Complemented isometric copies of in dual Banach spaces

Let be a real or complex Banach space and . Then contains a -complemented, isometric copy of if and only if contains a -complemented, isometric copy of if and only if contains a subspace -asymptotic to .

     

On the eigenvalue problem for perturbed nonlinear maximal monotone operators in reflexive Banach spaces

Let be a real reflexive Banach space with dual and open and bounded and such that  Let be maximal monotone with and and with and A general and more unified eigenvalue theory is developed for the pair of operators  Further conditions are given for the existence of a pair such that

The ``implicit" eigenvalue problem, with in place of is also considered.  The existence of continuous branches of eigenvectors of infinite length is investigated, and a Fredholm alternative in the spirit of Necas is given for a pair of homogeneous operators No compactness assumptions have been made in most of the results.  The degree theories of Browder and Skrypnik are used, as well as the degree theories of the authors involving densely defined perturbations of maximal monotone operators.  Applications to nonlinear partial differential equations are included.

     

Copies of in topological Riesz spaces

The paper is concerned with order-topological characterizations of topological Riesz spaces, in particular spaces of measurable functions, not containing Riesz isomorphic or linearly homeomorphic copies of or .

     

New results in the perturbation theory of maximal monotone and -accretive operators in Banach spaces

Let be a real Banach space and a bounded, open and convex subset of The solvability of the fixed point problem in is considered, where is a possibly discontinuous -dissipative operator and is completely continuous. It is assumed that is uniformly convex, and A result of Browder, concerning single-valued operators that are either uniformly continuous or continuous with uniformly convex, is extended to the present case. Browder's method cannot be applied in this setting, even in the single-valued case, because there is no class of permissible homeomorphisms. Let The effect of a weak boundary condition of the type on the range of operators is studied for -accretive and maximal monotone operators Here, with sufficiently large norm and Various new eigenvalue results are given involving the solvability of with respect to Several results do not require the continuity of the operator Four open problems are also given, the solution of which would improve upon certain results of the paper.

     

Global solutions of initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces

In this paper, the global solutions of initial value problems for nonlinear second-order integro-differential equations of mixed type in Banach spaces are investigated. The existence and uniqueness of solutions and their iterative approximation are obtained by using Mönch fixed point theorem and new comparison results. The results presented here essentially improve, generalize and unify many well-known results.     

The auxiliary principle and an algorithm for a system of generalized set-valued mixed variational-like inequality problems in Banach spaces

In this paper, we introduce and study a new system of generalized set-valued mixed variational-like inequality problems (SGSMVLIP) and its related auxiliary problems in reflexive Banach spaces. The auxiliary principle technique is applied to study the existence and an iterative algorithm of solutions for the system of generalized set-valued mixed variational-like inequality problems. At first, the existence and uniqueness of solutions of the auxiliary problems for (SGSMVLIP) is shown. Next, an iterative algorithm for solving (SGSMVLIP) is constructed by using the existence and uniqueness result. Finally, we prove the existence of solutions of (SGSMVLIP) and discuss the convergence analysis of the algorithm. These results improve, unify and generalize many corresponding known results given in the literature.     

The index of an isolated critical point for a class of non-differentiable elliptic operators in reflexive Banach spaces

This paper is motivated by the problem of computing the index of an isolated critical point for a certain class of nonlinear elliptic operators. Such a class includes operators A which are defined by

     

一致凸Banach空间非扩张映象带误差的Ishikawa型的三重迭代序列的收敛性

在一致凸Banach空间上,研究了半紧的非扩张压缩映象‖Tx-Ty‖≤‖x-y‖的Ishikawa型的三重迭代序列的收敛性问题,建立并证明了带误差的Ishikawa三重迭代逼近收敛定理,从而独特的推广了Mann和Ishikawa迭代方法,改进和发展了文献[1]-[7]的主要结果.     

On Hanner type inequalities with a weight for Banach spaces

We shall present several Hanner type inequalities with a weight constant and characterize 2-uniformly smooth and 2-uniformly convex Banach spaces with these inequalities. p-Uniformly smooth and q-uniformly convex Banach spaces will be also characterized with another Hanner type inequalities with a weight in the other side term. The best value of the weight in these inequalities will be determined for Lp spaces. Also we shall present a duality theorem between these inequalities in a generalized form.     

A limit-point criterion for a class of Sturm-Liouville operators defined in spaces

Using a recent result of Chernyavskaya and Shuster we show that the maximal operator determined by on , -\infty$">, where and the mean value of computed over all subintervals of of a fixed length is bounded away from zero, shares several standard ``limit-point at " properties of the case. We also show that there is a unique solution of that is in all , .