MODULARS ON SEMI-ORDERED LINEAR SPACES I

A Note on Naturally Ordered Sets in Semi-metric Spaces

Semi-linear Varieties of Lattice-Ordered Algebras

We consider varieties of pointed lattice-ordered algebras satisfying a restricted distributivity condition and admitting a very weak implication. Examples of these varieties are ubiquitous in algebraic logic: integral or distributive residuated lattices; their {·}-free subreducts; their expansions (hence, in particular, Boolean algebras with operators and modal algebras); and varieties arising ...

Kantorovich type inequalities for ordered linear spaces

In this paper Kantorovich type inequalities are derived for linear spaces endowed with bilinear operations ◦1 and ◦2. Sufficient conditions are found for vector-valued maps Φ and Ψ and vectors x and y under which the inequality Φ(x) ◦2 Φ(y) ≤ C + c 2 √ Cc Ψ(x ◦1 y) is satisfied. Complementary inequalities are also given. Some results of Dragomir [J. Inequal. Pure Appl. Math., 5 (3), Art. 76, 20...

On Convex Functions with Values in Semi–linear Spaces

The following result of convex analysis is well–known [2]: If the function f : X → [−∞, +∞] is convex and some x0 ∈ core (dom f) satisfies f(x0) > −∞, then f never takes the value −∞. From a corresponding theorem for convex functions with values in semi–linear spaces a variety of results is deduced, among them the mentioned theorem, a theorem of Deutsch and Singer on the single–valuedness of co...

Semi compactness and semi-I-compactness in ditopological texture spaces

In this paper we generalize the notion of Semi-continuity and MS-continuity and go on to study Semi-compactness, Semi-cocompactness, Semi-stability and Semi-costability in a ditopological texture space. We also extends the notion of Semi-compactness and Semi-cocompactness to a ditopological texture space modulo an ideal [13].