STABILITY AND SUPERSTABILITY OF JORDAN HOMOMORPHISMS AND JORDAN DERIVATIONS ON BANACH ALGEBRAS AND C~＊-ALGEBRAS： A FIXED POINT APPROACH

Using fixed point methods, we prove the Hyers-Ulam-Rassias stability and superstability of Jordan homomorphisms (Jordan *-homomorphisms), and Jordan derivations (Jordan *-derivations) on Banach algebras (C*-algebras) for the generalized Jensen-type functional equationwhere r is a fixed positive real number in (1, ∞).     

Weakly compact homomorphisms of regular Banach algebras

Let A be a uniformly regular Ditkin algebra. It is shown that every weakly compact homomorphism of A into a Banach algebra is finite-dimensional.     

A structure of ring homomorphisms on commutative Banach algebras

We give a structure theorem for a ring homomorphism of a commutative regular Banach algebra into another commutative Banach algebra. In particular, it is shown that:

(i)

A ring homomorphism of a commutative -algebra onto another commutative -algebra with connected infinite Gelfand space is either linear or anti-linear.

(ii)

A ring automorphism of is either linear or anti-linear.

(iii)

, and the disc algebra are neither ring homomorphic images of nor .

     

Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation

In this paper, we prove the Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation. This is applied to investigate homomorphisms between quasi-Banach algebras. The concept of Hyers-Ulam-Rassias stability originated from Th.M. Rassias' stability theorem that appeared in his paper [Th.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978) 297-300].     

Compact homomorphisms of regular banach algebras

Let A be a complex commutative Banach algebra and let M_A be the maximal ideal space of A. We say that A has the bounded separating property if there exists a constant C > 0 such that for every two distinct points ?₁, ?₂ ∈ M_A, there is an element a ∈ A for which , and ‖a‖ ? C, where is the Gelfand transform of a ∈ A. We show that if A is a strongly regular Banach algebra with the bounded separating property, then every compact homomorphism from A into another Banach algebra is of finite dimensional range. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Generalized Ulam-Hyers stability of random homomorphisms in random normed algebras associated with the Cauchy functional equation

Using the fixed point method, we prove the generalized Ulam-Hyers stability of random homomorphisms in random normed algebras associated with the Cauchy functional equation.     

p-距离空间中的一类压缩映象的不动点定理

仿照距离空间,2-距离空间中的一些概念,引入了p-距离空间及p-距离空间中的一些基本概念.根据研究2-距离空间中不动点理论的思想和方法,利用泛函分析的理论,对p-距离空间中的不动点问题进行了研究.把2.距离空间中压缩型映像的不动点理论移植到了p-距离空间中,形成了p-距离空间中压缩型映像的一些基本不动点理论.其距.离空...     

On a fixed point result of Amini-Harandi in strictly convex Banach spaces

Summary Amini-Harandi proved that alternate convexically nonexpansive mappings on non-empty weakly compact convex subsets of strictly convex Banach spaces have fixed points. We prove that Amini-Harandi's result holds also in Banach spaces with the Kadec--Klee property and the result is true for a larger class of mappings. Moreover, we show that the Alspach mapping in L¹[0,1] is not a 2-alternate convexically nonexpansive mapping.     

A combinatorial Lefschetz fixed point formula

We define a class of simplicial maps — those which are “expanding directions preserving” — from a barycentric subdivision to the original simplicial complex. These maps naturally induce a self map on the links of their fixed points. The local index at a fixed point of such a map turns out to be the Lefschetz number of the induced map on the link of the fixed point in relative homology. We also show that a weakly hyperbolic [4] simplicial map sdⁿK →K is expanding directions preserving.     

A fixed point theorem for the infinite-dimensional simplex

We define the infinite-dimensional simplex to be the closure of the convex hull of the standard basis vectors in R^∞, and prove that this space has the fixed point property: any continuous function from the space into itself has a fixed point. Our proof is constructive, in the sense that it can be used to find an approximate fixed point; the proof relies on elementary analysis and Sperner's lemma. The fixed point theorem is shown to imply Schauder's fixed point theorem on infinite-dimensional compact convex subsets of normed spaces.     

Common fixed point theorems for maps under a contractive condition of integral type

Two common fixed point theorems for mapping of complete metric space under a general contractive inequality of integral type and satisfying minimal commutativity conditions are proved. These results extend and improve several previous results, particularly Theorem 4 of Rhoades [B.E. Rhoades, Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 63 (2003) 4007-4013] and Theorem 4 of Sessa [S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) (N.S.) 32 (46) (1982) 149-153].     

赋值Banach代数的偏序D^-度量空间和公共不动点定理

基于完备的D^*-度量空间,提出具有Banach代数的偏序D^*-度量空间的定义,通过迭代序列的构造,证明了新定义下不动点定理的存在性及唯一性理论.随后引入了关于两个连续自映射的公共不动点定理,并对其存在性和唯一性进行了研究.所得结果推广了现有文献.     

The split common fixed point problem for generalized demimetric mappings in two Banach spaces

ABSTRACT

In this paper, we consider the split common fixed point problem for new demimetric mappings in two Banach spaces. Using the hybrid method, we prove a strong convergence theorem for finding a solution of the split common fixed point problem in two Banach spaces. Furthermore, using the shrinking projection method, we obtain another strong convergence theorem for finding a solution of the problem in two Banach spaces. Using these results, we obtain well-known and new strong convergence theorems in Hilbert spaces and Banach spaces.     

Almost homomorphisms between unital <Emphasis Type="Italic">C</Emphasis>*-algebras: A fixed point approach

Let A , B be two unital C*-algebras. By using fixed pint methods, we prove that every almost unital almost linear mapping h : A → B which satisfies h(2 n uy) = h(2 n u)h(y) for all u ∈ U(A), all y ∈ A, and all n = 0, 1, 2, … , is a homomorphism. Also, we establish the generalized Hyers-Ulam-Rassias stability of *-homomorphisms on unital C*-algebras.     

g-非扩张型FUZZY映象序列的公共FUZZY混合不动点

提出fuzzy映象序列的公共fuzzy混合不动点的概念，研究了g-非扩张型fuzzy映象序列的公共fuzzy混合不动点定理，我们所得的定理改进和推广了近期相关的重要结果．     

Some new common fixed point results for generalized contractive multi-valued non-self-mappings

In this work, we study some new common fixed point results for generalized contractive multi-valued non-self-mappings on complete metric spaces.     

Some common fixed point theorems for weakly compatible mappings

Jungck's [G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986) 771-779] notion of compatible mappings is further extended and used to prove some common fixed point theorems for weakly compatible non-self mappings in complete convex metric spaces. We improve on the method of proof used by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9-12] and Ahmed and Rhoades [A. Ahmed, B.E. Rhoades, Some common fixed point theorems for compatible mappings, Indian J. Pure Appl. Math. 32 (2001) 1247-1254] and obtain generalization of some known results. In particular, a theorem by Rhoades [B.E. Rhoades, A fixed point theorem for non-self set-valued mappings, Int. J. Math. Math. Sci. 20 (1997) 9-12] is generalized and improved.     

New fixed point theorems of condensing mappings satisfying the interior condition in Banach spaces

In this paper, based on a basic result on condensing mappings satisfying the interior condition, some new fixed point theorems of the condensing mappings of this kind are obtained. As a result, the famous Altman’s theorem, Roth’s theorem and Petryshyn’s theorem are extended to condensing mappings satisfying the interior condition.