Related papers: A generalization of Tur\'{a}n's theorem

In this paper, we prove a generalization of Geraghty's fixed point theorem for multi--valued mappings.

We present a simple extension of Lindeberg's argument for the Central Limit Theorem to get a general invariance result. We apply the technique to prove results from random matrix theory, spin glasses, and maxima of random fields.

A sequence of generalizations of Cartan's conservation of torsion theorem is given for n-dimensional differentiable manifolds having a general linear connection.

In this paper we prove the Bohr Theorem for slice regular functions. Following the historical path that led to the proof of the classical Bohr Theorem, we also extend the Borel-Carath\'eodory Theorem to the new setting.

We prove Koll\'ar's injectivity theorem for globally $F$-regular varieties.

This note presents a proof of P\'olya's random walk theorem using classical methods from special function theory and asymptotic analysis.

Using toric geometry we prove a B\'ezout type theorem for weighted projective spaces.

We study the Hadwiger-Alesker finiteness theorem from the standpoint of Lie theory and announce a generalization.

Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…

A proof of Thompson's conjecture for real semi-simple Lie groups has been given by Kapovich, Millson, and Leeb. In this note, we give another proof of the conjecture by using a theorem of Alekseev, Meinrenken, and Woodward from symplectic…

Arvanitakis established recently a theorem which is a common generalization of Michael's convex selection theorem and Dugundji's extension theorem. In this note we provide a short proof of a more general version of Arvanitakis' result.

Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.

In this paper, by using analytical methods we obtain a generalization of the famous Kodaira embedding theorem.

This paper provides a uniform explanation of different extensions and generalizations of the butterfly theorem based on the Desargues involution theorem.

We extend the quantitative Balian-Low theorem of Nitzan and Olsen to higher dimensions.

In this paper some Tur\'an type inequalities for classical and generalized Mittag-Leffler functions are considered. The method is based on proving monotonicity for special ratio of sections for series of Mittag-Leffler functions. Some…

In this article we will introduce a central problem in additive combinatorics, which arised from the famous van der Waerden theorem and an early conjecture of Erd\H{o}s and Tur\'{a}n. The first important theorem was due to Roth in 1953.…

We provide a simple proof of Pascal's Theorem on cyclic hexagons, as well as a generalization by M\"obius, using hyperbolic geometry.

A short proof of the Mazur-Ulam theorem concerning isometries of real normed spaces.

We prove the finiteness of $B$-representations of generalised log canonical pairs. As a consequence, we prove that, the (relative) abundance for a generalised semi-log canonical pair is implied by the abundance for its normalisation.…