In this paper, we provide inverses for some generalized hyperbolic functions. We also study some properties of these inverse functions. Furthermore, by using basic techniques, we establish some inequalities (or bounds) for the inverse functions. As a by-product of the established results, we obtain some inequalities (or bounds) for the logarithmic function.
{"title":"On Some Properties of Generalized Inverse Hyperbolic Functions","authors":"K. Nantomah, O. Kasimu","doi":"10.28924/apjm/7-15","DOIUrl":"https://doi.org/10.28924/apjm/7-15","url":null,"abstract":"In this paper, we provide inverses for some generalized hyperbolic functions. We also study some properties of these inverse functions. Furthermore, by using basic techniques, we establish some inequalities (or bounds) for the inverse functions. As a by-product of the established results, we obtain some inequalities (or bounds) for the logarithmic function.","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41964102","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}
Pub Date : 2020-06-05DOI: 10.22541/au.159138366.66795364
F. Martínez, I. Martínez, Mohammed K. A. Kaabar, S. Paredes
In this paper, some important results of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using conformable fractional derivatives. The ratio test has been specifically established to calculate the radius of convergence of a fractional power series, and several theorems of differentiability and integrability of the sum of a power series have been discussed in the sense of conformable fractional definition. In addition, the proposed series solution has been applied for the case of conformable fractional Airy differential equation.
{"title":"Some new results on Conformable Fractional Power Series","authors":"F. Martínez, I. Martínez, Mohammed K. A. Kaabar, S. Paredes","doi":"10.22541/au.159138366.66795364","DOIUrl":"https://doi.org/10.22541/au.159138366.66795364","url":null,"abstract":"In this paper, some important results of the classical power series are generalized for the fractional power series. Some of these theorems are constructed by using conformable fractional derivatives. The ratio test has been specifically established to calculate the radius of convergence of a fractional power series, and several theorems of differentiability and integrability of the sum of a power series have been discussed in the sense of conformable fractional definition. In addition, the proposed series solution has been applied for the case of conformable fractional Airy differential equation.","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43205441","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":"Secret Coding Method on Star Graphs with Graph Labeling","authors":"","doi":"10.28924/apjm/7-12","DOIUrl":"https://doi.org/10.28924/apjm/7-12","url":null,"abstract":"","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69256182","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 the Fourier-Stieltjes Transform of Compact Operator Valued Measures Associated to Discrete Series Representations","authors":"","doi":"10.28924/apjm/7-11","DOIUrl":"https://doi.org/10.28924/apjm/7-11","url":null,"abstract":"","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69256533","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":"A Study of r-Ideals, K-Ideals and m−k Ideals of Ordered Semirings","authors":"","doi":"10.28924/apjm/7-2","DOIUrl":"https://doi.org/10.28924/apjm/7-2","url":null,"abstract":"","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69256823","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":"Incompleteness in the Bell Theorem Involving All Settings of Measuring Apparatus","authors":"","doi":"10.28924/apjm/7-8","DOIUrl":"https://doi.org/10.28924/apjm/7-8","url":null,"abstract":"","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69259816","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":"A Numerical Approximation to the Unique Solution of KdVB Equation under the Prabhakar Function","authors":"","doi":"10.28924/apjm/7-9","DOIUrl":"https://doi.org/10.28924/apjm/7-9","url":null,"abstract":"","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69259973","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":"Dynamic Differential Oligopoly Game with Hyperbolic Demand, Cubic Cost and Capital Accumulation","authors":"","doi":"10.28924/apjm/7-10","DOIUrl":"https://doi.org/10.28924/apjm/7-10","url":null,"abstract":"","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69256470","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 Classification of Permutations","authors":"","doi":"10.28924/apjm/7-16","DOIUrl":"https://doi.org/10.28924/apjm/7-16","url":null,"abstract":"","PeriodicalId":33214,"journal":{"name":"Asia Pacific Journal of Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69256568","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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