An attempt to define the concept of a functor covering both cases (covariant and contravariant) resulted in a structure consisting of two fields: the object map and the morphism map, the first one mapping the Cartesian squares of the set of objects rather than the set of objects. We start with an auxiliary notion of bifunction, i.e. a function mapping the Cartesian square of a set A into the Ca...

We provide sufficient conditions for a monotone function with finite set of outcomes to be cyclically monotone. Using these conditions, we show that any defined on the domain gross substitutes is The result also extends generalized and complements.

This paper provides an expository introduction to monotone and near-monotone biochemical network structures. Monotone systems respond in a predictable fashion to perturbations, and have very robust dynamical characteristics. This makes them reliable components of more complex networks, and suggests that natural biological systems may have evolved to be, if not monotone, at least close to monoto...

Abstract In this paper, we introduce a new algorithm by incorporating an inertial term with subgradient extragradient to solve the equilibrium problems involving pseudomonotone and Lipschitz-type continuous bifunction in real Hilbert spaces. A weak convergence theorem is well established under certain mild conditions for control parameters involved. Some of applications variational inequalities...

Abstract The primary objective of this study is to develop two new proximal-type algorithms for solving equilibrium problems in real Hilbert space. Both are analogous the well-known two-step extragradient algorithm variational inequality problem spaces. proposed iterative use a step size rule based on local bifunction information instead line search technique. Two weak convergence theorems both...

This paper provides an expository introduction to monotone and nearmonotone biochemical network structures. Monotone systems respond in a predictable fashion to perturbations, and have very robust dynamical characteristics. This makes them reliable components of more complex networks, and suggests that natural biological systems may have evolved to be, if not monotone, at least close to monoton...

We survey an algebraic approach to proving impossibility results in distributed computing. The approach is emerging around monotone groups, a new class of algebraic groups we define here as a tight suit to monotone Read&Modify&Write (or RMW) operations in a distributed system. The yields of this approach have been the first impossibility results for implementations of monotone RMW operations th...

In this paper, we present an example in which the sum of two maximal abstract monotone operators is maximal. Also, we shall show that the necessary condition for Rockafellar’s surjectivity which was obtained in ([19], Theorem 4.3) can be sufficient.