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Axioms
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Advances in Functional Analysis and Banach Space
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Advances in Functional Analysis and Banach Space

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 31 May 2026 | Viewed by 844

Special Issue Editors

Dr. Shaoqiang Shang

E-Mail Website
Guest Editor
College of Mathematical Sciences, Harbin Engineering University, Harbin 150001, China
Interests: Banach space, geometry theory and its applications
Prof. Dr. Sidney A. Morris

E-Mail Website
Guest Editor
1. School of Engineering, IT and Physical Sciences, Federation University Australia, Ballarat, VIC 3353, Australia
2. Department of Mathematical and Physical Sciences, La Trobe University, Melbourne, VIC 3086, Australia
Interests: topological groups, especially locally compact groups; pro-Lie groups; topological algebra; topological vector spaces; Banach spaces; topology; group theory; functional analysis; universal algebra; transcendental number theory; numerical geometry; history of mathematics; information technology security; health informatics; international education; university education; online education; social media in the teaching of mathematics; stock market prediction
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Functional analysis is a branch of mathematics and a fundamental theory of modern mathematics. An important branch of functional analysis is Banach theory, which studies the geometric structure of Banach spaces (including convexity theory, norm differentiability theory, geometric constants, etc.), as well as the application of Banach space geometry in convex optimization theory, approximation theory, fixed point theory, etc. Banach theory is also the foundation of operator theory. Banach spaces have good geometric properties that ensure good operator properties, such as in the wide application of Banach space geometry theory in operator-generalized inverse theory.

Banach space theory is widely used to solve ordinary differential equations and partial differential equations, providing a mathematical framework for quantum mechanics. Mathematical physics, mechanical engineering, and control engineering are some sciences that can benefit from Banach space theory.

Axioms plans to launch a Special Issue on functional analysis and operator Banach space theory. This Special Issue will invite researchers to introduce their latest innovations, trends, areas of focus, practical challenges encountered, and solutions adopted in the field of Banach space theory. This Special Issue welcomes original and unpublished mathematical papers on the latest developments with high standards and significant implications.

Dr. Shaoqiang Shang
Prof. Dr. Sidney A. Morris
Guest Editors

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 250 words) can be sent to the Editorial Office for assessment.

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. Axioms 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

  • Banach space geometry theory
  • fixed point theory
  • orlicz space
  • coarse isometry
  • approximation

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Published Papers (2 papers)

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Research

11 pages, 549 KB  
Article
Several Geometric Properties in Banach Spaces and Their Further Application in Orlicz Spaces
by Xiaoxia Wang, Yunan Cui and Yaoming Niu
Axioms 2025, 14(12), 928; https://doi.org/10.3390/axioms14120928 - 17 Dec 2025
Viewed by 207
Abstract
In this paper, locally nearly uniformly convex (LNUC) is studied in Banach space. Furthermore, the implication relationship between (LNUC) and the Kadec–Klee property (KK), the fixed–point property [...] Read more.
In this paper, locally nearly uniformly convex (LNUC) is studied in Banach space. Furthermore, the implication relationship between (LNUC) and the Kadec–Klee property (KK), the fixed–point property (FPP) are investigated in Banach space. Finally, the relationship between the uniform Kadec−Klee property (UKK), the coordinate-wise uniform Kadec–Klee property (UKKC), the coordinate-wise Kadec–Klee property (Hc) and δ2 conditions are investigated in Orlicz sequence spaces equipped with the Orlicz norm, meanwhile we get a criteria that Orlicz sequence spaces equipped with the Orlicz norm are (LNUC). Full article
(This article belongs to the Special Issue Advances in Functional Analysis and Banach Space)
21 pages, 342 KB  
Article
Strongly F-Convex Functions with Structural Characterizations and Applications in Entropies
by Hasan Barsam, Slavica Ivelić Bradanović, Matea Jelić and Yamin Sayyari
Axioms 2025, 14(12), 926; https://doi.org/10.3390/axioms14120926 - 16 Dec 2025
Viewed by 291
Abstract
Strongly convex functions form a central subclass of convex functions and have gained considerable attention due to their structural advantages and broad applicability, particularly in optimization and information theory. In this paper, we investigate the class of strongly F-convex functions, which generalizes [...] Read more.
Strongly convex functions form a central subclass of convex functions and have gained considerable attention due to their structural advantages and broad applicability, particularly in optimization and information theory. In this paper, we investigate the class of strongly F-convex functions, which generalizes the classical notion of strong convexity by introducing an auxiliary convex control function F. We establish several fundamental structural characterizations of this class and provide a variety of nontrivial examples such as power, logarithmic, and exponential functions. In addition, we derive refined Jensen-type and Hermite–Hadamard-type inequalities adapted to the strongly F-convex concept, thereby extending and sharpening their classical forms. As applications, we obtain new analytical inequalities and improved error bounds for entropy-related quantities, including Shannon, Tsallis, and Rényi entropies, demonstrating that the concept of strong F-convexity naturally yields strengthened divergence and uncertainty estimates. Full article
(This article belongs to the Special Issue Advances in Functional Analysis and Banach Space)
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