arXiv subjects

Sedigheh Barootkoob

Publications and source records attributed to Sedigheh Barootkoob.

2 recordsLinked to original sources

arXiv2026

Discontinuity at the fixed point in suprametric spaces

The aim of this paper is to generalize some fixed point theorems in the class of convex contraction of order $m$ on a complete suprametric space. Then, we will prove that the class of convex contraction of order m is strong enough to generate a fixed point on a complete suprametric spaces but do not force the mapping to be continuous at the fixed point, and it can be replaced by relatively weaker conditions of $k$-continuity or $T$-orbitally lower semi-continuous. On this way a new and distinct solution to the open problem of Rhoades (Contemp Math 72:233-245,1988) is found. In sequel, we will prove some fixed point results in the setting suprametric spaces which are generalizations of the results regarding Sehgal, Ćirić and Fisher's quasi-contraction. Some examples and application will be approved our results.

math.GM↗

arXiv2020

On biamenability of Banach algebras

In this paper, we introduce the concept of biamenability of Banach algebras and we show that despite the apparent similarities between amenability and biamenability of Banach algebras, they lead to very different, and somewhat opposed, theories. In this regard, we show that commutative Banach algebras such as R and C tend to lack biamenability, while they may be amenable and highly noncommutative Banach algebras such as B(H) for an infinite dimensional Hilbert space H tend to be biamenable, while they are not amenable. Also, we show that although the unconditional unitization of an amenable Banach algebra is amenable but in general unconditional unitization of a Banach algebra is not biamenable. This concept is used for finding the character space of some Banach algebras.

math.FA↗