On an inequality of G. Gruss
On - associated comonotone functions
We give a positive answer to two open problems stated by Boczek and Kaluszka in their paper [1]. The first one deals with an algebraic characterization of comonotonicity. We show that the class of binary operations solving this problem contains any strictly monotone right-continuous operation. More precisely, the comonotonicity of functions is equivalent not only to -associatedness of functions (as proved by Boczek and Kaluszka), but also to their -associatedness with being an arbitrary strictly...
On certain inequalities improving the Hermite-Hadamard inequality.
On continuity and monotonicity of Darboux transformations.
On generalized preinvex functions and monotonicities.
On Kemperman's inequality 2f(x)≤ f(x+h)+f(x+2h)
On l'Hospital-type rules for monotonicity.
On quasi-continuous iteration semigroups and groups of real functions
On Regularly Varying Functions With Applications To Functions Theory.
On some alternative functional equations. (Short Communication).
On the characterization of quasiarithmetic means with weight function.
On the continuity and monotonicity of restrictions of connected functions
On the identric and logarithmic means.
On the impossibility of approximating convex functions with ones.
On Whitney pairs
A simple arc ϕ is said to be a Whitney arc if there exists a non-constant function f such that for every . G. Petruska raised the question whether there exists a simple arc ϕ for which every subarc is a Whitney arc, but for which there is no parametrization satisfying . We answer this question partially, and study the structural properties of possible monotone, strictly monotone and VBG* functions f and associated Whitney arcs.
O-Regualarly Varying Functions
Orlicz spaces, α-decreasing functions, and the Δ₂ condition
We prove some quantitatively sharp estimates concerning the Δ₂ and ∇₂ conditions for functions which generalize known ones. The sharp forms arise in the connection between Orlicz space theory and the theory of elliptic partial differential equations.
Positive derivatives and increasing functions.
Properties of connected functions in terms of their levels
Representation theorems for sequences of the classes and .