in geordneten Banachräumen. - Optimal bounds for the critical value in a semi-linear boundary value problem on a surface. - Some inequalities of Sobolev type on two-dimensional spheres. - Inequalities in Economics, Optimization and Applications. - Entropies, generalized entropies, inequalities and the maximum entropy principle. - Inequalities and mathematical programming, III. - Functions generating Schur-convex sums. - How to make fair decisions? . - On the ? T-product of symmetric and subsymmetric distributions functions. - Problems and Remarks. - The behaviour of comprehensive classes of means under equal increments of their variables. - A problem concerning some metrics. - Three problems. - Problems on Landau s inequality. - A generalization of Young s inequality. - On packings of congruent balls in the unit ball.