In chapter 4 , we introduce a new two - step method which is from the famous one - point iteration of order three called halley method to approximate a solution of a nonlinear equation in banach space 第四章，我们介绍了一族对三阶收敛的halley法变形得到的二步法来近似banach空间的非线性方程的解。
In the first part of this article , a new class of set - valued variational inclusion problem in banach spaces was introduced and some new type of iterative algorithms for solving the problems are studied 本文在第一部分提出了banach空间中一类新的广义集值变分包含问题，并采用一种新的算法讨论了其解的存在性。
There are many important applications in approximate theory , control theory and variation inequalities etc . according to the requirement of various subjects and applications , orlicz spaces is extended from the classical spaces lp 一致凸是banach空间的重要几何概念，其在逼近论、控制论、变分不等式等领域有着重要的应用。
Two results are obtained . the same method is applied to the first order periodic value boundary problem of discontinuous equations in banach space . two existence and uniqueness results are also obtained 并用类似的方法得到了banach空间中含有间断项的常微分方程一阶周期边值问题在[ 0 ， a ] ( a 0 )上整体解的两个存在唯一性结果。
The purpose of this paper is to discuss two classes of nonlinear equations , one of which is nonlinear operator equations with concavity or convexity and the other is nonlinear integro - differential equations in banach space 在本文中，我们主要讨论了banach空间中两类非线性方程，其一为具有凹凸性的非线性算子方程，其二为非线性积分-微分方程
This thesis is divided into four chapters . in the first chapter and the second chapter , we study the existence of solutions of impulsive differential equations in banach spaces , the main results derive from paper [ 36 ] and [ 37 ] 本文共分四章，在第一章和第二章中，我们研究banach空间中脉冲积分-微分方程解的存在性，其主要结果来源于作者的工作[ 36 ]和[ 37 ] 。
When we use mathematical methods to study natural and social phenomena or to solve engineering technique problems , we often regard the solutions of most practical problems as the ones of nonlinear equations in form of f ( x ) = 0 ( 1 ) in banach space 我们在利用数学手段研究自然现象和社会现象，或解决工程技术问题时，常常会把不少的实际问题归结为banach空间中形如f ( x ) = 0 ( 1 )的非线性方程的求解。
In the third part , i genelized one theorem of lambert ' s from a hilbert space to a semi - self - conjugate vector space , and some results of reflexivity are attained . in the fourth part , i discussed the algebraic reflexivity of a ( strictly ) cyclic linear transformation on a vector space 1 ，把这个结论从hilbert空间推广到半自共轭的banach空间，得出一些自反性的结论；第4章讨论了线性空间上的(严格)循环的线性变换的代数性自反。
4 . by using the theory of cones and the partial - ordered method with upper solution or lower solution . existence and uniqueness of global solutions on interval [ 0 , a ] ( a > 0 ) for the first order initial value problem of discontinuous equations in banach space ( 1 ) is discussed 利用半序方法，只用上解或下解得到了banach空间中含有间断项的常微分方程初值问题( 1 )在[ 0 ， a ] ( a 0 )上整体解的两个存在唯一性结果，并给出了解的误差估计式。
In this article , we mainly dicuss special nonlinear operator ' s and set - valued mapping ' s ishikawa and mann iteration in any banach space . as whole , we mainly touch on some aspects as follow : - strongly pseudocontractire operator ' s ishikawa and mann iteration in a cone 本文主要是在任意的banach空间中讨论特定类型的非线性算子与集值映射的ishikawa与mann迭代，归纳起来，主要有下面几个方面：锥上-强伪压缩算子的ishikawa与mann迭代
