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

We introduce the concept of shifting distance functions, and we establish a new fixed point theorem which generalizes the Banach contraction principle. An example is provided to illustrate our result.

In this paper we give a new proof, relying on Banach's contraction mapping principle, of a celebrated theorem of Andr\'e Bloch. Also, via the same contraction mapping principle, we give a proof of a Bloch type theorem for normalised Wu…

In two dimensions, Gallagher's theorem is a strengthening of the Littlewood conjecture that holds for almost all pairs of real numbers. We prove an inhomogeneous fibre version of Gallagher's theorem, sharpening and making unconditional a…

We present a new proof of the Joints Theorem without taking derivatives. Then we generalize the proof to prove the Multijoints Conjecture and Carbery's generalization. All results are in any dimension over an arbitrary field.

We generalize the injectivity theorem of Esnault and Viehweg, and apply it to the structure of log canonical type divisors.

In this paper we give a generalization of Iseki's formula and use it to prove the transformation law of $\theta_1(z, \tau)$.

We apply methods of derived and non-commutative algebraic geometry to understand ramification phenomena on arithmetic schemes. As an application, we prove the Deligne-Milnor conjecture and, in the pure characteristic case, a generalization…

In this paper we first prove a version of $L^{2}$ existence theorem for line bundles equipped a singular Hermitian metrics. Aa an application, we establish a vanishing theorem which generalizes the classical Nadel vanishing theorem.

Taylor's theorem (and its variants) is widely used in several areas of mathematical analysis, including numerical analysis, functional analysis, and partial differential equations. This article explains how Taylor's theorem in its most…

We postulate a new nonlinear generalization of the Dirac equation for an electron. Basic properties of the new equation are considered.

We obtain some results related to Romanoff's theorem.

In this article, we prove a generalization of a theorem (Ogg's conjecture) due to Bary Mazur for arbitrary $N\in \N$ and for {\it number fields}. The main new observation is a modification of a theorem due to Glenn Stevens for the…

This paper proposes a generalized ABC conjecture and assuming its validity settles a generalized version of Fermats last theorem.

We present a generalization of the topological inequality of Thorpe between the Euler characteristic and $k^{th}$-Pontryagin number of a $4k$-manifold. We also correct and complete some of the arguments from the work of Thorpe in which this…

We revise a proof of a Mazur-Ulam theorem for generalized gyrovector spaces.

We give a simple proof of the Emch closing theorem by introducing a new invariant measure on the circle. Special cases of that measures are well-known and have been used in the literature to prove Poncelet's and Zigzag theorems. Some…

We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena

We present a new proof of generalized Flett's mean value theorem due to Pawlikowska (from Demonstratio Math. 1999) using only the original Flett's mean value theorem. Also, a Trahan-type condition is established in general case.

We characterize the initial positions from which the first player has a winning strategy in a certain two-player game. This provides a generalization of Hall's theorem. Vizing's edge coloring theorem follows from a special case.

A vector variational principle is proved.