Related papers: Old and new on the 3-convex functions
This paper establishes three minimax theorems for possibly nonconvex functions on Euclidean spaces or on infinite-dimensional Hilbert spaces. The theorems also guarantee the existence of saddle points. As a by-product, a complete solution…
In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new…
The purpose of the present paper is to show few examples of nonlinear PDEs (mostly with strong geometric features) for which there is a hidden convex structure. This is not only a matter of curiosity. Once the convex structure is…
This paper explains unexpected links between the 3 topics in the title and frames them in a large canvas.
Matrix versions of some basic convexity inequalities are given. Further results on the same topic are proved in the recent papers on arxiv: 1. Hermitian operators and convex functions, 2. A concavity inequality for symmetric norms, 3.…
A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.
In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are h-convex and we point out the results for some special…
The effectiveness of projection methods for solving systems of linear inequalities is investigated. It is shown that they have a computational advantage over some alternatives and that this makes them successful in real-world applications.…
The classical quadratic formula and some of its lesser known variants for solving the quadratic equation are reviewed. Then, a new formula for the roots of a quadratic polynomial is presented.
We overview the main ideas and techniques of the functional-analytical approach to some extremal problems of convex geometry that stem from the Queen Dido problem.
In this paper we present another proof of the analytic version of the Hahn-Banach theorem in terms of convex functionals.
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…
The aim of this note is threefold: first, to present a few relevant facts about the way in which the technique of enriching contractive mappings was introduced; secondly, to expose the main contributions in the area of enriched mappings…
I first comment on some recent advances in computing equipment for CPU-intensive numerical simulations, and on possible developments in the near future. I then discuss some particularly important and yet unsolved problems in dynamics and…
A class of generalized Schr\"{o}dinger elliptic problems involving concave-convex and other types of nonlinearities is studied. A reasonable overview about the set of solutions is provided when the parameters involved in the equation assume…
In this paper, some new inequalities of the Hermite-Hadamard type for h- convex functions whose modulus of the derivatives are h-convex and applications for special means are given.
This is a survey paper on algorithms for solving problems in 3-dimensional topology. In particular, it discusses Haken's approach to the recognition of the unknot, and recent variations.
We present existence results for weak solutions to a broad class of degenerate McKean-Vlasov equations with rough coefficients, expanding upon and refining the techniques recently introduced by the third author. Under certain structural…
The so-called polynomial equations play an important role both in algebra and in the theory of functional equations. If the unknown functions in the equation are additive, relatively many results are known. However, even in this case, there…
In this paper, the notion of convexity of picture fuzzy multisets was introduced and some of their properties were presented after studying the concept of picture fuzzy multisets.