A common fixed point theorem for a commuting family of weak$^{\ast }$ continuous nonexpansive mappings

The super fixed point property for asymptotically nonexpansive mappings

We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive mappings in uniformly nonsquare and uniformly noncreasy Banach spaces. The results are generalized for commuting families of asymptotically nonexpansive mappings.

Common fixed point theorems for nonexpansive mappings using the lower semicontinuity property

Suppose that E is a Banach space, τ a topology under which the norm of E becomes τ-lower semicontinuous and S a commuting family of τ-continuous nonexpansive mappings defined on a τ-compact convex subset C of E: It is shown that the set of common fixed points of S is a nonempty nonexpansive retract of C. Along the way, a few other related fixed point theorems are derived.

Fixed point properties and Q-nonexpansive retractions in locally convex spaces

Suppose that Q is a family of seminorms on a locally convex space E which determines the topology of E. We study the existence of Q-nonexpansive retractions for families of Q-nonexpansive mappings and prove that a separated and sequentially complete locally convex space $E$ that has the weak fixed point property, has the weak fixed point property for commuting separable semitopological semigroups of Q-nonexpansive mappings. This proves the Bruck's problem [5] for locally convex spaces. Moreover, we prove the existence of Q-nonexpansive retractions for the right amenable Q-nonexpansive semigrou…

Compact asymptotic center and common fixed point in strictly convex Banach spaces

In this paper, we present some common fixed point theorems for a commuting pair of mappings, including a generalized nonexpansive single valued mapping and a generalized nonexpansive multivalued mapping in strictly convex Banach spaces. The results obtained in this paper extend and improve some recent known results.

非膨胀映射的次不变度量泛函

Subinvariant metric functionals for nonexpansive mappings

本文研究了Banach空间非紧子集中非膨胀映射交换族的次不变度量泛函存在性，证明了特定条件下度量泛函的唯一极小化元蕴含不动点存在，凸显了其在寻找不动点中的实用性。

Weyl's theorem for commuting tuple of paranormal and $\ast$-paranormal operators

In this article, we show that a commuting pair $T=(T_1,T_2)$ of $\ast$-paranormal operators $T_1$ and $T_2$ with quasitriangular property satisfy the Weyl's theorem-I, that is $$σ_T(T)\setminusσ_{T_W}(T)=π_{00}(T)$$ and a commuting pair of paranormal operators satisfy Weyl's theorem-II, that is $$σ_T(T)\setminusω(T)=π_{00}(T),$$ where $σ_T(T),\, σ_{T_W}(T),\,ω(T)$ and $π_{00}(T)$ are the Taylor spectrum, the Taylor Weyl spectrum, the joint Weyl spectrum and the set consisting of isolated eigenvalues of $T$ with finite multiplicity, respectively. Moreover, we prove that Weyl's theorem-II holds …