{"title":"A variational principle, fixed points and coupled fixed points on $$\\mathbb {P}$$ sets","authors":"Valentin Georgiev, Atanas Ilchev, Boyan Zlatanov","doi":"10.1007/s11784-024-01123-w","DOIUrl":null,"url":null,"abstract":"<p>We prove a generalization of Ekeland’s variational principal using the notion of <span>\\(\\mathbb {P}\\)</span> sets. Using this result, we give proofs for fixed point theorems on partially ordered sets. Furthermore, one can obtain theorems for coupled fixed points using this technique. We demonstrate the procedure for proving such theorems.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":"41 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Fixed Point Theory and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11784-024-01123-w","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We prove a generalization of Ekeland’s variational principal using the notion of \(\mathbb {P}\) sets. Using this result, we give proofs for fixed point theorems on partially ordered sets. Furthermore, one can obtain theorems for coupled fixed points using this technique. We demonstrate the procedure for proving such theorems.
期刊介绍：
The Journal of Fixed Point Theory and Applications (JFPTA) provides a publication forum for an important research in all disciplines in which the use of tools of fixed point theory plays an essential role. Research topics include but are not limited to:
(i) New developments in fixed point theory as well as in related topological methods,
in particular:
Degree and fixed point index for various types of maps,
Algebraic topology methods in the context of the Leray-Schauder theory,
Lefschetz and Nielsen theories,
Borsuk-Ulam type results,
Vietoris fractions and fixed points for set-valued maps.
(ii) Ramifications to global analysis, dynamical systems and symplectic topology,
in particular:
Degree and Conley Index in the study of non-linear phenomena,
Lusternik-Schnirelmann and Morse theoretic methods,
Floer Homology and Hamiltonian Systems,
Elliptic complexes and the Atiyah-Bott fixed point theorem,
Symplectic fixed point theorems and results related to the Arnold Conjecture.
(iii) Significant applications in nonlinear analysis, mathematical economics and computation theory,
in particular:
Bifurcation theory and non-linear PDE-s,
Convex analysis and variational inequalities,
KKM-maps, theory of games and economics,
Fixed point algorithms for computing fixed points.
(iv) Contributions to important problems in geometry, fluid dynamics and mathematical physics,
in particular:
Global Riemannian geometry,
Nonlinear problems in fluid mechanics.
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