In this paper, we prove the compactness theorem for gradient Ricci solitons. Let (Mα, gα) be a sequence of compact gradient Ricci solitons of dimension n ≥ 4, whose curvatures have uniformly bounded L n 2 norms, whose Ricci curvatures are uniformly bounded from below with uniformly lower bounded volume and with uniformly upper bounded diameter, then there must exists a subsequence (Mα, gα) conv...

The notion of B-convexity for operator spaces, which a priori depends on a set of parameters indexed by Σ, is defined. Some of the classical characterizations of this geometric notion for Banach spaces are studied in this new context. For instance, an operator space is BΣ-convex if and only if it has Σ-subtype. The class of uniformly non-L(Σ) operator spaces, which is also the class of BΣ-conve...

A new hybrid projection algorithm is considered for a finite family of λi-strict pseudocontractions. Using the metric projection, some strong convergence theorems of common elements are obtained in a uniformly convex and 2-uniformly smooth Banach space. The results presented in this paper improve and extend the corresponding results of Matsushita and Takahshi, 2008, Kang and Wang, 2011, and man...

In this paper, we prove some strong and weak convergence theorems using a modified iterative process for nonself asymptotically nonexpansive mappings in a uniformly convex Banach space. This will improve and generalize the corresponding results in the existing literature. Finally, we will state that our theorems can be generalized to the case of finitely many mappings. c © 2007 Elsevier Ltd. Al...

We study the limit distribution of zeros of certain sequences of holomorphic sections of high powers L of a positive holomorphic Hermitian line bundle L over a compact complex manifold M . Our first result concerns ‘random’ sequences of sections. Using the natural probability measure on the space of sequences of orthonormal bases {SN j } of H(M,L ), we show that for almost every sequence {SN j ...

We study the asymptotic behavior of the sequence of the iterates for a nonexpansive mapping, defined on a suitable subset of a Banach space with Opial's condition. Some results are stated also for semigroups of nonexpansive mappings and for mappings of asymptotically nonexpansive type in uniformly convex Banach spaces with Opial's condition.

*Correspondence: [email protected]; [email protected] Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China Abstract Let E be a uniformly convex and uniformly smooth Banach space, let C be a nonempty closed convex subset of E, let {Tn} : C→ C be a countable family of weak relatively nonexpansive mappings such that F = ⋂∞ n=1 F(Tn) = ∅. For any given gauss x0 ∈ C,...

In this paper, we study the properties of the metric projection operator (the nearest point projection operator) and its continuity. Then we use it to solve variational inequalities in general Banach spaces and to approximate the solutions in uniformly convex and uniformly smooth Banach spaces.

In this paper, a new iterative scheme by hybrid method is constructed. Strong convergence of the scheme to a common element of the set of fixed points of an infinite family of relatively quasi-nonexpansive mappings and set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth is proved. Our results extend important recent ...