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Let R be a ring, M be a R-bimodule and m, n be two fixed nonnegative integers with m + n ≠ 0. An additive mapping δ from R into M is called an (m, n)-Jordan derivation if (m + n)δ(A2) = 2mAδ(A) + 2nδ(A)A for every A in R. In this paper, we prove that every (m, n)-Jordan derivation with m ≠ n from a C* -algebra into its Banach bimodule is zero. An additive mapping δ from R into M is called a (m, n)-Jordan derivable mapping at W in R if (m + n)δ(AB + BA) = 2mδ(A)B + 2mδ(B)A + 2nAδ(B) + 2nBδ(A) for each A and B in R with AB = BA = W. We prove that if M is a unital A-bimodule with a left (right) separating set generated algebraically by all idempotents in A, then every (m, n)-Jordan derivable mapping at zero from A into M is identical with zero. We also show that if A and B are two unital algebras, M is a faithful unital (A, B)-bimodule and U=[AMNB] is a generalized matrix algebra, then every (m, n)-Jordan derivable mapping at zero from U into itself is equal to zero. [ABSTRACT FROM AUTHOR]

Let ( T, d) be a dendrite with finite branch points and f be a continuous map from T to T. Denote by ω( x, f) and P( f) the ω-limit set of x under f and the set of periodic points of f, respectively. Write Ω( x, f) = { y| there exist a sequence of points x ∈ T and a sequence of positive integers n < n < ··· such that lim x = x and lim $$f^{n_{k}}$$ ( x ) = y}. In this paper, we show that the following statements are equivalent: (1) f is equicontinuous. (2) ω( x, f) = Ω( x, f) for any x ∈ T. (3) ∩ f ( T) = P( f), and ω( x, f) is a periodic orbit for every x ∈ T and map h: x → ω( x, f) ( x ∈ T) is continuous. (4) Ω( x, f) is a periodic orbit for any x ∈ T. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the convergence problem of the iteration scheme x n+1 = λ n+1 y +(1–λ n+1) T n+1 x n for a family of infinitely many nonexpansive mappings T 1, T 2, . . . in a Hilbert space. It is proved that under suitable conditions this iteration scheme converges strongly to the nearest common fixed point of this family of nonexpansive mappings. The results presented in this paper extend and improve some recent results. [ABSTRACT FROM AUTHOR]

In this paper, by using the parametric representation of spirallike mappings, we construct to obtain the growth theorem of spirallike mappings on Reinhardt domain B. Moreover, the distortion theorem of spirallike mappings is obtained. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the following implicit iteration scheme recently introduced by Xu and Ori [ Numer. Funct. Anal. Optim., 22, (2001) 767–773]: and to prove several strongly and weakly convergent theorems of the iteration for a finite family of pseudocontractive mappings under condition α n ∈ (0, b] ⊂ (0, 1). [ABSTRACT FROM AUTHOR]

This paper considers the isometric extension problem concerning the mapping from the unit sphere S 1( E) of the normed space E into the unit sphere S 1( l ∞(Γ)). We find a condition under which an isometry from S 1( E) into S 1( l ∞(Γ)) can be linearly and isometrically extended to the whole space. Since l ∞(Γ) is universal with respect to isometry for normed spaces, isometric extension problems on a class of normed spaces are solved. More precisely, if E and F are two normed spaces, and if V 0: S 1( E) → S 1( F) is a surjective isometry, where c 00(Γ) ⊆ F ⊆ l ∞(Γ), then V 0 can be extended to be an isometric operator defined on the whole space. [ABSTRACT FROM AUTHOR]

Let X, Y be two finite–dimensional topological vector spaces, Z a Hausdorff topological vector space, K ⊂ X and D ⊂ Z be two nonempty sets, C be a pointed, closed, and convex cone in Y with int C ≠ Ø. Let S : K → 2 K and T : K → 2 D be two multivalued mappings, and φ : K× D× K → Y be a trifunction. In this paper, we consider the generalized vector quasi–equilibrium problem, which is formulated by finding $\hat x$ ∈ K and ŷ ∈ T( $\hat x$ ) such that $\hat x$ ∈ S( $\hat x$ ) and φ( $\hat x$ , ŷ, u) /∈ −int C for all u ∈ S( $\hat x$ ). We establish an existence result in which T is not supposed to have any continuity property. Our results extend and improve the corresponding results of Cubiotti, Yao and Guo. [ABSTRACT FROM AUTHOR]

A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established. The results presented in this paper substantially extend the results due to Chang (2001), Osilike and Aniagbosor (2000), Rhoades (1994) and Schu (1991). [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam-Rassias stability of universal Jensen’s equations in Banach modules over a unitalC*-algebra. It is applied to show the stability of universal Jensen’s equations in a Hilbert module over a unitalC*-algebra. Moreover, we prove the stability of linear operators in a Hilbert module over a unitalC*-algebra. [ABSTRACT FROM AUTHOR]

In this paper, we .rst derive the representation theorem of onto isometric mappings in the unit spheres ofl1(G) type spaces, and then conclude that such mappings can be extended to the whole space as real linear isometries by using a previous result of the author. [ABSTRACT FROM AUTHOR]

Abstract We study the Bloch constant for K-quasiconformal holomorphie mappings of the unit ball B of C[sup n] into C[sup n]. The final result we prove in this paper is: if f is a K-quasiconformal holomorphic mapping of B into C[sup n] such that det(f(0)) = 1, then f(B) contains a schlicht ball of radius at least, [Multiple line equation(s) cannot be represented in ASCII text] where C[sub n] > 1 is a constant depending on n only, and C[sub n] Arrow right Square root of 10 as n Arrow right Infinity Keywords K-quasiformal mapping, Bloch constant [ABSTRACT FROM AUTHOR]