Extreme and exposed points of spaces of integral polynomials

Extreme and Exposed Points of Spaces of Integral Polynomials

We show that if E is a real Banach space such that E′ has the approximation property and such that `1 6↪→ ⊗̂ n,s, E then the set of extreme points of the unit ball of PI(E) is equal to {±φn : φ ∈ E′, ‖φ‖ = 1}. Under the additional assumption that E′ has a countable norming set we see that the set of exposed points of the unit ball of PI(E) is also equal to {±φn : φ ∈ E′, ‖φ‖ = 1}.

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

existence and approximate $l^{p}$ and continuous solution of nonlinear integral equations of the hammerstein and volterra types

بسیاری از پدیده ها در جهان ما اساساً غیرخطی هستند، و توسط معادلات غیرخطی ‎‏بیان شد‎‎‏ه اند. از آنجا که ظهور کامپیوترهای رقمی با عملکرد بالا، حل مسایل خطی را آسان تر می کند. با این حال، به طور کلی به دست آوردن جوابهای دقیق از مسایل غیرخطی دشوار است. روش عددی، به طور کلی محاسبه پیچیده مسایل غیرخطی را اداره می کند. با این حال، دادن نقاط به یک منحنی و به دست آوردن منحنی کامل که اغلب پرهزینه و ...

Extreme Points and Rotundity of Orlicz-sobolev Spaces

On the Extreme Points and Strongly Extreme Points in Köthe–bochner Spaces

We give the necessary conditions of extreme points and strongly extreme points in the unit ball of Köthe–Bochner spaces. The conditions have been shown to be sufficient earlier.