Common fixed points in cone metric spaces

In this paper we consider a notion of g-weak contractive mappings in the setting of cone metric spaces and we give results of common fixed points. This results generalize some common fixed points results in metric spaces and some of the results of Huang and Zhang in cone metric spaces. Supported by Universitá degli Studi di Palermo, R. S. ex 60%.     

Fixed point theorems for a class of nonlinear mappings related to maximal monotone operators in Banach spaces

In this paper, the class of nonspreading mappings in Banach spaces is introduced. This class contains the recently introduced class of firmly nonexpansive type mappings in Banach spaces and the class of firmly nonexpansive mappings in Hilbert spaces. Among other things, we obtain a fixed point theorem for a single nonspreading mapping in Banach spaces. Using this result, we also obtain a common fixed point theorem for a commutative family of nonspreading mappings in Banach spaces. Received: 10 August 2007     

Strongly relatively nonexpansive sequences in Banach spaces and applications

We introduce the concept of a strongly relatively nonexpansive sequence in a Banach space and investigate its properties. Then we apply our results to the problem of approximating a common fixed point of a countable family of relatively nonexpansive mappings in a uniformly convex and uniformly smooth Banach space.      

Some results for a finite family of uniformly L-Lipschitzian mappings in Banach spaces

The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper improve and extend some recent results in Chang [1], Cho et al. [2] Ofoedu [5], Schu [7] and Zeng [8, 9]. The present studies were supported by “the Natural Science Foundation of China (No. 10771141),” the Natural Science Foundation of Zhejiang Province (Y605191), the Natural Science Foundation of Heilongjiang Province (A0211), the Scientific Research Foundation from Zhejiang Province Education Committee (20051897).     

Viscosity approximation methods for a family of m-accretive mappings in reflexive Banach spaces

The purpose of this paper is to introduce a general iterative algorithm by viscosity method to approximate a common point of a finite family of m-accretive mappings in a reflexive Banach space which has a weakly continuous duality mapping. We obtain strong convergence theorems under some mild conditions imposed on parameters.      

Covering spheres of Banach spaces by balls

If the unit sphere of a Banach space X can be covered by countably many balls no one of which contains the origin, then, as an easy consequence of the separation theorem, X* is w*-separable. We prove the converse under suitable renorming. Moreover, the balls of the countable covering can be chosen as translates of the same ball. Research of V. P. Fonf was supported in part by Israel Science Foundation, Grant # 139/02 and by the Istituto Nazionale di Alta Matematica of Italy. Research of C. Zanco was supported in part by the Ministero dell’Università e della Ricerca Scientifica e Tecnologica of Italy and by the Center for Advanced Studies in Mathematics at the Ben-Gurion University of the Negev, Beer-Sheva, Israel.     

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space with the resolvent norm that is constant in a neighbourhood of zero.      

On the constellations of Weierstrass points

We prove that the constellation of Weierstrass points characterizes the isomorphism-class of double coverings of curves of genus large enough. The author was supported by a grant from the International Atomic Energy Agency and UNESCO.     

Weak and strong solvability of parabolic variational inequalities in Banach spaces

We consider parabolic variational inequalities having the strong formulation

Fixed point indices and periodic points of holomorphic mappings

Let Δ ⁿ be the ball |x| <  1 in the complex vector space , let be a holomorphic mapping and let M be a positive integer. Assume that the origin is an isolated fixed point of both f and the Mth iteration f ^M of f. Then for each factor m of M, the origin is again an isolated fixed point of f ^m and the fixed point index of f ^m at the origin is well defined, and so is the (local) Dold’s index [Invent. Math. 74(3), 419–435 (1983)] at the origin:

Unified characterizations for modifications ofR 0 andR 1 topological spaces

Cammaroto and Noiri [14] introduced a separation axiom calledm-R ₀ in anm-space (X, m). In this paper, we introduce the notion ofm-R ₁ spaces and offer many characterizations ofm-R ₀ (resp.m-R ₁) spaces which enable us to obtain unified characterizations of separation axiomsR ₀, semi-R ₀, pre-R ₀,α-R ₀,δ-semiR ₀, (δ, p)-R ₀ (resp.R ₁, semi-R ₁, pre-R ₁,α-R ₁,δ-semiR ₁, (δ, p)-R ₁).     

On summability of pairs of convolution sequences of probability measures on locally compact semigroups

In this paper we study the problem of convergence in the weak and the vague topology of the sequence

Nonnegative Moore-Penrose inverses of operators over Hilbert spaces

The objective of this paper is to study the nonnegativity of the Moore-Penrose inverse of an operator between real Hilbert spaces. A sufficient condition ensuring this is given in terms of certain spectral property of all positive splittings of the given operator. A partial converse is proved.      

Pointwise convergence for semigroups in vector-valued <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> spaces

Suppose that {T _t  : t  ≥  0} is a symmetric diffusion semigroup on L ²(X) and denote by its tensor product extension to the Bochner space , where belongs to a certain broad class of UMD spaces. We prove a vector-valued version of the Hopf–Dunford–Schwartz ergodic theorem and show that this extends to a maximal theorem for analytic continuations of on . As an application, we show that such continuations exhibit pointwise convergence.     

Banach algebra techniques for spectral multiplicity

In this paper, we use Banach algebra techniques to prove addition formulas for spectral multiplicities of direct sums of operator families. This work has been supported by the Scientific and Technological Research Council of Turkey (TUBITAK) with project 107T649.     

Onm-compact spaces

We give characterizations ofm-compact andm-closed spaces by means of nets and filterbases. We study the images ofm-compact andm-closed sets under various modifications ofM-continuous functions. We introduce the notion ofmc-compact space and investigate some relations betweenmc-compact spaces andM-continuous functions.     

Matrix symbol of order two for some Banach algebras

Two classes of Banach algebras which admit a matrix symbol of order 2 are described, and an explicit form of the symbol is obtained. Also we describe all polynomialsF(X, Y) andF(X, Y, Z) such that the norms of polynomialsF(B, B ^*) (whenB ²=0) andF(S, W, W ^* ) (whenS ² =I, W ² =0, S ^*=S) depend only on the polynomialF and on the norms B, W. Applications to Banach algebras generated by singular integral operators and some their perturbations are considered.     

A weak nonsmooth palais-smale condition and coercivity

In this paper we show that a generally nonsmooth locally Lipschitz function which satisfies the nonsmooth C-condition (nonsmooth Cerami condition) and is bounded from below, is coercive. The Cerami condition is a weak form of the well-known Palais-Smale condition, which suffices to prove minimax principles.     

On a Certain class of minimum effort problems in Banach spaces

In this paper we have developed a model to find the best control which will minimize the control effort to take the system near the target which is only approximately controllable, by a functional analytic approach. A complete characterization of the solution is given in terms of a hyperplane without assuming any type of normality conditions.