Fuzzy anti-bounded linear functional and fuzzy antidual spaces are defined. Hahn-Banach theorem and some of its consequences on fuzzy anti-normed linear space are studied. Two fundamental theorems; namely, open mapping theorem and closed graph theorem are established. Keywords-Fuzzy anti-norm, α-norm, Fuzzy anti-complete, Fuzzy anti-bounded linear functional, Fuzzy anti-dual space.

A positively convex module is a non-empty set closed under positively convex combinations but not necessarily a subset of a linear space. Positively convex modules are a natural generalization of positively convex subsets of linear spaces. Any positively convex module has a canonical semimetric and there is a universal positively affine mapping into a regularly ordered normed linear space and a...

1.1. Introducton to Banach Spaces Definition 1.1. Let X be a K–vector space. A functional p ∶ X → [0,+∞) is called a seminorm, if (a) p(λx) = ∣λ∣p(x), ∀λ ∈ K, x ∈X, (b) p(x + y) ≤ p(x) + p(y), ∀x, y ∈X. Definition 1.2. Let p be a seminorm such that p(x) = 0 ⇒ x = 0. Then, p is a norm (denoted by ∥ ⋅ ∥). Definition 1.3. A pair (X, ∥ ⋅ ∥) is called a normed linear space. Lemma 1.4. Each normed sp...

For given k ∈ (0, 1) and r > 0, a self-mapping T : M → M is said to be r-roughly k-contractive provided ‖Tx− Ty‖ ≤ k ‖x− y‖+ r (x, y ∈ M). To state fixed-point properties of such a mapping, the self-Jung constant Js(X) is used, which is defined as the supremum of the ratio 2 rconv S(S)/ diam S over all non-empty, non-singleton and bounded subsets S of some normed linear space X, where rconv S(S...

The notion of lacunary ideal convergence in intuitionistic fuzzy normed linear space (IFNLS) was introduced by the present corresponding author [P. Debnath, Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Comput. Math. Appl., 63 (2012), 708-715] and an open problem in that paper was whether every lacunary I-convergent sequence is lacunary I-Cauchy. Further, a new concep...

In this paper, we give some properties of the sets Be(a, r) and Be[a, r]. This enables us to obtain a result analogue of “Open mapping theorem”for 2-normed space 2000 Mathematics Subject Classification: 41A65, 41A15.

the present paper introduces the notion of the complete fuzzy norm on a linear space. and, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. some characterizations of their properties are obtained.