Equations fonctionnelles et estimations de normes de matrices.
Existence criteria for positive solutions of a nonlinear difference inequality
This paper is concerned with a class of nonlinear difference inequalities which include many different classes of difference inequalities and equations as special cases. By means of a Riccati type transformation, necessary and sufficient conditions for the existence of eventually positive solutions and positive nonincreasing solutions are obtained. Various type of comparison theorems are also derived as applications, which extends many theorems in the literature.
Extensions of Popoviciu's inequality using a general method.
Fixed-point theorems for multi-valued functions and their applications to functional equations [Book]
Functional equations and nowhere differentiable functions.
Functional equations and nowhere differentiable functions. (Summary).
Functional equations for pecular functions.
Functional inequalities associated with Jordan-von Neumann-type additive functional equations.
Fuzzy stability of additive functional inequalities with the fixed point alternative.
General solution of a system of functional equations satisfied by sums of powers on arithmetic progressions.
Generalized distributivity for real, continuous functions. I: Structure theorems and surjective solutions.
Generalized distributivity for real, continuous functions. II: Local solutions in the continuous case.
Generalized inequalities for indefinite forms.
Generalized midconvexity
There are many types of midconvexities, for example Jensen convexity, t-convexity, (s,t)-convexity. We provide a uniform framework for all the above mentioned midconvexities by considering a generalized middle-point map on an abstract space X. We show that we can define and study the basic convexity properties in this setting.
Generalized orthogonal stability of some functional equations.
Holomorphic solutions of an inhomogeneous Cauchy equation.
Homogeneity properties of subadditive functions.
Hyers-Ulam stability of functional equations in several variables.
Implications between approximate convexity properties and approximate Hermite-Hadamard inequalities
The connection between the functional inequalities and is investigated, where D is a convex subset of a linear space, f: D → ℝ, α H;α J: D-D → ℝ are even functions, λ ∈ [0; 1], and ρ: [0; 1] →ℝ+ is an integrable nonnegative function with ∫01 ρ(t) dt = 1.
Improved -convexity inequalities.