[PDF] Top 20 Convex Structures in Normed Spaces

... Abstract: A convexity on a nonempty set X is a collection 𝐶 of subsets of X which is closed under intersection and union of sets totally ordered under inclusion. The norm on a Normed linear space X defines a ... See full document

... for all x i , y i ∈ X , i = 1, 2, · · · , n. Morveover, f preserves any positive integer k in two directions. Proof. (1) Firstly, We show that both spaces have dimension greater than n, Let us first assume that ... See full document

... appropriate spaces as 2-normed ...2-normed spaces via this ...quasi convex 2-normed linear space, since the triangle inequality fails in quasi convex 2-normed ... See full document

... Some new characterization of best approximants from convex sub- sets and level sets of convex mappings in normed linear spaces in terms of norm derivatives and sub-orthogonality in Birkh[r] ... See full document

... One important problem in vector optimization is to find efficient points of a set. As observed by Kuhn, Tucker and later by Geoffrion, some efficient points exhibit certain abnormal properties. To eliminate such abnormal ... See full document

... Chu et al. [3] defined the concept of n-isometry which is suitable for representing the no- tion of n-distance preserving mappings in linear n-normed spaces and studied the Aleksandrov problem in linear ... See full document

... Thus to try and find a pseudoconvex non-convex subset in Banach space one must look for badly non weakly compact subsets of non reflexive spaces... normed space however, any non-convex s[r] ... See full document

... The classical Jensen inequality and Hermite–Hadamard inequality are ones of the most important inequalities in convex analysis and they have various applications in mathematics, statistics, economics and ... See full document

... linear normed space, and the center and the radius of the largest ball contained in it, provided that C has a nonempty boundary set with respect to the flat space generated by ...certain spaces, ... See full document

... The concept 2 normed space was introduced by S. Gahler. After Daminni and A.White introduced the ideas of strictly 2 convex 2 –normed space. They gave several important result on strictly ... See full document

... Locally convex probabilistic normed spaces are an interesting topic. In fact, some papers [–] discussed the subject, and we enjoy the topic too. On the basis of these papers, we try to search more ... See full document

... in normed spaces by Kolk [], in locally convex Hausdorff topological spaces by Maddox [], in topological Hausdorff groups by Çakallı [] and in probabilistic normed space by Karakuş ... See full document

... Motivated by this fact, we here introduce the notion of strong orthogonality as follows. Strongly orthogonal in the sense of Birkhoff-James: In a normed linear space X, an element x is said to be strongly ... See full document

... This result can also be viewed as an estimation theorem for the continuous convex mappings defined on a normed space in terms of semi-inner product ( .,... DRAGOMIR , A characterization [r] ... See full document

... Jensen’s inequality is pivotal in the Theory of Inequalities because it implies at once many other classical inequalities including the H¨ older, Minkowski, Beckenbach- Dresher and Young[r] ... See full document

... Motivated by the concepts of bounded linear functionals, and duality mappings on normed linear spaces [2, 9], bounded linear 2-functionals on 2-normed spaces were introduced by White [15[r] ... See full document

... Gozali et al. also introduced the notion of bounded n-linear functionals in n-normed spaces in [6]. Zofia Lewandowska introduced notions of 2-linear operators on 2-normed sets in [9]. Agus L. ... See full document

... Remark . In [] and [], the condition a b ≤ ab for all a, b ∈ [, ] is used. But this condition cannot hold in intuitionistic fuzzy normed spaces. In fact, if this condition holds, by using (iii) and ... See full document

... If the problem accepts a solution, we say that the equation is stable. The first sta- bility problem concerning group homomorphisms was raised by Ulam [35] in 1940. In the next year, Hyres [11] gave a positive answer to ... See full document

... By the Aoki-Rolewicz Theorem [54], each quasi-norm is equivalent to some p-norm (see also [7]) Since it is much easier to work with p-norms, henceforth we restrict our attention mainly to p-norms. Moreover in [59], J. ... See full document