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.

Convergence Theorems of φ-pseudo Contractive Type Mappings in Normed Linear Spaces

In this paper, by virtue of an inequality and sane analysis techniques, we prove sane convergence theorems cm the iterative process for nonlinear mappings of-pseudo contractive type in named linear spaces, which extend and improve the corresponding results obtained by others recently.

ON THE CONVERGENCE PROBLEMS OF ISHIKAWA AND MANN ITERATIVE PROCESSES WITH ERROR FOR Φ-PSEUDO CONTRACTIVE TYPE MAPPINGS

The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors'recent results.

UNIQUE COMMON FIXED POINT OF A FAMILY OF SELF-MAPS WITH SAME TYPE CONTRACTIVE CONDITION IN 2-METRIC SPACE

In this paper, we prove that a family of self-maps {Ti,j}i,j∈N in 2-metric space has a unique common fixed point if （i） {Ti,j}i,j∈N satisfies the same type contractive condition for each j ∈ N; （ii） Tm,μ .Tn,v = Tn,v.Tm.μ for all m,n,μ,v ∈ N with μ≠v. Our main result generalizes and improves many known unique common fixed point theorems in 2-metric spaces.

Software Defect Prediction Based on Stacked Contractive Autoencoder and Multi-Objective Optimization

Software defect prediction plays an important role in software quality assurance.However,the performance of the prediction model is susceptible to the irrelevant and redundant features.In addition,previous studies mostly regard software defect prediction as a single objective optimization problem,and multi-objective software defect prediction has not been thoroughly investigated.For the above two reasons,we propose the following solutions in this paper:(1)we leverage an advanced deep neural network-Stacked Contractive AutoEncoder(SCAE)to extract the robust deep semantic features from the original defect features,which has stronger discrimination capacity for different classes(defective or non-defective).(2)we propose a novel multi-objective defect prediction model named SMONGE that utilizes the Multi-Objective NSGAII algorithm to optimize the advanced neural network-Extreme learning machine(ELM)based on state-of-the-art Pareto optimal solutions according to the features extracted by SCAE.We mainly consider two objectives.One objective is to maximize the performance of ELM,which refers to the benefit of the SMONGE model.Another objective is to minimize the output weight norm of ELM,which is related to the cost of the SMONGE model.We compare the SCAE with six state-of-the-art feature extraction methods and compare the SMONGE model with multiple baseline models that contain four classic defect predictors and the MONGE model without SCAE across 20 open source software projects.The experimental results verify that the superiority of SCAE and SMONGE on seven evaluation metrics.

STABILITY RESULTS FOR GENERALIZED CONTRACTIVE MAPPINGS

Using a more general contractive definition, this paper continues the study on T stable Ishikawa iteration procedure and generalizes most of the results of Harder and Hicks [1] , Osilike [5] and Rhoades [6-8] . A note on [6][8] is also presented. [WT5,5”HZ]

Viscosity approximation methods with weakly contractive mappings for nonexpansive mappings

Let K be a closed convex subset of a real reflexive Banach space E, T：K→K be a nonexpansive mapping, and f：K→K be a fixed weakly contractive （may not be contractive） mapping. Then for any t∈（0, 1）, let x1∈K be the unique fixed point of the weak contraction x1→tf（x）＋（1-t）Tx. If T has a fixed point and E admits a weakly sequentially continuous duality mapping from E to E^＊, then it is shown that {xt} converges to a fixed point of T as t→0. The results presented here improve and generalize the corresponding results in （Xu, 2004）.

SOME NEW ITERATED FUNCTION SYSTEMS CONSISTING OF GENERALIZED CONTRACTIVE MAPPINGS

Iterated function systems （IFS） were introduced by Hutchinson in 1981 as a natural generalization of the well-known Banach contraction principle. In 2010, D. R. Sahu and A. Chakraborty introduced K-Iterated Function System using Kannan mapping which would cover a larger range of mappings. In this paper, following Hutchinson, D. R. Sahu and A. Chakraborty, we present some new iterated function systems by using the so-called generalized contractive mappings, which will also cover a large range of mappings. Our purpose is to prove the existence and uniqueness of attractors for such class of iterated function systems by virtue of a Banach-like fixed point theorem concerning generalized contractive mappings.

Common Fixed Points for Two Contractive Mappings of Integral Type in Metric Spaces

In this paper, we obtain unique common fixed point theorems for two mappings satisfying the variable coefficient linear contraction of integral type and the implicit contraction of integral type respectively in metric spaces.

