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Mathematics
Special Issues
Nonlinear and Convex Analysis
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Nonlinear and Convex Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: closed (31 January 2020) | Viewed by 6973

Special Issue Editor

Prof. Dr. Hsien-Chung Wu

E-Mail Website
Guest Editor
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan
Interests: fuzzy sets; optimization; nonlinear analysis
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Nonlinear and convex analysis has played important roles in mathematics, engineering, economics, and physics. Nonlinear analysis is very prolific in modern mathematical analysis. Solving the nonlinear problems that are coming from different areas is always based on the techniques developed in nonlinear analysis. Convexity in mathematical analysis is an ancient idea, which is always adopted to formulate mathematical problems so that they are more solvable by applying the existent mathematical tools and computer resources. The topics of this Special Issue include but are not limited to:

  • Applied functional analysis;
  • Convex risk measure in mathematical finance;
  • Differential and integral equations;
  • Equilibrium theory in mathematical economics;
  • Fixed point theory and its applications;
  • Game theory in mathematical economics;
  • Nonlinear and convex analysis using fuzzy mathematics;
  • Nonsmooth analysis and optimization;
  • Set-valued analysis;
  • Topological methods in nonlinear analysis;
  • Variational analysis.

Prof. Dr. Hsien-Chung Wu
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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • Convex sets and convex functions
  • Convex risk measure
  • Fixed point
  • Game theory
  • Nash equilibrium
  • Nondifferentiability
  • Variational inequalities

Published Papers (3 papers)

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Research

22 pages, 326 KiB  
Article
Normed Interval Space and Its Topological Structure
by Hsien-Chung Wu
Mathematics 2019, 7(10), 983; https://doi.org/10.3390/math7100983 - 16 Oct 2019
Viewed by 1894
Abstract
Based on the natural vector addition and scalar multiplication, the set of all bounded and closed intervals in R cannot form a vector space. This is mainly because the zero element does not exist. In this paper, we endow a norm to the [...] Read more.
Based on the natural vector addition and scalar multiplication, the set of all bounded and closed intervals in R cannot form a vector space. This is mainly because the zero element does not exist. In this paper, we endow a norm to the interval space in which the axioms are almost the same as the axioms of conventional norm by involving the concept of null set. Under this consideration, we shall propose two different concepts of open balls. Based on the open balls, we shall also propose the different types of open sets, which can generate many different topologies. Full article
(This article belongs to the Special Issue Nonlinear and Convex Analysis)
9 pages, 227 KiB  
Article
Asymmetric Orlicz Radial Bodies
by Hai Li, Weidong Wang and Tongyi Ma
Mathematics 2019, 7(7), 590; https://doi.org/10.3390/math7070590 - 1 Jul 2019
Viewed by 1573
Abstract
Based on the L p -harmonic radial combination, Li and Wang researched the asymmetric L p -harmonic radial bodies, which belong to the asymmetric L p -Brunn-Minkowski theory initiated by Ludwig, Haberl and Schuster. In this paper, combined with Orlicz radial combination, we [...] Read more.
Based on the L p -harmonic radial combination, Li and Wang researched the asymmetric L p -harmonic radial bodies, which belong to the asymmetric L p -Brunn-Minkowski theory initiated by Ludwig, Haberl and Schuster. In this paper, combined with Orlicz radial combination, we introduce the asymmetric Orlicz radial bodies and research their properties. Further, we also establish some inequalities for this concept. Full article
(This article belongs to the Special Issue Nonlinear and Convex Analysis)
12 pages, 271 KiB  
Article
Generalized Geodesic Convexity on Riemannian Manifolds
by Izhar Ahmad, Meraj Ali Khan and Amira A. Ishan
Mathematics 2019, 7(6), 547; https://doi.org/10.3390/math7060547 - 16 Jun 2019
Cited by 4 | Viewed by 2443
Abstract
We introduce log-preinvex and log-invex functions on a Riemannian manifold. Some properties and relationships of these functions are discussed. A characterization for the existence of a global minimum point of a mathematical programming problem is presented. Moreover, a mean value inequality under geodesic [...] Read more.
We introduce log-preinvex and log-invex functions on a Riemannian manifold. Some properties and relationships of these functions are discussed. A characterization for the existence of a global minimum point of a mathematical programming problem is presented. Moreover, a mean value inequality under geodesic log-preinvexity is extended to Cartan-Hadamard manifolds. Full article
(This article belongs to the Special Issue Nonlinear and Convex Analysis)
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