ELXED POINT THEOREM OF COMPOSITION g-CONTRACTION MAPPING AND ITS APPLICATIONS

Any composition sequential mapping, periodic composition mapping of a complete non-empty metric space M into M with geometric mean contraction ratio less than 1 ( simplifying as 'g-contraction mapping' ) has a unique fixed point in M . Applications of the theorem to the proof of existence and uniqueness of the solutions of a set of non-linear differential equations and a coupled integral equations of symmetric bending of shallow shell of revolution are given.

A fixed point theorem for Proinov mappings with a contractive iterate

In this paper,we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point.In other words,we combine and unify the basic approaches of Proinov and Sehgal in the framework of the complete metric spaces.We consider examples to illustrate the validity of the obtained result.

MEIR-KEELER TYPE CONTRACTIONS FOR TRIPLED FIXED POINTS

In 2011, Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces. In our paper, we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction：

Four-Step Iteration Scheme to Approximate Fixed Point for Weak Contractions

Fixed point theory is one of the most important subjects in the setting of metric spaces since fixed point theorems can be used to determine the existence and the uniqueness of solutions of such mathematical problems.It is known that many problems in applied sciences and engineering can be formulated as functional equations.Such equations can be transferred to fixed point theorems in an easy manner.Moreover,we use the fixed point theory to prove the existence and uniqueness of solutions of such integral and differential equations.Let X be a non-empty set.A fixed point for a self-mapping T on X is a point𝑒𝑒∈𝑋𝑋that satisfying T e=e.One of the most challenging problems in mathematics is to construct some iterations to faster the calculation or approximation of the fixed point of such problems.Some mathematicians constructed and generated some new iteration schemes to calculate or approximate the fixed point of such problems such as Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Berinde(2004b);Agarwal,O’Regan and Sahu(2007)].The main purpose of the present paper is to introduce and construct a new iteration scheme to calculate or approximate the fixed point within a fewer number of steps as much as we can.We prove that our iteration scheme is faster than the iteration schemes given by Sintunavarat et al.[Sintunavarat and Pitea(2016);Agarwal,O’Regan and Sahu(2007);Mann(1953);Ishikawa(1974)].We give some numerical examples by using MATLAB to compare the efficiency and effectiveness of our iterations scheme with the efficiency of Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Abbas and Nazir(2014);Agarwal,O’Regan and Sahu(2007)]schemes.Moreover,we introduce a problem raised from Newton’s law of cooling as an application of our new iteration scheme.Also,we support our application with a numerical example and figures to illustrate the validity of our iterative scheme.

New Fixed Point Results of Generalized g-Quasi-Contractions in Cone b-Metric Spaces Over Banach Algebras

In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.

On the (<i>r</i>,<i>φ</i>,<i>ψ</i>)-Suzuki Contraction for the Multi-Valued Mappings

In this work we try to give a new contraction type in multi-valued mapping on complete metric spaces. We prove the existence of fixed point for (r,φ,ψ)-Suzuki contraction in such spaces. Around our paper, the function ψ is absolutely continuous, and in this case, the contraction proposed by as has a fixed point.

关于魔力弹簧的收缩时间和上端运动问题

针对有关魔力弹簧研究中的几个问题进行探讨和澄清.建立了预收缩力弹簧的模型,推出其形变规律.根据质心运动定理,导出这种弹簧自由下落时,收缩到原长所用的时间、其上端的运动方程和速度公式.研究表明,对于通常演示所用的魔力弹簧,在自由下落时的收缩阶段,其上端不是作匀速直线运动.

强b-距离空间中的集值拟压缩不动点定理

本文研究了强b-距离空间中的集值拟压缩不动点定理.利用一个新的引理,在强b-距离空间的框架中建立了集值拟压缩不动点定理.该定理将距离空间中LU等人(2022)的结果推广了到强b-距离空间,并且改进了李淑方(2023)在b-距离空间的结_果.特别地,当1≤s≤1+√5/2时,我们将压缩系数范围扩大为[0,1/3√1-2s);当s>1+√5/2时,我们将压缩系数~范围扩大为[0,1/√1+s).

强b-距离空间中的集值拟压缩型不动点定理

在强b-距离空间的框架中建立了集值拟压缩型不动点定理,该定理将距离空间中Lu等人的结果完全地推广到了强b-距离空间,同时改进了李淑方在b-距离空间的结果。

变分不等式问题和半压缩映射有限簇的强收敛定理

在Hilbert空间中,首先,构造了一种新的平行迭代方法用于逼近伪单调变分不等式的解集和半压缩映射有限簇的公共不动点集的公共元;其次,在适当假设条件下,证明了该算法生成的迭代序列的强收敛性;最后,给出具体的数值实验检验了所提出算法的有效性。

一类非线性混合分数阶微分方程系统解的稳定性

研究了一类含Caputo型非线性混合分数阶微分方程耦合系统的边值问题,首先,利用Banach压缩映射原理讨论了该系统解的存在唯一性,并利用Dhage不动点定理研究了该系统解的存在性;然后,研究了该系统解的Ulam-Hyers稳定性、G-Ulam-Hyers稳定性和Ulam-Hyers-Rassia稳定性,并利用算例验证了所得结果的正确性.

