On a class of sets connected with a convex function

“…For instance, if a set ⊂ F (with F ∈ {R, C}) has a positive inner Lebesgue measure or contains a subset of the second category and with the Baire property, then int( − ) ̸ = 0 (see, e.g., [56]). For related results we refer to [56][57][58].…”

Section: Theorem 7 Let B( ) Be the Algebra Of All Bounded Linear Opementioning

confidence: 99%

“…[56]). For more information on B F and further references concerning the subject, we refer the reader to, for example, [56][57][58].…”

Section: Lie Derivationsmentioning

confidence: 99%

Survey on Recent Ulam Stability Results Concerning Derivations

Brzdęk

Cădariu

Ciepliński

et al. 2016

Journal of Function Spaces

View full text Add to dashboard Cite

show abstract

“…It appears that the strong regularity assumption can be weakened. In [5] it is proved the following theorem. During the 7th ICFEI K. Baron asked, whether this result holds true in more general case.…”

mentioning

confidence: 94%

Sum of graphs of continuous functions and boundedness of additive operators

Jabłoński

2005

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

Assume that f : D 1 → R and g : D 2 → R are uniformly continuous functions, where D 1 , D 2 ⊂ X are nonempty open and arc-connected subsets of a real normed space X. We prove that then either f and g are affine functions, that is f (x) = x * (x) + a and g(x) = x * (x) + b with some x * ∈ X * and a, b ∈ R or the algebraic sum of graphs of functions f and g has a nonempty interior in a product space X × R treated as a normed space with a norm (x, α) =x 2 + |α| 2 .

show abstract

On a class of sets connected with a convex function

Cited by 12 publications

References 2 publications

On approximate generalized Lie derivations

On approximate generalized Lie derivations

Survey on Recent Ulam Stability Results Concerning Derivations

Sum of graphs of continuous functions and boundedness of additive operators

Contact Info

Product

Resources

About