The third axiom of filling properties - Pandiya, Ridwan (Examples and counterexamples, 2025)
Since its first appearance in 1983, the filled function method, which was initiated to solve global optimization problems, has developed very rapidly. From the results conducted by many scholars, the ideal filled function has at least two properties: parameter-free and continuously differentiable. Several researchers have attempted to provide filled functions with such properties that meet the three axioms (filling properties) required by the filled function definition. The third axiom specifically states that the filled function has a minimum point in the region of attraction. This paper examines the fact that the currently available continuously differentiable parameter-free filled functions do not fulfil the third axiom of the filling properties by providing several counterexamples.