A maximal theorem with function-theoretic applications

A cone theoretic Krein-Milman theorem in semitopological cones

In this paper, a Krein-Milman  type theorem in $T_0$ semitopological cone is proved,  in general. In fact, it is shown that in any locally convex $T_0$ semitopological cone, every convex compact saturated subset is the compact saturated convex hull of its extreme points, which improves the results of Larrecq.

A Maximal Element Theorem in FWC-Spaces and Its Applications

A maximal element theorem is proved in finite weakly convex spaces (FWC-spaces, in short) which have no linear, convex, and topological structure. Using the maximal element theorem, we develop new existence theorems of solutions to variational relation problem, generalized equilibrium problem, equilibrium problem with lower and upper bounds, and minimax problem in FWC-spaces. The results repres...

A Strong Maximum Modulus Theorem for Maximal Function Algebras

A Covering Theorem with Applications

We prove a Covering Theorem that allows us to prove modified norm inequalities for general maximal operators. We will also give applications to convergence of a sequence of linear operators and the differentiation of the integral.

The Implicit Function Theorem with Applications in Dynamics and Control

The implicit function theorem is a statement of the existence, continuity, and differentiability of a function or set of functions. The theorem is closely related to the convergence of Newton’s method for nonlinear equations, the existence and uniqueness of solutions to nonlinear differential equations, and the sensitivity of solutions to these nonlinear problems. The implicit function theorem ...