Related papers: A variation of Gronwall's lemma

In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.

The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a difference analogue of the Logarithmic Derivative Lemma is…

In this paper we introduce two new generalized variational inequalities, and we give some existence results of the solutions for these variational inequalities involving operators belonging to a recently introduced class of operators. We…

By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.

We establish a version of Gabber's presentation lemma in the setting of varieties with an action by the finite group of order 2.

We remark on the Garnier system in two variables.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

We prove the Yoneda lemma inside an elementary higher topos, generalizing the Yonda lemma for spaces.

We prove a uniformization theorem in complex algebraic geometry.

We prove a Fourier restriction estimate under the assumption that certain convolution power of the measure admits an $r$-integrable density.

In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two conjectures as possible extensions, and give a…

We extend Hadamard's Lemma to the setting of a separable Hilbert space.

We prove a noncommutative version of Bishop's peak interpolation-set theorem.

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

We give a short proof of the strong law of large numbers based on duality for random walk

It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.

We present a probabilistic proof of Euler's pentagonal number theorem based on a shuffling model.

We give a new proof of Chen-Lin result with Li-Zhang method.

We consider Brouwer's fixed point theorem and Sperner's lemma in one dimension. We present a proof of the Brouwer theorem using the Sperner lemma, and vice versa. However, we also show that they are not equivalent, because the Sperner lemma…