Journal of Function Spaces and Applications最新文献

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Research on the Effect of MT+FES Training on Sensorimotor Cortex. MT+FES 训练对感觉运动皮层的影响研究。

IF 3.1

Journal of Function Spaces and Applications

Pub Date : 2022-06-03 eCollection Date: 2022-01-01 DOI: 10.1155/2022/6385755

Yuan-Xing Wang, Zhi-Zeng Luo

Purpose: Aiming at the motor recovery of patients with unilateral upper limb motor dysfunction after stroke, we propose a mirror therapy (MT) training method, which uses surface electromyography (sEMG) to identify movements on one side and control the other side to perform functional electrical stimulation (FES) while mirror therapy is used. And we verify the effect of this training method by analyzing the activity changes of the sensorimotor cortex.

Method: Ten subjects (6 men and 4 women) were randomly divided into two groups according to 3 men and 2 women in each group: the experimental group (n = 5) received FES+MT training, and the control group (n = 5) received MT training. Both groups were trained at a fixed time at 9 : 00 am every day, each time lasting 20 minutes, once a day, 5 days a week, continuous training for 4 weeks, and the training action was elbow flexion training. During the training of the elbow flexion exercise, the experimental group applied FES with a frequency of 30 Hz, a pulse width of 100 μs, and a current of 10 mA to the muscles corresponding to the elbow flexion exercise, and rested for 10 s after 10-s stimulation. We collect the EEG of the elbow flexion motor imagery of all subjects before and after training, and calculate the eigenvalue E, and analyze the effect of FES+MT training on the activity of the cerebral sensorimotor cortex.

Results: After repeated measure (RM) two-way ANOVA of the two groups, comparing the subjects' μ rhythm elbow flexion motor imagery eigenvalue E, the experimental group (after training) > the control group (after training) > before training.

Conclusion: The FES+MT training method has obvious activation effect on the cerebral sensorimotor cortex.

目的：针对脑卒中后单侧上肢运动功能障碍患者的运动恢复，我们提出了一种镜像疗法（MT）训练方法，即利用表面肌电图（sEMG）识别一侧的运动，并在镜像疗法的同时控制另一侧进行功能性电刺激（FES）。我们通过分析感觉运动皮层的活动变化来验证这种训练方法的效果：10名受试者（6男4女）按每组3男2女随机分为两组：实验组（n=5）接受FES+MT训练，对照组（n=5）接受MT训练。两组均在每天上午 9 ：00，每次持续 20 分钟，每天一次，每周 5 天，连续训练 4 周，训练动作为屈肘训练。在屈肘运动训练过程中，实验组对与屈肘运动相对应的肌肉施加频率为 30 Hz、脉宽为 100 μs、电流为 10 mA 的 FES，刺激 10 s 后休息 10 s。收集所有受试者训练前后屈肘运动意象的脑电图，计算特征值E，分析FES+MT训练对大脑感觉运动皮层活动的影响：经两组重复测量（RM）双因素方差分析，比较受试者的μ节律屈肘运动意象特征值E，实验组（训练后）>对照组（训练后）>训练前：结论：FES+MT 训练方法对大脑感觉运动皮层有明显的激活作用。

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引用次数: 0

On a Unique Solution of a T-Maze Model Arising in the Psychology and Theory of Learning 心理学和学习理论中t -迷宫模型的唯一解

Journal of Function Spaces and Applications

Pub Date : 2021-10-24 DOI: 10.1155/2021/6081250

A. Turab, Wajahat Ali, J. J. Nieto

In the form of a T, a T-maze is an experimental design in which each trial consists of decisions between two or more options. It contains choices with particular kinds of symmetries that have gained considerable attention in psychology and learning theories. One of the simplest mazes utilized by rats is the T-maze since it requires just a single point of preference. At a T-maze base, the mouse chooses to turn right or left to get food. This paper aims at analyzing the rat’s behavior in such circumstances and proposing a suitable mathematical model for it. The existence and uniqueness of a solution to the proposed T-maze model are investigated by using the appropriate fixed point method.

