Advances in Nonlinear Analysis and Its Application

A special issue of Axioms (ISSN 2075-1680).

Deadline for manuscript submissions: 31 December 2026 | Viewed by 576

Special Issue Editor

Special Issue Information

Dear Colleagues, 

Nonlinear analysis has played an important role in applied mathematics, and it is very prolific in modern mathematical analysis. Many mathematical problems modelled from the fields of biology, engineering, economics, and physics are categorized as nonlinear problems. Solving these nonlinear problems requires the techniques developed in nonlinear analysis. This Special Issue will focus on recent advances in nonlinear analysis and its applications. Topics of interest include, but are not limited to, the following: 

  • Applied functional analysis;
  • Differential and integral equations;
  • Equilibrium theory in mathematical economics;
  • Fixed point theory and its applications;
  • Game theory in mathematical economics;
  • Nonlinear analysis using fuzzy sets;
  • Non-smooth analysis and optimization;
  • Set-valued analysis and optimization;
  • Topological methods in nonlinear analysis;
  • Variational analysis.

Prof. Dr. Hsien-Chung Wu
Guest Editor

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Keywords

  • fixed point
  • fuzzy sets
  • nash equilibrium
  • non-differentiability
  • set optimization
  • variational inequalities

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Published Papers (1 paper)

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Research

47 pages, 490 KB  
Article
Simple Type of Support Functions of Fuzzy Sets and Its Applications
by Hsien-Chung Wu
Axioms 2026, 15(4), 296; https://doi.org/10.3390/axioms15040296 - 17 Apr 2026
Viewed by 241
Abstract
The support functions of crisp sets have been widely used in the topic of nonlinear analysis. This observation inspires to introduce the support functions of fuzzy sets. Two different support functions of fuzzy sets were introduced in the literature by using different domains [...] Read more.
The support functions of crisp sets have been widely used in the topic of nonlinear analysis. This observation inspires to introduce the support functions of fuzzy sets. Two different support functions of fuzzy sets were introduced in the literature by using different domains of functions. This paper will focus on the simple type of support functions that are defined on a simple domain. Three applications using the simple type of support functions are studied in this paper. The first one is to generate fuzzy sets from the real-valued functions that satisfy some regular conditions such that the simple type of support function of a generated fuzzy set is identical with the pre-determined real-valued function. The second one is to study the embedding theorems of some interesting families of fuzzy sets. In this case, the continuities of simple types of support functions should be studied under some suitable topologies. In order to make the embedded Banach spaces as small as possible, the concept of weak* topology should be involved in the study. The third one is to solve the fuzzy optimization problems using the embedding theorems. Full article
(This article belongs to the Special Issue Advances in Nonlinear Analysis and Its Application)
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