I. Sadeqi
Department of Mathematics, Sahand university of technology, Tabriz- Iran
[ 1 ] - ON APPROXIMATE CAUCHY EQUATION IN FELBIN'S TYPE FUZZY NORMED LINEAR SPACES
n this paper we study the Hyers-Ulam-Rassias stability of Cauchyequation in Felbin's type fuzzy normed linear spaces. As a resultwe give an example of a fuzzy normed linear space such that thefuzzy version of the stability problem remains true, while it failsto be correct in classical analysis. This shows how the category offuzzy normed linear spaces differs from the classical normed linearspac...
[ 2 ] - GRADUAL NORMED LINEAR SPACE
In this paper, the gradual real numbers are considered and the notion of the gradual normed linear space is given. Also some topological properties of such spaces are studied, and it is shown that the gradual normed linear space is a locally convex space, in classical sense. So the results in locally convex spaces can be translated in gradual normed linear spaces. Finally, we give an examp...
[ 3 ] - On Polar Cones and Differentiability in Reflexive Banach Spaces
Let $X$ be a Banach space, $Csubset X$ be a closed convex set included in a well-based cone $K$, and also let $sigma_C$ be the support function which is defined on $C$. In this note, we first study the existence of a bounded base for the cone $K$, then using the obtained results, we find some geometric conditions for the set $C$, so that ${mathop{rm int}}(mathrm{dom} sigma_C) neqem...
[ 4 ] - A cone theoretic Krein-Milman theorem in semitopological cones
In this paper, a Krein-Milman type theorem in $T_0$ semitopological cone is proved, in general. In fact, it is shown that in any locally convex $T_0$ semitopological cone, every convex compact saturated subset is the compact saturated convex hull of its extreme points, which improves the results of Larrecq.
[ 5 ] - Menger probabilistic normed space is a category topological vector space
In this paper, we formalize the Menger probabilistic normed space as a category in which its objects are the Menger probabilistic normed spaces and its morphisms are fuzzy continuous operators. Then, we show that the category of probabilistic normed spaces is isomorphicly a subcategory of the category of topological vector spaces. So, we can easily apply the results of topological vector spaces...
[ 6 ] - Bishop-Phelps type Theorem for Normed Cones
In this paper the notion of support points of convex sets in normed cones is introduced and it is shown that in a continuous normed cone, under the appropriate conditions, the set of support points of a bounded Scott-closed convex set is nonempty. We also present a Bishop-Phelps type Theorem for normed cones.
[ 7 ] - A Version of Favard's Inequality for the Sugeno Integral
In this paper, we present a version of Favard's inequality for special case and then generalize it for the Sugeno integral in fuzzy measure space $(X,Sigma,mu)$, where $mu$ is the Lebesgue measure. We consider two cases, when our function is concave and when is convex. In addition for illustration of theorems, several examples are given.
[ 8 ] - Vector Optimization Problems and Generalized Vector Variational-Like Inequalities
In this paper, some properties of pseudoinvex functions, defined by means of limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality, the Stampacchia vector variational-like inequality, and the weak formulations of these two inequalities defined by means of limiting subdifferential are studied. Moreover, some relationships between the vector vari...
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