B-Implicit Contractive Conditions and Unique（Common） Fixed Points on Complex Valued Metric Spaces

A class B of complex functions is introduced and several existence theorems of unique(common) fixed points for mappings satisfying a B-implicit contraction are presented.Moreover, the existence results of common fixed points for two mappings on a nonempty set with two complex valued metrics are provided. Our outcomes generalize and improve some known results, especially, for instance, Banach contraction principle, Chatterjea-type fixed point theorem and the corresponding fixed point theorems.

Relation Contractive Selfmaps Involving Cauchy Sequences

We obtain two generalizations of a known theorem of A. Alam and M. Imdad (J. Fixed Point Theory Appl. 17 (2015) 693-702) showing that some standard proofs can be obtained involving only Cauchy sequences of the successive approximations. Suitable examples prove the effective generalization of our results in metric spaces not necessarily complete.

AN INDEFINITE-PROXIMAL-BASED STRICTLY CONTRACTIVE PEACEMAN-RACHFORD SPLITTING METHOD

The Peaceman-Rachford splitting method is efficient for minimizing a convex optimization problem with a separable objective function and linear constraints.However,its convergence was not guaranteed without extra requirements.He et al.(SIAM J.Optim.24:1011-1040,2014)proved the convergence of a strictly contractive Peaceman-Rachford splitting method by employing a suitable underdetermined relaxation factor.In this paper,we further extend the so-called strictly contractive Peaceman-Rachford splitting method by using two different relaxation factors.Besides,motivated by the recent advances on the ADMM type method with indefinite proximal terms,we employ the indefinite proximal term in the strictly contractive Peaceman-Rachford splitting method.We show that the proposed indefinite-proximal strictly contractive Peaceman-Rachford splitting method is convergent and also prove the o(1/t)convergence rate in the nonergodic sense.The numerical tests on the l 1 regularized least square problem demonstrate the efficiency of the proposed method.

On Characterization of Iterative Approximation for Asymptotically Pseudocontractive Mappings

Let C be a nonempty bounded closed convex subset of a Banach space X, and T : C → C be uniformly L-Lipschitzian with L ≥ 1 and asymptotically pseudocontractive with a sequence {kn}(?)[1, ∞), limn→∞ kn = 1. Fix u ∈ C. For each n ≥ 1, xn is a unique fixed point of the contraction Sn(x) = (1 - (tn)/(Lkn))u + (tn)/(Lkn)Tnx(?)x ∈ C, where {tn}(?)[0,1). Under suitable conditions, the strong convergence of the sequence{xn}to a fixed point of T is characterized.

Automated Vulnerability Detection of Blockchain Smart Contacts Based on BERT Artificial Intelligent Model

The widespread adoption of blockchain technology has led to the exploration of its numerous applications in various fields.Cryptographic algorithms and smart contracts are critical components of blockchain security.Despite the benefits of virtual currency,vulnerabilities in smart contracts have resulted in substantial losses to users.While researchers have identified these vulnerabilities and developed tools for detecting them,the accuracy of these tools is still far from satisfactory,with high false positive and false negative rates.In this paper,we propose a new method for detecting vulnerabilities in smart contracts using the BERT pre-training model,which can quickly and effectively process and detect smart contracts.More specifically,we preprocess and make symbol substitution in the contract,which can make the pre-training model better obtain contract features.We evaluate our method on four datasets and compare its performance with other deep learning models and vulnerability detection tools,demonstrating its superior accuracy.

Cone Metric Spaces and Fixed Point Theorems in Diametrically Contractive Mappings

In this paper, some topological concepts and definitions are generalized to cone metric spaces. It is proved that every cone metric space is first countable topological space and that sequentially compact subsets axe compact. Also, we define diametrically contractive mappings and asymptotically diametrically contractive mappings on cone metric spaces to obtain some fixed point theorems by assuming that our cone is strongly minihedral.

Effect of Acupoint Sanyinjiao(SP6) Moxibustion on the First Stage of Labor and Uterine Contractive Pain in Primiparae

Objective：To observe the effect of acupoint Sanyinjiao（SP6） moxibustion（S-Mox） on the duration of the first labor stage and uterine contractive pain in primiparae.Methods：Sixty primipara women in labor were equally assigned according to their choice to three groups：women in the S-Mox group received bilateral S-Mox for 30 min,women in the non-acupoint group received moxibustion（Mox） applied on non-acupoints for 30 min,and those in the control group did not receive Mox intervention.The duration of the first labor stage was recorded and the degree of labor pain was estimated by a visual analogue scale（VAS） before and after Mox. Results：The duration of the first stage active phase in the S-Mox group was significantly shorter than that in the other two groups（P0.05,P0.01）;the VAS score after Mox was lower in the S-Mox group,showing a statistical difference in comparison with the control group（P0.05）.Conclusions：Applying S-Mox could markedly shorten the active phase of the first stage of labor and lower the VAS score of uterine contractive pain,which means alleviating the pain caused by vaginal delivery.Its mechanism is worthy of further study.