T形迷宫是一种实验设计，其中每次试验由两个或多个选项之间的决策组成。它包含了在心理学和学习理论中获得了相当多关注的具有特定对称性的选择。老鼠使用的最简单的迷宫之一是t型迷宫，因为它只需要一个偏好点。在t型迷宫的基础上，老鼠选择向左或向右转来获取食物。本文旨在分析大鼠在这种情况下的行为，并提出一个合适的数学模型。利用适当的不动点方法研究了t -迷宫模型解的存在唯一性。

引用次数: 3

On the Algebraic Characteristics of Fuzzy Sub e-Groups 关于模糊子群的代数特征

Journal of Function Spaces and Applications

Pub Date : 2021-10-20 DOI: 10.1155/2021/5253346

Supriya Bhunia, G. Ghorai, M. Kutbi, Muhammad Gulzar, Ashraful Alam

Fuzzy set is a modern tool for depicting uncertainty. This paper introduces the concept of fuzzy sub e-group as an extension of fuzzy subgroup. The concepts of identity and inverse are generalized in fuzzy sub e-groups. Every fuzzy subgroup is proven to be a fuzzy sub e-group, but the converse is not true. Various properties of fuzzy sub e-groups are established. Moreover, the concepts of proper fuzzy sub e-group and super fuzzy sub e-group are discussed. Further, the concepts of fuzzy e-coset and normal fuzzy sub e-group are presented. Finally, we describe the effect of e-group homomorphism on normal fuzzy sub e-groups.

模糊集是描述不确定性的现代工具。本文引入了模糊子群的概念，作为模糊子群的一个推广。在模糊子群中推广了恒等式和逆的概念。证明了每个模糊子群都是一个模糊子群，但反之则不成立。建立了模糊子群的各种性质。此外，还讨论了真模糊子群和超模糊子群的概念。进一步，给出了模糊e集和正规模糊子群的概念。最后，我们描述了e-群同态对正规模糊子群的影响。

引用次数: 10

New Results on Perov-Interpolative Contractions of Suzuki Type Mappings 关于Suzuki型映射的逆插值缩约的新结果

Journal of Function Spaces and Applications

Pub Date : 2021-10-20 DOI: 10.1155/2021/9587604

E. Karapınar, A. Fulga, Seher Sultan Yeşilkaya

In this paper, we introduce some common fixed point theorems for interpolative contraction operators using Perov operator which satisfy Suzuki type mappings. Further, some results are given. These results generalize several new results present in the literature.

本文利用Perov算子，给出了满足Suzuki型映射的内插收缩算子的几个常见不动点定理。进一步给出了一些结果。这些结果概括了文献中出现的几个新结果。

引用次数: 16

Extragradient Method for Fixed Points in CAT(0) Spaces CAT（0）空间中不动点的外梯度方法

Journal of Function Spaces and Applications

Pub Date : 2021-08-26 DOI: 10.1155/2021/7808255

Yupei Lv, K. Shabbir, Sundus Shahzeen, Farman Ali, J. Kafle

This paper is dedicated to construct a viscosity extragradient algorithm for finding fixed points in a CAT(0) space. The mappings we consider are nonexpansive. Strong convergence of the algorithm is obtained. The results established in this work extend and improve some recent discovers in the literature.

本文致力于构造一种在CAT（0）空间中寻找不动点的粘性超梯度算法。我们考虑的映射是非扩张的。该算法具有较强的收敛性。这项工作中建立的结果扩展和改进了文献中的一些最新发现。

引用次数: 1

A Strong Convergence Theorem for a Finite Family of Bregman Demimetric Mappings in a Banach Space under a New Shrinking Projection Method 在一种新的收缩投影方法下，Banach空间中有限族Bregman半对称映射的强收敛定理

Journal of Function Spaces and Applications

Pub Date : 2021-07-28 DOI: 10.1155/2021/9551162

Bijan Orouji, E. Soori, D. O’Regan, R. Agarwal

In this paper, using a new shrinking projection method and new generalized - demimetric mappings, we consider the strong convergence for finding a common point of the sets of zero points of maximal monotone mappings, common fixed points of a finite family of Bregman - demimetric mappings, and common zero points of a finite family of Bregman inverse strongly monotone mappings in a reflexive Banach space. To the best of our knowledge, such a theorem for Bregman - demimetric mapping is the first of its kind in a Banach space. This manuscript is online on arXiv by the link http://arxiv.org/abs/2107.13254 .

