The first two implications are trivial. In [2], the second author showed that every almost α-continuous function is η-continuous. In [1], Dickman, Porter and Rubin proved that every η-continuous is θ-continuous and hence weakly continuous. Although θ-continuous functions behave, in general, nicely, they may cause some unexpected problems. For example, if f :X → Y is θ-continuous, then f :X → f(...

In this paper, we introduce the concept of IVF weakly M -continuity and investigate some characterizations for IVF weakly M -continuous mappings between an IVF minimal space and an IVF topological space.

A function f :R → {0, 1} is weakly symmetric (weakly symmetrically continuous) at x ∈ R provided there is a sequence hn → 0 such AMS classification numbers: Primary 26A15; Secondary 03E50, 03E35.

Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, non-expansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which ...

A weak form of weak quasi-continuity, which we call subweak quasi-continuity, is introduced. It is shown that subweak quasi-continuity is strictly weaker than weak quasicontinuity. Subweak quasi-continuity is used to strengthen several results in the literature concerning weak quasi-continuity. Specifically, results concerning the graph, graph function, and restriction of a weakly quasi-continu...

Let S be a dense sub-semigroup of R+, and let X be a separable, reflexive Banach space. This note contains a proof that every weakly continuous contractive semigroup of operators on X over S can be extended to a weakly continuous semigroup over R+. We obtain similar results for nonlinear, nonexpansive semigroups as well. As a corollary we characterize all densely parametrized semigroups which a...

Abstract. In this paper, the authors defined a multifunction F : X → Y to be upper (resp. lower) weakly α-continuous if for each x ∈ X and each open set V of Y such that F (x) ⊂ V (resp. F (x) ∩ V 6= ∅), there exists an α-open set U of X containing x such that U ⊂ F(Cl(V )) (resp. U ⊂ F−(Cl(V ))). They give some characterizations and several properties concerning upper (lower) weakly α-continuo...