Related papers: Fixed Points of Mean Section Operators
The spherical mean transform associates to a function $f$ its integral averages over all spheres. We consider the spherical mean transform for functions supported in the unit ball $\mathbb{B}$ in $\mathbb{R}^n$ for odd $n$, with the centers…
We consider nonconstant periodic constrained minimizers of semilinear elliptic equations for integro-differential operators in $\mathbb{R}$. We prove that, after an appropriate translation, each of them is necessarily an even function which…
In this paper, we endow the space of continuous translation invariant valuation on convex sets generated by mixed volumes coupled with a suitable Radon measure on tuples of convex bodies with two appropriate norms. This enables us to…
We extend the fixed point result for Path-Averaged Contractions (PA-contractions) from complete metric spaces to complete b-metric spaces. We prove that every PA-contraction on a complete b-metric space has a unique fixed point, provided…
The paper characterizes the convex hull of the closure of the cone-volume set $C_\cv(U)$, consisting of all cone-volume vectors of polygons with outer unit normals vectors contained in $U$, for any finite set $U \subseteq \R^2, \pos(U) =…
Given a compact convex domain $C\subset \mathbb{R}^k$ and bounded measurable functions $f_1,\ldots,f_n:C\to \mathbb{R}$, define the sup-convolution $(f_1\ast \ldots \ast f_n)(z)$ to be the supremum average value of…
We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…
In recent work of Kennard, Khalili Samani, and the last author, they generalize the Half-Maximal Symmetry Rank result of Wilking for torus actions on positively curved manifolds to $\mathbb{Z}_2$-tori with a fixed point. They show that if…
The continuity of the inverse Klain map is investigated and the class of centrally symmetric convex bodies at which every valuation depends continuously on its Klain function is characterized. Among several applications, it is shown that…
In this work, we will present variants Fixed Point Theorem for the affine and classical contexts, as a consequence of general Brouwer's Fixed Point Theorem. For instance, the affine results will allow working on affine balls, which are…
In this paper we establish some common fixed point theorem for a new class of pair of contractions mappings, called $\psi-(\alpha,\beta, m)$-contraction pairs, which we will assume occasionally weakly compatible and satisfying the property…
We prove that a compact Riemannian manifold of dimension $m \geq 3$ with harmonic curvature and $\lfloor\frac{m-1}{2}\rfloor$-positive curvature operator has constant sectional curvature, extending the classical Tachibana theorem for…
This article derives closed-form parametric formulas for the Minkowski sums of convex bodies in d-dimensional Euclidean space with boundaries that are smooth and have all positive sectional curvatures at every point. Under these conditions,…
We generalise the analysis in [arXiv:0904.1744] to superspace, and explicitly prove that for any embedding of surface operators in a general, twisted N=2 pure abelian theory on an arbitrary four-manifold, the parameters transform naturally…
An equidistant set in the Euclidean space consists of points having equal distances to both members of a given pair of sets, called focal sets. Having no effective formulas to compute the distance of a point and a set, it is hard to…
As in two and four dimensions, supersymmetric conformal field theories in three dimensions can have exactly marginal operators. These are illustrated in a number of examples with N=4 and N=2 supersymmetry. The N=2 theory of three chiral…
We extended the study of the linear fractional self maps (e.g. by Cowen-MacCluer and Bisi-Bracci on the unit balls) to a much more general class of domains, called generalized type-I domains, which includes in particular the classical…
We find necessary and sufficient conditions on the convolution kernels $ \varphi $ so that certain operators on twisted Fock spaces $\mathcal{F}^\lambda(\C^{2n})$ are bounded.
For holomorphic pairs of symbols $(u, \psi)$, we study various structures of the weighted composition operator $ W_{(u,\psi)} f= u \cdot f(\psi)$ defined on the Fock spaces $\mathcal{F}_p$. We have identified operators $W_{(u,\psi)}$ that…
In this article, we derive a common fixed point result for a pair of single valued and set-valued mappings on a metric space having graphical structure. In this case, the set-valued map is assumed to be closed valued instead of closed and…