A Contractive Sliding-mode MPC Algorithm for Nonlinear Discrete-time Systems

This paper investigates a sliding-mode model predictive control （MPC） algorithm with auxiliary contractive sliding vector constraint for constrained nonlinear discrete-time systems. By adding contractive constraint into the optimization problem in regular sliding-mode MPC algorithm, the value of the sliding vector is decreased to zero asymptotically, which means that the system state is driven into a vicinity of sliding surface with a certain width. Then, the system state moves along the sliding surface to the equilibrium point within the vicinity. By applying the proposed algorithm, the stability of the closed-loop system is guaranteed. A numerical example of a continuous stirred tank reactor （CSTR） system is given to verify the feasibility and effectiveness of the proposed method.

A Framework for Enhancing Privacy and Anonymity in Blockchain-Enabled IoT Devices

With the increase in IoT(Internet of Things)devices comes an inherent challenge of security.In the world today,privacy is the prime concern of every individual.Preserving one’s privacy and keeping anonymity throughout the system is a desired functionality that does not come without inevitable trade-offs like scalability and increased complexity and is always exceedingly difficult to manage.The challenge is keeping confidentiality and continuing to make the person innominate throughout the system.To address this,we present our proposed architecture where we manage IoT devices using blockchain technology.Our proposed architecture works on and off blockchain integrated with the closed-circuit television(CCTV)security camera fixed at the rental property.In this framework,the CCTV security camera feed is redirected towards the owner and renter based on the smart contract conditions.One entity(owner or renter)can see the CCTV security camera feed at one time.There is no third-party dependence except for the CCTV security camera deployment phase.Our contributions include the proposition of framework architecture,a novel smart contract algorithm,and the modification to the ring signatures leveraging an existing cryptographic technique.Analyses are made based on different systems’security and key management areas.In an empirical study,our proposed algorithm performed better in key generation,proof generation,and verification times.By comparing similar existing schemes,we have shown the proposed architectures’advantages.Until now,we have developed this system for a specific area in the real world.However,this system is scalable and applicable to other areas like healthcare monitoring systems,which is part of our future work.

A Review on the Security of the Ethereum-Based DeFi Ecosystem

Decentralized finance(DeFi)is a general term for a series of financial products and services.It is based on blockchain technology and has attracted people’s attention because of its open,transparent,and intermediary free.Among them,the DeFi ecosystem based on Ethereum-based blockchains attracts the most attention.However,the current decentralized financial system built on the Ethereum architecture has been exposed to many smart contract vulnerabilities during the last few years.Herein,we believe it is time to improve the understanding of the prevailing Ethereum-based DeFi ecosystem security issues.To that end,we investigate the Ethereum-based DeFi security issues:1)inherited from the real-world financial system,which can be solved by macro-control;2)induced by the problems of blockchain architecture,which require a better blockchain platform;3)caused by DeFi invented applications,which should be focused on during the project development.Based on that,we further discuss the current solutions and potential directions ofDeFi security.According to our research,we could provide a comprehensive vision to the research community for the improvement of Ethereum-basedDeFi ecosystem security.

Privacy Enhanced Mobile User Authentication Method Using Motion Sensors

With the development of hardware devices and the upgrading of smartphones,a large number of users save privacy-related information in mobile devices,mainly smartphones,which puts forward higher demands on the protection of mobile users’privacy information.At present,mobile user authenticationmethods based on humancomputer interaction have been extensively studied due to their advantages of high precision and non-perception,but there are still shortcomings such as low data collection efficiency,untrustworthy participating nodes,and lack of practicability.To this end,this paper proposes a privacy-enhanced mobile user authentication method with motion sensors,which mainly includes:(1)Construct a smart contract-based private chain and federated learning to improve the data collection efficiency of mobile user authentication,reduce the probability of the model being bypassed by attackers,and reduce the overhead of data centralized processing and the risk of privacy leakage;(2)Use certificateless encryption to realize the authentication of the device to ensure the credibility of the client nodes participating in the calculation;(3)Combine Variational Mode Decomposition(VMD)and Long Short-TermMemory(LSTM)to analyze and model the motion sensor data of mobile devices to improve the accuracy of model certification.The experimental results on the real environment dataset of 1513 people show that themethod proposed in this paper can effectively resist poisoning attacks while ensuring the accuracy and efficiency of mobile user authentication.