zero point problems of the sum of two monotone mappings and fixed point problems of a strictly pseudocontractive mapping are investigated‎. ‎a strong convergence theorem for the common solutions of the problems is established in the framework of hilbert spaces‎.

‎In this paper‎, ‎some properties of pre-monotone operators are proved‎. ‎It is shown that in a reflexive Banach space‎, ‎a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous‎. ‎The notion of $sigma$-convexity is introduced and the‎ ‎relations between the $sigma$-monotonicity and $sigma$-convexity is i...

We investigate the representation of functions on streams in some denotational domains. As expected, a total continuous stream function can always be represented by a Scott-continuous function, and moreover by a strongly stable map in the corresponding Hypercoherence. It seems however difficult to represent an arbitrary stream function by a monotone map on Scott domains such that the stream fun...

In [8], Dontchev and Hager have shown that a monotone set-valued map defined from a Banach space to its dual which satisfies the Aubin property around a point (x, y) of its graph is actually single-valued in a neighbourhood of x. We prove a result which is the counterpart of the above for quasimonotone set-valued maps, based on the concept of single-directional property. As applications, we pro...

Let S, T be semilattices. Let us assume that if S is upper-bounded, then T is upper-bounded. A map from S into T is said to be a semilattice morphism from S into T if: (Def. 1) For every finite subset X of S holds it preserves inf of X . Let S, T be semilattices. Observe that every map from S into T which is meet-preserving is also monotone. Let S be a semilattice and let T be an upper-bounded ...

Assumption 2 (Condition I) Let K be a class of L-structures which admit a monotone idempotent closure operation cl taking subsets of M ∈ K to substructures of M such that cl has finite character. Strictly speaking, we should write clM (X) rather than cl(X) but we will omit the M where it is clear from context. Definition 3 Let A be a subset of H, H ′ ∈ K. A map from X ⊂ H − A to X ′ ⊂ H ′ − A i...

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...

In this paper, we consider the monotone inclusion problem consisting of the sum of a continuous monotone map and a point-to-set maximal monotone operator with a separable two-block structure and introduce a framework of block-decomposition prox-type algorithms for solving it which allows for each one of the single-block proximal subproblems to be solved in an approximate sense. Moreover, by sho...

If L is a selfdual Lagrangian L on a reflexive phase space X ×X∗, then the vector field x → ∂̄L(x) := {p ∈ X∗; (p, x) ∈ ∂L(x, p)} is maximal monotone. Conversely, any maximal monotone operator T on X is derived from such a potential on phase space, that is there exists a selfdual Lagrangian L on X ×X∗ (i.e, L∗(p, x) = L(x, p)) such that T = ∂̄L. This solution to problems raised by Fitzpatrick can...

We investigate the topological entropy of a green interval map. Defining the complexity we estimate from above the topological entropy of a green interval map with a given complexity. The main result of the paper — stated in Theorem 0.2 — should be regarded as a completion of results of [4]. 0. Introduction and main result The purpose of this paper is to evaluate the topological entropy of gree...