{"title":"用不动点法逼近一种先进的多维往复式二次映射","authors":"B. S. Senthil Kumar, H. Dutta, S. Sabarinathan","doi":"10.5269/bspm.62943","DOIUrl":null,"url":null,"abstract":"There are many results on stability of various forms of functional equations available in the theory of functional equations. The intention of this paper is to introduce an advanced and a new multi-dimensional reciprocal-quadratic functional equation involving $p>1$ variables. It is interesting to note that it has two different solutions, namely, quadratic and multiplicative inverse quadratic functions. We solve its various stability problems in the setting of non-zero real numbers and non-Archimedean fields via fixed point approach.","PeriodicalId":44941,"journal":{"name":"Boletim Sociedade Paranaense de Matematica","volume":" ","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximating an advanced multi-dimensional reciprocal-quadratic mapping via a fixed point approach\",\"authors\":\"B. S. Senthil Kumar, H. Dutta, S. Sabarinathan\",\"doi\":\"10.5269/bspm.62943\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"There are many results on stability of various forms of functional equations available in the theory of functional equations. The intention of this paper is to introduce an advanced and a new multi-dimensional reciprocal-quadratic functional equation involving $p>1$ variables. It is interesting to note that it has two different solutions, namely, quadratic and multiplicative inverse quadratic functions. We solve its various stability problems in the setting of non-zero real numbers and non-Archimedean fields via fixed point approach.\",\"PeriodicalId\":44941,\"journal\":{\"name\":\"Boletim Sociedade Paranaense de Matematica\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-12-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Boletim Sociedade Paranaense de Matematica\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5269/bspm.62943\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Boletim Sociedade Paranaense de Matematica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5269/bspm.62943","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
Approximating an advanced multi-dimensional reciprocal-quadratic mapping via a fixed point approach
There are many results on stability of various forms of functional equations available in the theory of functional equations. The intention of this paper is to introduce an advanced and a new multi-dimensional reciprocal-quadratic functional equation involving $p>1$ variables. It is interesting to note that it has two different solutions, namely, quadratic and multiplicative inverse quadratic functions. We solve its various stability problems in the setting of non-zero real numbers and non-Archimedean fields via fixed point approach.