A new constantWD(X) is introduced into any real 2n-dimensional symmetric normed space X . By virtue of this constant, an upper bound of the geometric constant D(X), which is used to measure the difference between Birkhoff orthogonality and isosceles orthogonality, is obtained and further extended to an arbitrarym-dimensional symmetric normed linear space (m≥ 2). As an application, the result is...

The terminology and notation used here are introduced in the following articles: [18], [8], [20], [5], [7], [6], [3], [1], [17], [13], [19], [14], [2], [4], [15], [10], [11], [9], and [12]. One can prove the following propositions: (1) Let X, Y , Z be complex linear spaces, f be a linear operator from X into Y , and g be a linear operator from Y into Z. Then g · f is a linear operator from X in...

in this paper, we consider a generalization of the real normed spaces and give some examples.

For convex continuous functions f, g defined respectively in neighborhoods of points x, y in a normed linear space, a formula for the distance between ∂f(x) and ∂g(y) in terms of f, g (i.e. without using the dual) is proved. Some corollaries, like a new characterization of the subdifferential of a continuous convex function at a point, are given. This, together with a theorem from [4], implies ...

We prove a theorem that generalizes various results ([4, Theorem 1], [9, Theorem 1-8], [7], [8, Lemma 4.1]) concerning eigenvalues and spectral points in the boundary of the spatial numerical range and numerical range of a continuous linear operator T on a complex normed space X. The proof is similar to the proof of [4, Theorem 1] and uses a fixed point theorem as do the proofs of [4, Theorem 1...

In this paper, we extend the concept of set-valued fuzzy measures (introduced and studied by Guo and Zhang [2004. On set-valued fuzzy measures. Information Sciences 160 (2004) 13–25]) to the class of multivalued set functions taking values in the family of non-empty closed subsets of a real normed space. Also, we introduce the notions of atom and non-atomicity of a multivalued set function and ...

We determine some stability results concerning the pexiderized quadratic functional equation in non-Archimedean fuzzy normed spaces. Our result can be regarded as a generalization of the stability phenomenon in the framework of L-fuzzy normed spaces. AMS Mathematics Subject Classification (2010): 00A11; Primary 46S40; Secondary 39B52, 39B82, 26E50, 46S50.

We study new sequence spaces associated to sequences in normed spaces and the band matrix F̂ defined by the Fibonacci sequence. We give some characterizations of continuous linear operators and weakly unconditionally Cauchy series by means of completeness of the new sequence spaces. Also, we characterize the barreledness of a normed space via weakly∗ unconditionally Cauchy series in [Formula: se...