Abstract Inequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.
{"title":"Generalized Briot-Bouquet differential equation based on new differential operator with complex connections","authors":"R. Ibrahim, Rafida M. Elobaid, S. J. Obaiys","doi":"10.2478/gm-2020-0008","DOIUrl":"https://doi.org/10.2478/gm-2020-0008","url":null,"abstract":"Abstract Inequality study is a magnificent field for investigating the geometric behaviors of analytic functions in the open unit disk calling the subordination and superordination. In this work, we aim to formulate a generalized differential-difference operator. We introduce a new class of analytic functions having the generalized operator. Some subordination results are included in the sequel.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"77 1","pages":"105 - 114"},"PeriodicalIF":0.0,"publicationDate":"2020-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80036473","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":"Modified variational iteration and homotopy analysis method for solving variable coefficient variant boussinesq system","authors":"Fadhil H. Easif, Saad A. Manaa, Ahmed J. Sabali","doi":"10.31559/glm.8.1.4","DOIUrl":"https://doi.org/10.31559/glm.8.1.4","url":null,"abstract":"","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43924326","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}
In this paper, Modified Variational Iteration Method (MVIM) and Homotopy Analysis Method (HAM) are used to find approximate solutions for the Variable-Coefficient Variant Boussinesq System the (VCVB) system is able to describe the nonlinear and dispersive long gravity waves in shallow water traveling in two horizontal directions with varying depth, as an example we took the Boussinesq-Burgers (B-B) system, (B-B) system arise in the study of fluid flow and describing the long-wave propagation of shallow water waves. The solutions of these equations helpful for the coastal and civil engineering’s
{"title":"Modified variational iteration and homotopy analysis method for solving variable coefficient variant boussinesq system","authors":"Fadhil H. Easif, Saad A. Manaa, Ahmed J. Sabali","doi":"10.31559/glm2020.8.1.4","DOIUrl":"https://doi.org/10.31559/glm2020.8.1.4","url":null,"abstract":"In this paper, Modified Variational Iteration Method (MVIM) and Homotopy Analysis Method (HAM) are used to find approximate solutions for the Variable-Coefficient Variant Boussinesq System the (VCVB) system is able to describe the nonlinear and dispersive long gravity waves in shallow water traveling in two horizontal directions with varying depth, as an example we took the Boussinesq-Burgers (B-B) system, (B-B) system arise in the study of fluid flow and describing the long-wave propagation of shallow water waves. The solutions of these equations helpful for the coastal and civil engineering’s","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49314260","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":"Quaternion-valued functions in hyperholomorphic Fα G(p,q,s) spaces","authors":"A. Kamal, T. Yassen","doi":"10.31559/glm2020.8.1.3","DOIUrl":"https://doi.org/10.31559/glm2020.8.1.3","url":null,"abstract":"","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41326745","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}
In this article, we construct networks of Collatz sequences such that the initial odd terms of these sequences increase monotonically. We also show how the subsequence of odd numbers in a Collatz sequence can be extended backwards, forever. Convergent sequences cannot contain divergent subsequences. Thus, we conclude that the Collatz Conjecture is false.
{"title":"Two different scenarios when the Collatz Conjecture fails","authors":"M. Ahmed","doi":"10.31559/glm2021.11.2.4","DOIUrl":"https://doi.org/10.31559/glm2021.11.2.4","url":null,"abstract":"In this article, we construct networks of Collatz sequences such that the initial odd terms of these sequences increase monotonically. We also show how the subsequence of odd numbers in a Collatz sequence can be extended backwards, forever. Convergent sequences cannot contain divergent subsequences. Thus, we conclude that the Collatz Conjecture is false.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42339932","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}
Abstract In the present paper we establish some theorems on the existence of common approximate fixed points for a pair of generalized contractive type mappings with the property that the diameter of the set of common ∈−fixed points is tending to zero as ∈ tends to zero.
{"title":"On Some Common Approximate Fixed Point Theorems","authors":"K. Roy, M. Saha","doi":"10.2478/gm-2019-0012","DOIUrl":"https://doi.org/10.2478/gm-2019-0012","url":null,"abstract":"Abstract In the present paper we establish some theorems on the existence of common approximate fixed points for a pair of generalized contractive type mappings with the property that the diameter of the set of common ∈−fixed points is tending to zero as ∈ tends to zero.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"29 1","pages":"23 - 34"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74615869","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}
Abstract A new subfamily of p–valent analytic functions with negative coefficients in terms of q–analogue of generalized Ruschweyh operator is considered. Several properties concerning coefficient bounds, weighted and arithmetic mean, radii of starlikeness, convexity and close-to-convexity are obtained. A family of class preserving integral operators and integral representation are also indicated.
{"title":"q–analogue of generalized Ruschweyh operator related to a new subfamily of multivalent functions","authors":"S. Najafzadeh, M. Acu","doi":"10.2478/gm-2019-0015","DOIUrl":"https://doi.org/10.2478/gm-2019-0015","url":null,"abstract":"Abstract A new subfamily of p–valent analytic functions with negative coefficients in terms of q–analogue of generalized Ruschweyh operator is considered. Several properties concerning coefficient bounds, weighted and arithmetic mean, radii of starlikeness, convexity and close-to-convexity are obtained. A family of class preserving integral operators and integral representation are also indicated.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"42 1","pages":"59 - 69"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85121890","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}
Abstract In this paper we obtain estimations of the errors in approximation by positive linear operators which fix certain functions. We use both the first and the second order classical moduli of smoothness and a generalized modulus of continuity of order two. Some applications involving Bernstein type operators, Kantorovich type operators and genuine Bernstein-Durrmeyer type operators are presented.
{"title":"Quantitative results for positive linear operators which preserve certain functions","authors":"M. Birou","doi":"10.2478/gm-2019-0017","DOIUrl":"https://doi.org/10.2478/gm-2019-0017","url":null,"abstract":"Abstract In this paper we obtain estimations of the errors in approximation by positive linear operators which fix certain functions. We use both the first and the second order classical moduli of smoothness and a generalized modulus of continuity of order two. Some applications involving Bernstein type operators, Kantorovich type operators and genuine Bernstein-Durrmeyer type operators are presented.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"24 1","pages":"85 - 95"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81710484","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}
Abstract In the present investigation, by making use of strong differential subordinations and superordinations, we introduce and study two new classes of holomorphic functions containing generalized differential operator. Also we determine important properties for functions belongs to these classes.
{"title":"Two New Classes of Analytic Functions Defined by Strong Differential Subordinations and Superordinations","authors":"A. Wanas","doi":"10.2478/gm-2019-0010","DOIUrl":"https://doi.org/10.2478/gm-2019-0010","url":null,"abstract":"Abstract In the present investigation, by making use of strong differential subordinations and superordinations, we introduce and study two new classes of holomorphic functions containing generalized differential operator. Also we determine important properties for functions belongs to these classes.","PeriodicalId":32454,"journal":{"name":"General Letters in Mathematics","volume":"1999 1","pages":"11 - 3"},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82794213","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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