In this paper, we characterize the intuitionistic fuzzy δ-continuous, intuitionistic fuzzy weakly δ-continuous, intuitionistic fuzzy almost continuous, and intuitionistic fuzzy almost strongly θ-continuous functions in terms of intuitionistic fuzzy δ-closure and interior or θ-closure and interior.

It is shown, using the Borwein–Preiss variational principle that for every continuous convex function f on a weakly compactly generated space X, every x0 ∈ X and every weakly compact convex symmetric set K such that spanK = X, there is a point of Gâteaux differentiability of f in x0 +K. This extends a Klee’s result for separable spaces. The well-known Mazur’s theorem says that a continuous conv...

Let C(L) be the ring of real-valued continuous functions on a frame L. In this paper, strongly fixed ideals and characterization of maximal ideals of C(L) which is used with strongly fixed are introduced. In the case of weakly spatial frames this characterization is equivalent to the compactness of frames. Besides, the relation of the two concepts, fixed and strongly fixed ideals of C(L), is st...

LetX be a Banach space with dualX∗, and letK be a nonempty subset ofX. A gauge function is a continuous strictly increasing function φ : R → R such that φ 0 0 and limt→∞φ t ∞. The duality mapping Jφ : X → X∗ associated with a gauge function φ is defined by Jφ x : {f ∈ X∗ : 〈x, f〉 ‖x‖‖f‖, ‖f‖ φ ‖x‖ }, x ∈ X, where 〈·, ·〉 denotes the generalized duality pairing. In the particular case φ t t, the ...

Let E be a Banach space. There are several natural ways in which any polynomial P ∈ P(E) can be extended to P̃ ∈ P(E), in such a way that the extension mapping is continuous and linear (see, for example, [6]). Taking the double transpose of the extension mapping P → P̃ yields a linear, continuous mapping from P(E) into P(E). Further, since P(E) is a dual space, it follows that there is a natural ...

We give a characterization of K-weakly precompact sets in terms of uniform Gateaux differentiability of certain continuous convex functions.