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Symmetry
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Recent Advances on Nonlinear Analysis and Optimization in Symmetry and...
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Recent Advances on Nonlinear Analysis and Optimization in Symmetry and Asymmetry

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (1 January 2023) | Viewed by 6155

Special Issue Editor

Prof. Dr. Wei-Shih Du

E-Mail Website
Guest Editor
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 82444, Taiwan
Interests: nonlinear analysis and its applications; fixed point theory; variational principles and inequalities; optimization theory; equilibrium problems; fractional calculus theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

One of the main fascinating objectives of nonlinear analysis is to study differential and integral equations for various nonlinear operators, and local approximation problems. Nonlinear analysis has wide and significant applications in many areas of mathematics including functional analysis, variational analysis, convex analysis, nonlinear ordinary and partial differential equations, control theory, dynamical system theory, game theory, economics, signal processing, data mining, and so forth. Over the last half century, optimization problems have been intensively investigated and various feasible methods in analyzing convergence of problem-solving algorithms have been created. The Special Issue will attempt to cover the whole field of symmetry and asymmetry in its widest sense, together with its applications in many facets of nonlinear analysis and optimization. 

We cordially and earnestly invite researchers to contribute their original and high quality research papers which will inspire advances in nonlinear analysis, optimization, and their applications. Potential topics include, but are not limited to:

  • Fixed point theory in symmetry and asymmetry
  • Coincidence point and best proximity point theory in symmetry and asymmetry
  • Set-valued analysis in symmetry and asymmetry
  • Optimization in symmetry and asymmetry
  • Nonsmooth analysis in symmetry and asymmetry
  • Dynamical systems in symmetry and asymmetry
  • Matrix theory in symmetry and asymmetry
  • Game theory in symmetry and asymmetry
  • Control theory in symmetry and asymmetry
  • Calculus of variations and PDEs in symmetry and asymmetry
  • Variational and topological methods for ODEs and PDEs
  • Convex analysis
  • Functional analysis
  • Image and signal processing
  • Data mining

Prof. Dr. Wei-Shih Du
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Fixed point theory
  • Coincidence point and best proximity point theory
  • Functional analysis
  • Set-valued analysis
  • Dynamical systems
  • Optimization
  • Convex analysis
  • ODEs and PDEs
  • Nonsmooth analysis
  • Matrix theory
  • Control theory
  • Image and signal processing
  • Data mining

Published Papers (3 papers)

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Research

12 pages, 264 KiB  
Article
Resource-Allocation Mechanism: Game-Theory Analysis
by Shu-Lin Chang, Kun-Chang Lee, Ruey-Rong Huang and Yu-Hsien Liao
Symmetry 2021, 13(5), 799; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13050799 - 04 May 2021
Cited by 1 | Viewed by 2335
Abstract
Recently, owing to the trend of cross-disciplinary research in various fields, it is imperative to optimize the resource-allocation performance by analyzing allocation behavior and strategies from different perspectives as well as based on ideas from various fields. There are many decisive roles, such [...] Read more.
Recently, owing to the trend of cross-disciplinary research in various fields, it is imperative to optimize the resource-allocation performance by analyzing allocation behavior and strategies from different perspectives as well as based on ideas from various fields. There are many decisive roles, such as changes in allocation behavior, related allocation methods, and the interaction and work effectiveness of strategies, to be implemented. By using game-theory analysis under resource-allocation procedures, in this article, we analyzed, constructed, simulated, and derived an efficient resource-allocation mechanism. Additionally, we generalized a power index by evaluating the operators and their activity levels. This article adopted the axioms of level completeness, criterion for weighted circumstances property, level synchronization, pure excess equal symmetry, and specific consonance to offer characterizations to assess the related rationality and accuracy of the proposed power index. Based on the above discussion, different from the rule of thumb, expert meeting, or other existing concepts, in this research game theory is used to provide an alternative guide for resource-allocation procedures by the optimal or equilibrium state established. Full article
(This article belongs to the Special Issue Recent Advances on Nonlinear Analysis and Optimization in Symmetry and Asymmetry)
14 pages, 289 KiB  
Article
On Generalizations of Sampling Theorem and Stability Theorem in Shift-Invariant Subspaces of Lebesgue and Wiener Amalgam Spaces with Mixed-Norms
by Junjian Zhao, Marko Kostić and Wei-Shih Du
Symmetry 2021, 13(2), 331; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13020331 - 18 Feb 2021
Cited by 6 | Viewed by 1472
Abstract
In this paper, we establish generalized sampling theorems, generalized stability theorems and new inequalities in the setting of shift-invariant subspaces of Lebesgue and Wiener amalgam spaces with mixed-norms. A convergence theorem of general iteration algorithms for sampling in some shift-invariant subspaces of [...] Read more.
In this paper, we establish generalized sampling theorems, generalized stability theorems and new inequalities in the setting of shift-invariant subspaces of Lebesgue and Wiener amalgam spaces with mixed-norms. A convergence theorem of general iteration algorithms for sampling in some shift-invariant subspaces of Lp→(Rd) are also given. Full article
(This article belongs to the Special Issue Recent Advances on Nonlinear Analysis and Optimization in Symmetry and Asymmetry)
15 pages, 257 KiB  
Article
Consonance, Symmetry and Extended Outputs
by Yu-Hsien Liao
Symmetry 2021, 13(1), 72; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13010072 - 03 Jan 2021
Cited by 1 | Viewed by 1183
Abstract
In many real-world situations, performers always adopt different energy levels (strategies) to participate. Different from pre-existing results, this paper is devoted to proposing several generalized power outputs of the marginal index, the Banzhaf–Coleman index, and the Banzhaf–Owen index, respectively, by assigning different energy [...] Read more.
In many real-world situations, performers always adopt different energy levels (strategies) to participate. Different from pre-existing results, this paper is devoted to proposing several generalized power outputs of the marginal index, the Banzhaf–Coleman index, and the Banzhaf–Owen index, respectively, by assigning different energy levels to all performers. Since these extended power outputs may not be efficacious, we further define the efficacious extensions of these power outputs, respectively. For each of these efficacious power outputs, we demonstrate that there exists a corresponding reduced game and related consonance property that can be used to characterize it. By focusing on the properties of symmetry and accordance, several axiomatic results are also introduced. Full article
(This article belongs to the Special Issue Recent Advances on Nonlinear Analysis and Optimization in Symmetry and Asymmetry)
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