An Iterative Method for Split Variational Inclusion Problem and Split Fixed Point Problem for Averaged Mappings

In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area.

SOME RESULTS ON GENERALIZED EQUILIBRIUM PROBLEMS INVOLVING STRICTLY PSEUDOCONTRACTIVE MAPPINGS

In this paper,we consider an iterative sequence for generalized equilibrium problems and strictly pseudocontractive mappings.We show that the iterative sequence converges strongly to a common element of the solution set of generalized equilibrium problems and of the fixed point set of strictly pseudocontractive mappings.

A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM,FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS,AND QUASI-VARIATIONAL INCLUSION PROBLEM

In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].

GENERAL SPLIT FEASIBILITY PROBLEMS FOR TWO FAMILIES OF NONEXPANSIVE MAPPINGS IN HILBERT SPACES

The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.

ALGORITHMS FOR A SYSTEM OF GENERALIZED MIXED EQUILIBRIUM PROBLEMS AND A COUNTABLE FAMILY OF SOME NONLINEAR MULTI-VALUED NONEXPANSIVE-TYPE MAPS

In this paper, relaxed iterative algorithms of Krasnoselskii-type and Halpern-type that approximate a solution of a system of a generalized mixed equilibrium problem anda common fixed point of a countable family of totally quasi-C-asymptotically nonexpansivemulti-valued maps are constructed. Strong convergence of the sequence generated by thesealgorithms is proved in uniformly smooth and strictly convex real Banach spaces with Kadec-Klee property. Furthermore, several applications of our theorems are also presented. Finally,our theorems are significant improvements on several important recent results for this classof nonlinear problems.

STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEM AND BREGMAN TOTALLY QUASI-ASYMPTOTICALLY NONEXPANSIVE MAPPING IN BANACH SPACES

In this paper, we propose a new hybrid iterative scheme for finding a common solution of an equilibrium problem and fixed point of Bregman totally quasi-asymptotically nonexpansive mapping in reflexive Banach spaces. Moreover, we prove some strong convergence theorems under suitable control conditions. Finally, the application to zero point problem of maximal monotone operators is given by the result.

CONVERGENCE ANALYSIS FOR SYSTEM OF EQUILIBRIUM PROBLEMS AND LEFT BREGMAN STRONGLY RELATIVELY NONEXPANSIVE MAPPING

In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.

Hybrid Extragradient-Type Methods for Finding a Common Solution of an Equilibrium Problem and a Family of Strict Pseudo-Contraction Mappings

This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.

Self-Adaptive Algorithms for the Split Common Fixed Point Problem of the Demimetric Mappings

The split common fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear operator belongs to another fixed-point set. In this paper, we present new iterative algorithms for solving the split common fixed point problem of demimetric mappings in Hilbert spaces. Moreover, our algorithm does not need any prior information of the operator norm. Weak and strong convergence theorems are given under some mild assumptions. The results in this paper are the extension and improvement of the recent results in the literature.

Solution of the Third Kind Boundary Value Problem of Laplace’s Equation Based on Conformal Mapping

In order to overcome the difficulty in solving the boundary value problem of electrostatic field with complex boundary and to give a new method for solving the third boundary value problem of Laplace’s equation, in this paper, the third boundary value problem of Laplace’s equation is studied by combining conformal mapping with theoretical analysis, the several analytical solutions of third boundary value problems of Laplace’s equation are gives, the correctness of its solution is verified through computer numerical simulation, and a new idea and method for solving the third boundary value problem of Laplace’s equation is obtained. In this paper, the boundary condition of the solving domain is changed by the appropriate conformal mapping, so that the boundary value problem on the transformed domain is easy to be solved or be known, and then the third kind boundary value of the Laplace’s equation can be solved easily;its electric potential distribution is known. Furthermore, the electric field line and equipotential line are plotted by using the MATLAB software.

APPLYING OONN TO SOLVE MAP-COLORING PROBLEM

For solving the map-coloring problems,this paper presents an energy function,amore effective dynamic equation and a more simple convergence condition.For the first time westudy the map-coloring problems in the way of connecting discrete Hopfield neural network withthe orthogonal optimization,and as a practical example,a color map of China is given.

Continuous Selections and Fixed Points forφ-maps with Their Applications to Section Problems

The concept of finitely continuous topological space is introduced and the basic properties of the space are given. Several continuous selection theorems and fixed point theorems for Ф-maps are established, and as applications of the above fixed point theorems, some section problems are discussed. The results generalize and improve many corresponding conclusions.

