In a real normed space we introduce two notions of approximate Roberts orthogonality as follows:

$$x \\perp_R^\\varepsilon y \\, {\\rm if \\, and \\, only \\, if} \\left|\\|x + ty\\|^2 - \\|x - ty\\|^2\\right| \\leq 4\\varepsilon...

We introduce the relation ρλ-orthogonality in the setting of normed spaces as an extension of some orthogonality relations based on norm derivatives and present some of its essential properties. Among other things, we give a characterization...

Orthogonal constant mappings in isosceles orthogonal spaces...

Abstract. Let f denote a mapping from an orthogonality space (X;?) into a real Ba-

nach space Y. In this paper, we prove the Hyers–Ulam stability of the orthogonally cubic

functional equations f(2x+y)+f(2x¡y) = 2f(x+y)+2f(x¡y)+12f...

Inner product C∗-modules generalize inner product spaces by allowing inner prod-ucts to take values in an arbitrary C∗-algebra A instead of the C∗-algebra of complex numbers C. The classical Birkhoff–James orthogonality says that if x, y are elements...

The Hyers–Ulam stability of the conditional quadratic functional equation of Pexider type f ðx þ yÞþ

f ðx 2 yÞ¼ 2gðxÞþ 2hðyÞ; x ’ y is established where ’ is a symmetric orthogonality in the sense of

Ra ¨tz and f is odd....

compared to the use of force sensors and cameras which are often very expensive and require massive structures. In this paper, we evaluate the ability of the Fast Orthogonal Search (FOS) methodology to predict jaw motion using Electromyography (EMG) signals...

We introduce the concept of the approximate Roberts orthogonality set and investigate the geometric properties of such sets. In addition, we introduce a notion of the approximate $a$-isosceles-orthogonality and consider class of mappings, which...

We introduce a notion of approximate orthogonality preserving mappings between Hilbert C∗-modules. We define the concept of (δ,ε)-orthogonality preserving mapping and give some sufficient conditions for a linear mapping to be (δ,ε)-orthogonality...

In this paper, we obtain some characterizations of the (strong) Birkhoff--James orthogonality for elements of Hilbert $C^*$-modules

and certain elements of $\\B(\\mathscr{H})$.

Moreover, we obtain a kind of Pythagorean relation...