In this paper, we introduce soft complete continuity as a strong form of and continuity. Several characterizations, compositions, restriction theorems are obtained. Moreover, several preservation regarding compactness, Lindelofness, connectedness, regularity, normality, almost mild near paracompactness, metacompactness addition to these, the study deals with correlation between our new concepts...

Let Ω be an open set of R and let f : Ω × R × R be a nonnegative continuous function, convex with respect to ξ ∈ R. Following the well known theory originated by Serrin [14] in 1961, we deal with the lower semicontinuity of the integral F (u,Ω) = ∫ Ω f (x, u(x), Du(x)) dx with respect to the Lloc (Ω) strong convergence. Only recently it has been discovered that dependence of f (x, s, ξ) on the ...

in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...

The concept of continuity in a strong sense for the case functions with values metric spaces is studied. separate and joint properties this are investigated, several results by Russell generalized. A function $f:X \times Y \to Z$ strongly continuous respect to $x$ /$y$/ at point ${(x_0, y_0)\in X Y}$ provided an arbitrary $\varepsilon> 0$ there neighborhoods $U$ $x_0$ $X$ $V$ $y_0$ $Y$ such ...