In our present investigation, we introduce two new subclasses SΣm(α, λ,μ) and SΣm(β, λ,μ) of analytic and m-fold symmetric bi-univalent functions in the open unit disk E. Results concerning coefficient estimates for the functions of these classes are derived. Many interesting new and already existing corollaries are also presented.
{"title":"On certain classes of bi-univalent functions related to m-fold symmetry","authors":"S. Hussain, Shahid Khan, M. A. Zaighum, M. Darus","doi":"10.22436/JNSA.011.04.06","DOIUrl":"https://doi.org/10.22436/JNSA.011.04.06","url":null,"abstract":"In our present investigation, we introduce two new subclasses SΣm(α, λ,μ) and SΣm(β, λ,μ) of analytic and m-fold symmetric bi-univalent functions in the open unit disk E. Results concerning coefficient estimates for the functions of these classes are derived. Many interesting new and already existing corollaries are also presented.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"49 1","pages":"490-499"},"PeriodicalIF":0.0,"publicationDate":"2018-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86919423","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":"Dynamics of the fuzzy difference equation z n = max { 1 z n − m , α n z n − r }","authors":"T. Sun, H. Xi, G. Su, Bin Qin","doi":"10.22436/JNSA.011.04.04","DOIUrl":"https://doi.org/10.22436/JNSA.011.04.04","url":null,"abstract":"","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"29 1","pages":"477-485"},"PeriodicalIF":0.0,"publicationDate":"2018-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76070279","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":"Properties of hyperholomorphic functions and integrals for commutative-quaternionic valued functions","authors":"Ji Eun Kim","doi":"10.22436/jnsa.011.04.03","DOIUrl":"https://doi.org/10.22436/jnsa.011.04.03","url":null,"abstract":"","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"54 1","pages":"469-476"},"PeriodicalIF":0.0,"publicationDate":"2018-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81382337","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 investigate some new reverse Hölder-type inequalities on an arbitrary time scale via the diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals. These inequalities extend some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues.
{"title":"Some reverse Hölder inequalities with Specht's ratio on time scales","authors":"A. El-Deeb, H. A. Elsennary, W. Cheung","doi":"10.22436/JNSA.011.04.01","DOIUrl":"https://doi.org/10.22436/JNSA.011.04.01","url":null,"abstract":"In this article, we investigate some new reverse Hölder-type inequalities on an arbitrary time scale via the diamond-α dynamic integral, which is defined as a linear combination of the delta and nabla integrals. These inequalities extend some known dynamic inequalities on time scales, unify and extend some continuous inequalities and their corresponding discrete analogues.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"63 1","pages":"444-455"},"PeriodicalIF":0.0,"publicationDate":"2018-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91038590","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}
We study the global stability analysis of pathogen infection models with immune impairment. Both pathogen-to-susceptible and infected-to-susceptible transmissions have been considered. We drive the basic reproduction parameter R0, which determines the global dynamics of models. Using the method of Lyapunov function, we established the global stability of the steady states of the models. Numerical simulations are used to confirm the theoretical results.
{"title":"Stability of pathogen dynamics models with viral and cellular infections and immune impairment","authors":"A. Elaiw, A. A. Raezah, B. S. Alofi","doi":"10.22436/JNSA.011.04.02","DOIUrl":"https://doi.org/10.22436/JNSA.011.04.02","url":null,"abstract":"We study the global stability analysis of pathogen infection models with immune impairment. Both pathogen-to-susceptible and infected-to-susceptible transmissions have been considered. We drive the basic reproduction parameter R0, which determines the global dynamics of models. Using the method of Lyapunov function, we established the global stability of the steady states of the models. Numerical simulations are used to confirm the theoretical results.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"5 1","pages":"456-468"},"PeriodicalIF":0.0,"publicationDate":"2018-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76721174","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}
Minimal surfaces are well known as a class of surfaces with vanishing mean curvature which minimize area within a given boundary configuration since 19th century. This fact was implicitly proved by Lagrange for nonparametric surfaces in 1760, and then by Meusnier in 1776 who used the analytic expression for the mean curvature. Mathematically, a minimal surface corresponds to the solution of a nonlinear partial differential equation. By solving some differential equations, in this paper we give a complete and explicit classification of minimal translation surfaces in an n-dimensional Minkowski space.
{"title":"A classification of minimal translation surfaces in Minkowski space","authors":"Dan Yang, Wei Dan, Yu Fu","doi":"10.22436/jnsa.011.03.12","DOIUrl":"https://doi.org/10.22436/jnsa.011.03.12","url":null,"abstract":"Minimal surfaces are well known as a class of surfaces with vanishing mean curvature which minimize area within a given boundary configuration since 19th century. This fact was implicitly proved by Lagrange for nonparametric surfaces in 1760, and then by Meusnier in 1776 who used the analytic expression for the mean curvature. Mathematically, a minimal surface corresponds to the solution of a nonlinear partial differential equation. By solving some differential equations, in this paper we give a complete and explicit classification of minimal translation surfaces in an n-dimensional Minkowski space.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"24 1","pages":"437-443"},"PeriodicalIF":0.0,"publicationDate":"2018-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87115837","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":"Erratum to \"On some fixed points of α−ψ contractive mappings with rational expressions, J. Nonlinear Sci. Appl., 10 (2017), 1569 - 1581\"","authors":"E. Karapınar","doi":"10.22436/JNSA.011.03.10","DOIUrl":"https://doi.org/10.22436/JNSA.011.03.10","url":null,"abstract":"","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"53 1","pages":"425-427"},"PeriodicalIF":0.0,"publicationDate":"2018-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89453310","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, we study some results about the expression of solutions to some linear differential equations for the CaputoFabrizio fractional derivative. Furthermore, by the Banach contraction principle, the unique existence of the solution to an initial value problem for nonlinear differential equation involving the Caputo-Fabrizio fractional derivative is obtained.
