{"title":"Coupled fixed point results for new classes of functions on ordered vector metric space","authors":"","doi":"10.1007/s10474-024-01393-3","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>The contraction condition in the Banach contraction principle forces a function to be continuous. Many authors overcome this obligation and weaken the hypotheses via metric spaces endowed with a partial order. In this paper, we present some coupled fixed point theorems for the functions having mixed monotone properties on ordered vector metric spaces, which are more general spaces than partially ordered metric spaces. We also define the double monotone property and investigate the previous results with this property. In the last section, we prove the uniqueness of a coupled fixed point for non-monotone functions. In addition, we present some illustrative examples to emphasize that our results are more general than the ones in the literature.</p>","PeriodicalId":50894,"journal":{"name":"Acta Mathematica Hungarica","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10474-024-01393-3","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The contraction condition in the Banach contraction principle forces a function to be continuous. Many authors overcome this obligation and weaken the hypotheses via metric spaces endowed with a partial order. In this paper, we present some coupled fixed point theorems for the functions having mixed monotone properties on ordered vector metric spaces, which are more general spaces than partially ordered metric spaces. We also define the double monotone property and investigate the previous results with this property. In the last section, we prove the uniqueness of a coupled fixed point for non-monotone functions. In addition, we present some illustrative examples to emphasize that our results are more general than the ones in the literature.
期刊介绍:
Acta Mathematica Hungarica is devoted to publishing research articles of top quality in all areas of pure and applied mathematics as well as in theoretical computer science. The journal is published yearly in three volumes (two issues per volume, in total 6 issues) in both print and electronic formats. Acta Mathematica Hungarica (formerly Acta Mathematica Academiae Scientiarum Hungaricae) was founded in 1950 by the Hungarian Academy of Sciences.