Convergence of a Hybrid Projection Algorithm in Banach Spaces

In this paper, we consider a hybrid projection algorithm for two families of quasi-φ-nonexpansive mappings. We establish strong convergence theorems of common fixed points in the framework of Banach spaces. Our results improve and extend the corresponding results announced by many others.     

Strong Convergence Theorems for Perturbed Maximal Monotone Operators in Banach Spaces

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L~P-orthogonality in Banach Spaces

The notion of L~P-orthogonality was posed by F. Sullivan [1], but it hadnever been studied. The purpose of this paper is to give some results concerningthe L~P-orthogonality in Banach spaces.     

Strong Convergence of Iterative Algorithms for Variational Inequalities in Banach Spaces

Let C be a nonempty closed convex subset of a Banach space E with the dual E ^*, let T:C→E ^* be a Lipschitz continuous mapping and let S:C→C be a relatively nonexpansive mapping. In this paper, by employing the notion of generalized projection operator, we study the following variational inequality (for short, VI(T−f,C)): find x∈C such that

Viscosity Iteration in CAT(κ) Spaces

We study the approximation of fixed points of nonexpansive mappings in CAT(κ) spaces. We show that the iterative sequence generated by the Moudafi's viscosity type algorithm converges to one of the fixed points of the nonexpansive mapping depending on the contraction applied in the algorithm.     

Halpern Iteration in CAT（k） Spaces

In this paper we show that an iterative sequence generated by the Halpern algorithm converges to a fixed point in the case of complete CAT(κ) spaces. Similar results for Hadamard manifolds were obtained in [Li, C., López, G., Martín-Márquez, V.: Iterative algorithms for nonexpansive mappings on Hadamard manifolds. Taiwanese J. Math., 14, 541–559 (2010)], but we study a much more general case. Moreover, we discuss the Halpern iteration procedure for set-valued mappings.     

Implicit Complementarity Problems in Banach Spaces

We utilize the method of multivalued fixed point in this paper to prove the existence theorems of solutions for some implicit complementarity problems in Banach spaces.     

Convergence of Newton‘’s Method and Uniqueness of the Solution of Equations in Banach SpacesⅡ

Some results on convergence of Newton‘s method in Banach spaces are established under the assumption that the derivative of the opderators satisfies the radius or center Lipschitz condition with a weak L average.     

K—very Smooth Banach Spaces

We introduce the notion of K-very smoothness which is a generalization of very smoothness in Banach spaces. A necessary and sufficient condition for a Banach space to be K-very smooth is obtained. We also consider some relations between K-very smoothness and other geometrical notions.     

Approximation by Θ-Means of Walsh—Fourier Series in Dyadic Hardy Spaces and Dyadic Homogeneous Banach Spaces

Analysis Mathematica - In this article we discuss the behaviour of Θ-means of Walsh—Fourier series of a function in dyadic Hardy spaces Hp and dyadic homogeneous Banach spaces X. Namely,...     

Non-expansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces

In this article, we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces. The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.     

On the United Theory of the Family of Euler—Haller Type Methods with Cubical Convergence in Banach Spaces

The convergence problem of the family of Euler-Halley methods is considered under the Lipschitz condition with the L-average,and a united convergence theory with its applications is presented.     

Modified Extragradient Methods for a System of Variational Inequalities in Banach Spaces

In this paper, we introduce a new system of general variational inequalities in Banach spaces. We establish the equivalence between this system of variational inequalities and fixed point problems involving the nonexpansive mapping. This alternative equivalent formulation is used to suggest and analyze a modified extragradient method for solving the system of general variational inequalities. Using the demi-closedness principle for nonexpansive mappings, we prove the strong convergence of the proposed iterative method under some suitable conditions.     

Strong Convergence in Hilbert Spaces via Γ-Duality

We analyze a primal-dual pair of problems generated via a duality theory introduced by Svaiter. We propose a general algorithm and study its convergence properties. The focus is a general primal-dual principle for strong convergence of some classes of algorithms. In particular, we give a different viewpoint for the weak-to-strong principle of Bauschke and Combettes and unify many results concerning weak and strong convergence of subgradient type methods.     

On the Extension Operator in Banach Spaces

In [1], Roper and Suffridge introduced an extension operator. This operator is defined for normalized locally univalent function f on the unit disc U = {z∈C：｜z｜〈1} in C by Фn（f）（z）=（f（z1）,√ f′（z1）z0）, where z = （z1,z0） belongs to the unit ball Bn in Cn, z1∈U, z0 = （z2,...,zn） ∈ C^n-1.     

Semilinear Differential Inclusions in Separable Banach Spaces

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Modified Variational Iteration Method for Heat and Wave-Like Equations

In this paper, we apply the modified variational iteration method (MVIM) for solving the heat and wave-like equations. The proposed modification is made by introducing He’s polynomials in the correction functional. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are given to verify the reliability and efficiency of the method. The fact that proposed technique solves nonlinear problems without using the Adomian’s polynomials can be considered as a clear advantage of this algorithm over the decomposition method.     

Solutions of Superlinear Hammerstein Integral Equation in Banach Spaces and Applications

ＳｏｌｕｔｉｏｎｓｏｆＳｕｐｅｒｌｉｎｅａｒＨａｍｍｅｒｓｔｅｉｎＩｎｔｅｇｒａｌＥｑｕａｔｉｏｎｉｎＢａｎａｃｈＳｐａｃｅｓａｎｄＡｐｐｌｉｃａｔｉｏｎｓＬｏｕＢｅｎｄｏｎｇ（娄本东）（Ｄｅｐｔ．ｏｆＭａｔｈ．ＳｈａｎｄｏｎｇＵｎｉｖｅｒｓｉｔｙ，...     

Banach—Saks Property and Property (β) in Cesàro Sequence Spaces

A new constant C(X) for any Banach space X is introduced. It is proved that C(X) < 2 implies the weak Banach—Saks property for the space X. In particular, C(ces_p) is found for Cesàro sequence space ces_p (1 < p < ). Moreover, it is shown that the space ces_p (1 < p < ) has property ().AMS Subject Classification (2000), 46E30, 46E40, 46B20Supported by NSF and ECF of China.     

On the United Theory of the Family of Euler-Halley Type Methods with Cubical Convergence in Banach Spaces

The convergence problem of the family of Euler-Halley methods is considered under the Lipschitz condition with the L-average, and a united convergence theory with its applications is presented.