Functional Analysis and Fixed Points

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

Deadline for manuscript submissions: 30 September 2026 | Viewed by 420

Editors


E-Mail Website
Guest Editor
School of Mathematical Sciences, Tiangong University, Tianjin 300392, China
Interests: nonlinear functional analysis; operator theory; operator algebra

E-Mail Website
Guest Editor
School of Mathematical Sciences, Tiangong University, Tianjin 300392, China
Interests: nonlinear functional analysis; optimization

Special Issue Information

Dear Colleagues,

This Special Issue, "Functional Analysis and Fixed Points," aims to bring together recent advances in fixed-point theory and its deep connections with various branches of functional analysis. Fixed-point theory is a cornerstone of nonlinear analysis, providing essential tools for establishing the existence and uniqueness of solutions to equations arising in differential equations, optimization, variational inequalities, and economics. We invite original research articles and survey papers that explore new fixed-point theorems in metric, topological, and ordered spaces, their applications within functional analysis, and novel interactions with operator theory, the geometry of Banach spaces, and nonlinear spectral theory.

Prof. Dr. Luoyi Shi
Prof. Dr. Ziheng Zhang
Guest Editors

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Keywords

  • fixed-point theory
  • iterative algorithm
  • metric fixed-point theory
  • topological methods
  • operator theory
  • operator algebra
  • variational principles
  • Banach space geometry
  • applications to differential equations

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Published Papers (1 paper)

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Research

19 pages, 618 KB  
Article
On Weak Enriched \(\mathfrak{F}\) and \(\mathfrak{F}\)′- Contractions in Convex Metric and Convex G-Metric Spaces
by Jatinderdeep Kaur, Satvinder Singh Bhatia and Bhumika Rani
Symmetry 2026, 18(7), 1140; https://doi.org/10.3390/sym18071140 - 3 Jul 2026
Viewed by 99
Abstract
This paper introduces and investigates two new classes of contraction mappings—weak enriched F-contractions and weak enriched F-contractions, in the context of convex metric space (CMS) and convex G-metric space (CGMS). From a given self-mapping, the study constructs a new [...] Read more.
This paper introduces and investigates two new classes of contraction mappings—weak enriched F-contractions and weak enriched F-contractions, in the context of convex metric space (CMS) and convex G-metric space (CGMS). From a given self-mapping, the study constructs a new mapping via different convex combinations, termed the k-fold averaged mapping. The paper establishes that if the underlying space is complete and certain conditions are satisfied, then the k-fold averaged mapping possesses a unique fixed point, and the corresponding iterative scheme converges to this fixed point. It is further shown that the fixed point set of the original mapping is always contained in the fixed point set of k-fold averaged mapping, and under further conditions, both sets of fixed points are equal. These results broaden the scope of fixed point theory in convex metric settings by introducing and exploring these new contraction mappings. Several examples are provided to illustrate the applicability and effectiveness of the theoretical findings. Full article
(This article belongs to the Special Issue Functional Analysis and Fixed Points)
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