Related papers: A generalization of Routh's triangle theorem

We use actions by finite cyclic groups to derive generalizations of three classical theorems from elementary number theory.

In the present paper, we prove generalizations of Banach, Kannan, Chatterjea, \'Ciri\'c-Reich-Rus fixed point theorems, as well as of the fixed point theorem for mappings contracting perimeters of triangles. We consider corresponding…

We prove a generalization of Tur\'{a}n's theorem proposed by Balogh and Lidick\'{y}.

We generalize the H. Cartan's theory of holomorphic curves for a general open Riemann surface. Besides, a vanishing theorem for jet differentials and a Bloch's theorem for Riemann surfaces are obtained.

We derive a generalized matrix version of Pellet's theorem, itself based on a generalized Rouch\'{e} theorem for matrix-valued functions, to generate upper, lower, and internal bounds on the eigenvalues of matrix polynomials. Variations of…

The great innovation of the Generalized Theorem is that it gives us the philosophy to work out the knowledge that the number of roots of an equation depends on the subfields of the functional terms of the equation they generate. Thus, the…

We prove Roth type theorems in finite groups. Our main tool is the Triangle Removal Lemma of Ruzsa and Szemer\'edi.

We find Feynman-Kac type representation theorems for generalized diffusions. To do this we need to establish existence, uniqueness and regularity results for equations with measure-valued coefficients.

In this paper, we state and prove a generalization of \'Ciri\'c fixed point theorems in metric space by using a new generalized quasi-contractive map. These theorems extend other well known fundamental metrical fixed point theorems in the…

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 note, we prove a certain hypergraph generalization of the Balog-Szemeredi-Gowers Theorem. Our result shares some features in common with a similar such generalizsation due to Sudakov, Szemeredi and Vu, though the conclusion of our…

After having investigated and defined the ``surface of a translation-like triangle" in each non-constant curvature Thurston geometry \cite{Cs-Sz25}, we generalize the famous Menelaus' and Ceva's theorems for translation triangles in the…

We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.

In this paper we introduce generalised Markov numbers and extend the classical Markov theory for the discrete Markov spectrum to the case of generalised Markov numbers. In particular we show recursive properties for these numbers and find…

We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.

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.

We establish a simple generalization for the famous theorem of Morley about trisectors in triangle with a purely synthetic proof using only angle chasing and similar triangles. Furthermore, based on the converse construction, another simple…

A generalization of the law of total covariance is presented and proved.

In this paper we prove a generalization of famous Larchr's theorem concerning good lattice points.

We prove a unified convergence theorem, which presents in four equivalent forms of the famous Antosik-Mikusinski Theorems. In particular, we show that Swartz' three uniform convergence principles are all equivalent to the Antosik-Mikusinski…