Related papers: The mean value problem of Smale's problems

In this paper, we prove Smale's mean value conjecture by making use of quasiconformal deformations and holomorphic motions.

A proof of Smale's mean value conjecture from 1981 is given.

We give an analytic proof of the dual Smale's mean value conjecture in the case $n=7$.

We consider an extremal problem for polynomials, which is dual to the well-known Smale mean value problem. We give a rough estimate depending only on the degree.

In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].

The paper deals with some elementary problems about various mean value properties and their connections to harmonic functions and random walks.

A description of solutions of some integral equations has been obtained. A two-radii theorem is obtained as well.

Recent results concerning solutions of the modified Helmholtz equation are reviewed; namely, various mean value properties and their corollaries, converse and inverse of these properties, and relations between these solutions and harmonic…

In this work a mean value theorem of Pompeiu's type for functions of two variables is presented. Other related results are given as well.

The paper deals with continuous solutions of a Schilling's problem.

We establish that the initial value problem for a generalised Burgers equation considered in part I of this paper, is well-posed. We also establish several qualitative properties of solutions to the initial value problem utilised in part I…

This paper reviews the current state of the art of the mean value theorem due to Thomas M. Flett. We present the results with detailed proofs and provide many new proofs of known results. Moreover, some new observations and yet unpublished…

Motivated by a dictionary between polynomials and finite Blaschke products, we study both Smale's mean value conjecture and its dual conjecture for finite Blaschke products in this paper. Our result on the dual conjecture for finite…

We generalize the well-known mean value inequality of subharmonic functions for a slightly more general function class. We also apply this generalized mean value inequality to weighted boundary behavior and nonintegrability questions of…

In this work two-point boundary value problem for one class of second order ordinary differential equations with variable coefficients is solved.

We give an asymptotic formula for the mean value of the number of representations of an integer as sum of two squares known as the Gauss circle problem.

In this paper the Navier problem and the Dirichlet problem for Willmore curves in $\mathbb{R}^2$ is solved.

Using, as main tool, the convergence theorem for discrete martingales and the mean value property of harmonic functions we solve, a particular case of, Dirichlet problem.

We develop some of the basic theory for the obstacle problem on Riemannian Manifolds, and we use it to establish a mean value theorem. Our mean value theorem works for a very wide class of Riemannian manifolds and has no weights at all…

We show how one can ascertain the values of a complete set of mutually complementary observables of a prime degree of freedom.