arXiv subjects

Sompong Dhompongsa

Publications and source records attributed to Sompong Dhompongsa.

3 recordsLinked to original sources

arXiv2021

Fixed point properties and Q-nonexpansive retractions in locally convex spaces

Suppose that Q is a family of seminorms on a locally convex space E which determines the topology of E. We study the existence of Q-nonexpansive retractions for families of Q-nonexpansive mappings and prove that a separated and sequentially complete locally convex space $E$ that has the weak fixed point property, has the weak fixed point property for commuting separable semitopological semigroups of Q-nonexpansive mappings. This proves the Bruck's problem [5] for locally convex spaces. Moreover, we prove the existence of Q-nonexpansive retractions for the right amenable Q-nonexpansive semigroups.

math.FA↗

arXiv2020

A Practical Approach to Quasi-convex Optimization

A new and simple method for quasi-convex optimization is introduced from which its various applications can be derived. Especially, a global optimum under constrains can be approximated for all continuous functions.

math.OC↗

arXiv2020

A practical approach to optimization

We present a new approach for finding a minimal value of an arbitrary function assuming only its continuity. The process avoids verifying Lagrange- or KKT-conditions. The method enables us to obtain a Brouwer fixed point (of a continuous function mapping from a cube into itself).

math.OC↗