本文利用一种新的收缩投影方法和新的广义半对称映射，研究了在自反Banach空间中寻找最大单调映射的零点集、有限族Bregman -半对称映射的公共不动点和有限族Bregman逆强单调映射的公共零点的强收敛性。据我们所知，这样的布雷格曼-半对称映射定理在巴拿赫空间中是第一个。这份手稿可以通过链接http://arxiv.org/abs/2107.13254在arXiv上找到。

引用次数: 3

Common Fixed Point Results for Generalized g − α 广义g−α的公共不动点结果

Journal of Function Spaces and Applications

Pub Date : 2021-06-15 DOI: 10.1155/2021/5020027

Jianju Li, H. Guan

In this paper, we introduce a new class of admissible mappings and prove some common fixed point theorems involving this new class of mappings which satisfy generalized contractive conditions in the framework of metric spaces. We also provide two examples to show the applicability and validity of our results. Meanwhile, we present an application to the existence of solutions to an integral equation by means of one of our results.

本文在度量空间的框架中引入了一类新的可容许映射，并证明了涉及这类映射的满足广义压缩条件的几个公共不动点定理。最后给出了两个算例，说明了所得结果的适用性和有效性。同时，利用我们的一个结果，给出了在一类积分方程解的存在性上的一个应用。

引用次数: 3

Fixed Point of Generalized Weak Contraction in b -Metric Spaces b -度量空间中广义弱收缩的不动点

Journal of Function Spaces and Applications

Pub Date : 2021-06-15 DOI: 10.1155/2021/2042162

M. Iqbal, Afshan Batool, Ozgur Ege, M. Sen

In this manuscript, a class of generalized - weak contraction is introduced and some fixed point theorems in the framework of - metric space are proved. The result presented in this paper generalizes some of the earlier results in the existing literature. Further, some examples and an application are provided to illustrate our main result.

本文引入了一类广义-弱收缩，证明了在-度量空间框架中的不动点定理。本文提出的结果概括了现有文献中一些较早的结果。此外，还提供了一些示例和应用程序来说明我们的主要结果。

引用次数: 6

Logarithmic Coefficient Bounds and Coefficient Conjectures for Classes Associated with Convex Functions 凸函数相关类的对数系数界和系数猜想

Journal of Function Spaces and Applications

Pub Date : 2021-06-13 DOI: 10.1155/2021/6690027

D. Alimohammadi, E. Analouei Adegani, T. Bulboacă, N. Cho

Department of Mathematics, Faculty of Science, Arak University, Arak 38156-8-8349, Iran Faculty of Mathematical Sciences, Shahrood University of Technology, P.O. Box 316-36155, Shahrood, Iran Faculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, Romania Department of Applied Mathematics, College of Natural Sciences, Pukyong National University, Busan 48513, Republic of Korea

阿拉克大学理学院数学系，阿拉克38156-8349，伊朗数学科学学院，沙鲁德理工大学，邮箱316-36155，Shahrood，伊朗数学和计算机科学学院，巴贝什-博利亚伊大学，400084 Cluj Napoca，罗马尼亚普京国立大学自然科学学院应用数学系，釜山48513，大韩民国

引用次数: 13

Coincidence Point Results on Relation Theoretic F 关系论F的重合点结果

Journal of Function Spaces and Applications

Pub Date : 2021-06-10 DOI: 10.1155/2021/9937318

M. Aslam, H. Aydi, S. Batul, Amna Naz

Motivated by the ideas of - weak contractions and - contractions, the notion of - contractions is introduced and studied in the present paper. The idea is to establish some interesting results for the existence and uniqueness of a coincidence point for these contractions. Further, using an additional condition of weakly compatible mappings, a common fixed-point theorem and a fixed-point result are proved for - contractions in metric spaces equipped with a transitive binary relation. The results are elaborated by illustrative examples. Some consequences of these results are also deduced in ordered metric spaces and metric spaces endowed with graph. Finally, as an application, the existence of the solution of certain Voltera type integral equations is investigated.

在弱收缩和收缩思想的启发下，本文引入并研究了收缩的概念。这个想法是为了建立一些有趣的结果，证明这些收缩的重合点的存在性和唯一性。此外，利用弱相容映射的一个附加条件，证明了具有传递二元关系的度量空间中的压缩的一个公共不动点定理和一个不动点结果。通过举例说明了结果。在序度量空间和赋图的度量空间中也推导了这些结果的一些结果。最后，作为一个应用，研究了一类Voltera型积分方程解的存在性。

引用次数: 1

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