The Kolmogorov Inequalities for Multiply Monotone Functions Defined on a Half-line

Inequalities for the norms of finite difference operators of multiply monotone sequences

In this paper we shall present discrete Kolmogorov type inequalities for multiply monotone sequences defined on non-positive integers. Moreover, we will provide a more delicate information by obtaining the description of the following modulus of continuity ω j,r p,q (δ ,ε) = sup{‖Δx‖q : x,Δx, . . . ,Δ j x 0, ‖x‖p = δ , ‖Δx‖∞ = ε} for δ ε > 0 and values of j = r−2 or j = r−1 depending on values ...

Gap Functions and Descent Methods for Minty Variational Inequality

A new class of gap functions associated to the variational inequality introduced by Minty is defined. Descent methods for the minimization of the gap functions are analysed in order to develop exact and inexact line-search algorithms for solving strictly and strongly monotone variational inequalities, respectively.

Hermite-Hadamard inequality for geometrically quasiconvex functions on co-ordinates

In this paper we introduce the concept of geometrically quasiconvex functions on the co-ordinates and establish some Hermite-Hadamard type integral inequalities for functions defined on rectangles in the plane. Some  inequalities for product of two geometrically quasiconvex functions on the co-ordinates are considered.

A Relaxed Extra Gradient Approximation Method of Two Inverse-Strongly Monotone Mappings for a General System of Variational Inequalities, Fixed Point and Equilibrium Problems

GENERALIZED POSITIVE DEFINITE FUNCTIONS AND COMPLETELY MONOTONE FUNCTIONS ON FOUNDATION SEMIGROUPS

A general notion of completely monotone functionals on an ordered Banach algebra B into a proper H*-algebra A with an integral representation for such functionals is given. As an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. A generalized version of Bochner’s theorem on foundation se...