On Averages and Peaks

on semihypergroups and hypergroups

in this thesis, first the notion of weak mutual associativity (w.m.a.) and the necessary and sufficient condition for a $(l,gamma)$-associated hypersemigroup $(h, ast)$ derived from some family of $lesssim$-preordered semigroups to be a hypergroup, are given. second, by proving the fact that the concrete categories, semihypergroups and hypergroups have not free objects we will introduce t...

Problems on Averages and Lacunary Maximal Functions

We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First we obtain an H to L bound for lacunary maximal operators under a dimensional assumption on the underlying measure and an assumption on an Lp regularity bound for some p > 1. Secondly, we obtain a necessary and sufficient condition for L boundedness of lacunary maximal ...

On Asymptotic Differentiability of Averages

Radial Averages on Regular and Semiregular Graphs

In 1966, P. Günther proved the following result: Given a continuous function f on a compact surface M of constant curvature −1 and its periodic lift f̃ to the universal covering, the hyperbolic plane, then the averages of the lift f̃ over increasing spheres converge to the average of the function f over the surface M . In this article, we prove similar results for functions on the vertices and ed...

On peaks in carrying simplices

A necessary and sufficient condition is given for the carrying simplex of a dissipative totally competitive system of three ordinary differential equations to have a peak singularity at an axial equilibrium. For systems of Lotka–Volterra type that result translates into a simple condition on the coefficients.