{"title":"The uniqueness of solution for initial value problems for fractional differential equation involving the Caputo-Fabrizio derivative","authors":"Shuqin Zhang, Lei Hu, Sujing Sun","doi":"10.22436/JNSA.011.03.11","DOIUrl":"https://doi.org/10.22436/JNSA.011.03.11","url":null,"abstract":"In this paper, we study some results about the expression of solutions to some linear differential equations for the CaputoFabrizio fractional derivative. Furthermore, by the Banach contraction principle, the unique existence of the solution to an initial value problem for nonlinear differential equation involving the Caputo-Fabrizio fractional derivative is obtained.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"5 1","pages":"428-436"},"PeriodicalIF":0.0,"publicationDate":"2018-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88752019","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}
We prove the existence and uniqueness of fixed point belonging to the zero-set of a given function. The results are established in the setting of metric spaces and partial metric spaces. Our approach combines the recent notions of (F,φ)contraction and Z-contraction. The main result allows to deduce, as a particular case, some of the most known results in the literature. An example supports the theory.
{"title":"Fixed point belonging to the zero-set of a given function","authors":"F. Vetro","doi":"10.22436/jnsa.011.03.09","DOIUrl":"https://doi.org/10.22436/jnsa.011.03.09","url":null,"abstract":"We prove the existence and uniqueness of fixed point belonging to the zero-set of a given function. The results are established in the setting of metric spaces and partial metric spaces. Our approach combines the recent notions of (F,φ)contraction and Z-contraction. The main result allows to deduce, as a particular case, some of the most known results in the literature. An example supports the theory.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"188 1","pages":"417-424"},"PeriodicalIF":0.0,"publicationDate":"2018-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91506986","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, we apply Theorem 3.2 of [G. M. Lee, L.-J. Lin, J. Nonlinear Convex Anal., 18 (2017), 1781–1800] to study the variational inequality over split equality fixed point problems for three finite families of strongly quasi-nonexpansive mappings. Then we use this result to study variational inequalities over split equality for three various finite families of nonlinear mappings. We give a unified method to study split equality for three various finite families of nonlinear problems. Our results contain many results on split equality fixed point problems and multiple sets split feasibility problems as special cases. Our results can treat large scale of nonlinear problems by group these problems into finite families of nonlinear problems, then we use simultaneous iteration to find the solutions of these problems. Our results will give a simple and quick method to study large scale of nonlinear problems and will have many applications to study large scale of nonlinear problems.
在本文中，我们应用了定理3.2 [G]。M. Lee, l - j。林杰。非线性凸肛门。[j]， 18(2017)， 1781-1800]研究了三种强拟非扩张映射有限族的分裂不等式不动点问题。然后利用这一结果研究了三种不同的非线性映射有限族的分裂不等式上的变分不等式。给出了研究三种不同有限族非线性问题分裂等式的统一方法。我们的结果包含了许多关于分裂等式不动点问题和作为特例的多集分裂可行性问题的结果。我们的研究结果可以把大规模的非线性问题归为有限族的非线性问题，然后用同时迭代的方法求出这些问题的解。我们的研究结果将为研究大规模非线性问题提供一种简单快捷的方法，并将在研究大规模非线性问题中具有广泛的应用价值。
{"title":"Simultaneous iteration for variational inequalities over common solutions for finite families of nonlinear problems","authors":"Lai-Jiu Lin","doi":"10.22436/JNSA.011.03.08","DOIUrl":"https://doi.org/10.22436/JNSA.011.03.08","url":null,"abstract":"In this paper, we apply Theorem 3.2 of [G. M. Lee, L.-J. Lin, J. Nonlinear Convex Anal., 18 (2017), 1781–1800] to study the variational inequality over split equality fixed point problems for three finite families of strongly quasi-nonexpansive mappings. Then we use this result to study variational inequalities over split equality for three various finite families of nonlinear mappings. We give a unified method to study split equality for three various finite families of nonlinear problems. Our results contain many results on split equality fixed point problems and multiple sets split feasibility problems as special cases. Our results can treat large scale of nonlinear problems by group these problems into finite families of nonlinear problems, then we use simultaneous iteration to find the solutions of these problems. Our results will give a simple and quick method to study large scale of nonlinear problems and will have many applications to study large scale of nonlinear problems.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"48 1","pages":"394-416"},"PeriodicalIF":0.0,"publicationDate":"2018-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89552673","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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