COINCIDENCE THEOREMS INVOKING COMPOSITES OF ACYCLIC MAPPINGS AND APPLICATIONS

Some new coincidence theorems involving a new class of set-valued mappingscontaining composites of acyclic mappings defined on a contractible space are proved.As applications, some existence theorems of maximal elements and solutions of abstract variational inequalities, and best approximation theorems are proved. These theorems improve and generalize a number of known results in recent literature.

Topological degree for 1-set-contractive fields in M-PN spaces and its applications

In this paper, we define the topological degree for 1-set-contractive fields in PN spaces. Based on this, we obtain some new fixed point theorems for 1-set-contractive operators. As an application, we study the existence of solutions for a kind of nonlinear Volterra integral equations in Z-M-PN space.

THE BEST APPROXIMATION AND COINCIDENCE THEOREMS FOR COMPOSITES OF ACYCLIC MAPPINGS

Some new coincidence theorem s involving a new class of set_valued mappings containing composites of acyclic mappings defined in a contractible space are proved. For applications, some best approximation theorems and coincidence theorems for set-valued mappings are als o given. A number of known results in recent literature are improved and general ized by the theorems in this paper.

A Study of Caristi’s Fixed Point Theorem on Normed Space and Its Applications

In this work, we will discuss Caristi’s fixed point theorem for mapping results introduced in the setting of normed spaces. This work is a generalization of the classical Caristi’s fixed point theorem. Also, Caristi’s type of fixed points theorem was partial discussed in Reich, Mizoguchi and Takahashi’s and Amini-Harandi’s results, we developed ideas that many known fixed point theorems can easily be derived from the Caristi theorem.

A Study of Banach Fixed Point Theorem and It’s Applications

This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. The classical Banach fixed point theorem is a generalization of this work. A fixed point theory is a beautiful mixture of Mathematical analysis to explain some conditions in which maps give excellent solutions. Here later many mathematicians used this fixed point theory to establish their results, see for instance, Picard-Lindel of Theorem, The Picard theorem, Implicit function theorem etc. Also, we developed ideas that many of known fixed point theorems can easily be derived from the Banach theorem. It extends some recent works on the extension of Banach contraction principle to metric space with norm spaces.

基于Event-B的可靠智能合约自动生成方法

智能合约是一种以代码的方式执行合同条款的可计算交易协议,其应用场景与规模日益增长,承载着多达数十亿美元的各类资产。由于其代码缺陷可能会造成严重的经济损失,因此智能合约的可信开发成为技术关键。为此,提出了一种基于集合论语言Event-B的智能合约可信验证与自动生成方法。Event-B方法是一种基于精化的形式化方法,可用于规约、设计和验证软件系统。通过对智能合约的模型验证和可执行代码的自动生成技术,研发了自动转换工具EB2S,打通了形式化模型和智能合约编程语言的语义鸿沟和技术壁垒。最后,选取典型的在线支付智能合约场景,应用基于Event-B的智能合约模型自动生成合约代码,验证了EB2S转换工具的有效性。

非可微条件下全局隐函数存在性定理

应用Banach压缩映射原理证明了在非可微条件下的一个全局隐函数存在性定理,推广了教材和近期的一些结论,为培养学生创新意识和创新能力起到一定作用.

Convergence Theorems for λ-strict Pseudo-contractions in q-uniformly Smooth Banach Spaces

In this paper, we continue to discuss the properties of iterates generated by a strict pseudo- contraction or a finite family of strict pseudo-contractions in a real q-uniformly smooth Banach space. The results presented in this paper are interesting extensions and improvements upon those known ones of Marino and Xu [Marino, G., Xu, H. K.： Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces. J. Math. Anal. Appl., 324, 336-349 （2007）]. In order to get a strong convergence theorem, we modify the normal Mann＇s iterative algorithm by using a suitable convex combination of a fixed vector and a sequence in C. This result extends a recent result of Kim and Xu [Kim, T. H., Xu, H. K.： Strong convergence of modified Mann iterations. Nonl. Anal., 61, 51- 60 （2005）] both from nonexpansive mappings to λ-strict pseudo-contractions and from Hilbert spaces to q-uniformly smooth Banach spaces.

Weak Convergence Theorems for Strict Pseudo-contractions in Banach Spaces

In this paper, it is shown that there is a gap in the paper [Chidume, C. E., Shahzad, N.： Weak convergence theorems for a finite family of strict pseudo-contractions. Nonlinear Anal., 72, 1257–1265（2010）], consequently, the main results of the paper do not hold in uniformly smooth Banach spaces. Meanwhile, it is also shown that the main results（Lemma 3.4, Theorems 3.5–3.6, 3.8–3.9） in the paper [Cholamjiak, P., Suantai, S.： Weak convergence theorems for a countable family of strict pseudo-contractions in Banach spaces. Fixed Point Theory Appl., 2010, Article ID 632137, 16 pages（2010）] do not hold in Lpfor p 〉 3. Finally, some modified results are presented in the setting of uniformly smooth and uniformly convex Banach spaces which include Lpfor p ≥ 2 as special cases. Furthermore, our arguments are also different from the ones given by the authors above.