{"title":"On Suzuki$-$Proinov $mathpzc{Z^*}_{aE^*}^{aR}(alpha)-$Contraction in Modular $b-$Metric Spaces","authors":"Abdurrahman Büyükkaya, M. Öztürk","doi":"10.33434/cams.1414411","DOIUrl":"https://doi.org/10.33434/cams.1414411","url":null,"abstract":"In this paper, by taking ${{mathcal C}_mathcal{A}}-$simulation function and Proinov type function into account, we set up a new contraction mapping, which is referred to as Suzuki$-$Proinov $mathpzc{Z^*}_{aE^*}^{aR}(alpha)-$contraction and including both rational expressions that have quadratic terms and $aE-$type contraction. Furthermore, we demonstrate a common fixed point theorem through the mappings endowed with triangular $alpha-$admissibility in the setting of modular $b-$metric space. Besides that, we achieve some new outcomes that contribute to the current ones in the literature through the main theorem, and, as an application, we examine the existence of solutions to a class of functional equations emerging in dynamic programming.","PeriodicalId":491673,"journal":{"name":"Communications in advanced mathematical sciences","volume":"23 24","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139964282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Cobalancing Numbers: Another Way of Demonstrating Their Properties","authors":"Arzu ÖZKOÇ ÖZTÜRK, Volkan Külahli","doi":"10.33434/cams.1394777","DOIUrl":"https://doi.org/10.33434/cams.1394777","url":null,"abstract":"In this study, previously obtained cobalancing numbers are considered from a different perspective, and the properties of the numbers are re-examined. The main purpose is to change the recurrence relation of cobalancing numbers and calculate some relations and properties in a more diverse and easier way. The reason that led us to this method is that the recurrence relation of cobalancing numbers has a second-order but non-homogeneous difference equations. Thus, it will be much easier to find the Binet formula, generating function, sum formulas, and many other relations with a sequence that is homogeneous and has a third-degree recurrence relation. Also some identities that have not been found before in the sequence are also included in this study.","PeriodicalId":491673,"journal":{"name":"Communications in advanced mathematical sciences","volume":" 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139628805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On some combinatorial properties of bihyperbolic numbers of the Lucas type.","authors":"F. Torunbalcı Aydın","doi":"10.33434/cams.1372245","DOIUrl":"https://doi.org/10.33434/cams.1372245","url":null,"abstract":"In the literature until today, many authors have studied special sequences in different number systems. In this article, we examined the combinatorial properties of Lucas-type bihyperbolic numbers. Lucas bihyperbolic numbers were studied by Azak cite{aza} in 2020. For this reason, only bihyperbolic Jacobsthal-Lucas and Pell-Lucas numbers were examined using Jacobsthal-Lucas and Pell-Lucas numbers. We also give some algebraic properties of bihyperbolic Jacobsthal-Lucas and bihyperbolic Pell-Lucas numbers, such as the recursion relation, generating function, Binet formula, D'Ocagne identity, Cassini identity, Catalan identity and Honsberger identity.","PeriodicalId":491673,"journal":{"name":"Communications in advanced mathematical sciences","volume":"40 23","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138946670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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