Dirichlet-to-Neumann Map for a Hyperbolic Equation

In this paper, we provide an explicit expression for the full Dirichlet-to-Neumann map corresponding to a radial potential for a hyperbolic differential equation in 3-dimensional. We show that the Dirichlet-Neumann operators corresponding to a potential radial have the same properties for hyperbolic differential equations as for elliptic differential equations. We numerically implement the coefficients of the explicit formulas. Moreover, a Lipschitz type stability is established near the edge of the domain by an estimation constant. That is necessary for the reconstruction of the potential from Dirichlet-to-Neumann map in the inverse problem for a hyperbolic differential equation.

基于知识地图的高校实验室安全教育微课体系构建

为了改变当前实验室安全教育资源、内容、考核问题所导致的安全知识无法有效内化的现状,促进实验室安全教育效果提升,研究从记忆的原理出发,以建构主义、认知负荷、知识可视化等理论为指导,针对资源形式、内容组织、评价考核提出了系统性的解决方案,设计“通识—专业”模块化的安全教育体系,提出层级与网状相结合的安全教育知识地图构建方法,构建基于知识地图的问题导向式的安全教育微课,拓宽了安全教育理论范围。实践表明新体系可有效提升学生安全教育满意度及效果,具有一定的推广意义与实践价值。

思维导图联合问题式学习教学法在皮肤性病学临床本科教学中的应用

目的探讨思维导图联合问题式学习(PBL)教学法在皮肤性病学临床本科教学中的应用效果。方法选取96名在青岛大学附属医院皮肤科见习的青岛大学临床医学专业本科生为研究对象,随机分为试验组和对照组,每组48人。试验组采用思维导图联合PBL教学法,对照组采用传统PBL教学法,课程结束后通过理论考核和问卷调查方式进行教学效果的综合评估。结果试验组的理论考核成绩高于对照组,差异有统计学意义(t=3.10,P<0.05);试验组在提高自主学习能力、锻炼临床思维、整合课程学习、延长记忆时长方面均优于对照组,差异有统计学意义(均P<0.05)。结论在皮肤性病学临床本科教学中应用思维导图联合PBL教学法,教学效果优于PBL教学法。

矩形上全组合偏差的极值问题

根据Kalaj在圆环上给出的全组合偏差定义,给出了矩形上全组合偏差和组合偏差的定义.同时,在从矩形到矩形上并保持端点的所有同胚映射类中,分别考虑了组合偏差和全组合偏差的极值问题,利用面积长度方法和均值不等式证明了仿射映射为此两类极值问题的唯一解.该结果推广了相关文献的结果.

Banach空间中可数算子族的不动点集和广义混合均衡问题的公共解的强收敛性

在自反Banach空间框架中,提出一类新的收缩投影算法,来逼近一闭Bregman拟渐近非扩张可数算子族的不动点集和广义混合均衡问题的公共解,建立了一闭Bregman拟渐近非扩张可数算子族的不动点集和广义混合均衡问题的公共解的强收敛性结果,并用一数值例子来支撑文中所得的结果.无论算子族从有限个到可数个,还是算子从Bregman相对非扩张到Bregman拟渐近非扩张等方面,均对Jantakarn K和Kaewcharoen A(2021)的结果进行了的拓展和补充.

具有限族半压缩映射的修正惯性同步算法的强收敛性

研究一个新的具有限族半压缩映射的修正惯性同步算法。在希尔伯特空间框架下,结合压缩映射,在适当的条件下建立一些强收敛定理。同时,给出了一个数值例子来说明所建议的算法的有效性。

基于文献计量和知识图谱的电动车辆路径问题研究综述

为揭示电动车辆路径问题领域的研究与发展现状,对CNKI和Web of Science数据库中电动车辆路径问题1994-2022年间的期刊文献进行知识挖掘与分析。基于文献计量学的量化分析与知识图谱的可视化,通过分析文献外部特征和共被引情况,梳理研究热点及热点演进趋势,归纳研究主题,总结出电动车辆路径问题的知识域包括研究主题和应用场景,其中,研究主题由变体研究、充电调度、求解方法三部分构成;对电动车辆路径问题在复杂实际问题、高效求解算法方面的未来发展进行展望,这将为电动车辆路径问题研究的深入化与国际化提供一定的推动作用。

一种基于差异演化算法求解折扣{0-1}背包问题的应用研究

折扣{0-1}背包问题(Discounted(0-1)Knapsack Problem,D{0-1}KP)是一个经典的组合优化问题。将差异演化算法中实数编码映射为整数编码,进一步完善约束条件,求得D{0-1}KP最优解,并使用动态规划算法对改进算法进行验证,验证结果表明,改进后的差异演化算法能够用于求解数据规模大的D{0-1}KP,并能够得到适应度最高的最优个体,即最优解。在验证之后对差异演化算法中两个重要参数进行测试取值,得出使用差异演化算法求解D{0-1}KP收敛速度快、稳定性好的参数取值范围。