On the first derivative of real functions (Preliminary communication)
Let and be closed subsets of [0,1] with a subset of the limit points of . Necessary and sufficient conditions are found for the existence of a continuous function such that is an -limit set for and is the set of fixed points of in .
2000 Mathematics Subject Classification: 26A33, 33C20This paper is devoted to further development of important case of Wright’s hypergeometric function and its applications to the generalization of Γ-, B-, ψ-, ζ-, Volterra functions.
The main goal of this paper is to characterize the family of all functions f which satisfy the following condition: whenever g is a Darboux function and f < g on ℝ there is a Darboux function h such that f < h < g on ℝ.