In this paper, we introduce a new generalization of a class of inverse Lindley distributions called the generalized inverse Lindley power series (GILPS) distribution. This class of distributions is obtained by compounding the generalized class of inverse Lindley distributions with the power series family of distributions. The GILPS contains several lifetime subclasses such as inverse Lindley power series, two parameters inverse Lindley power series, and inverse power Lindley power series distributions. It can generate many statistical distributions such as the inverse power Lindley Poisson distribution, the inverse power Lindley geometric distribution, the inverse power Lindley logarithmic distribution, and the inverse power Lindley binomial distribution. The proposed class has flexibility in the sense that it can generate new lifetime distributions as well as some existing distributions. For the proposed class, several properties are derived such as hazard rate function, limiting behavior, quantile function, moments, moments generating function, and distributions of order statistics. The method of maximum likelihood estimation can be used to estimate the model parameters of this new class. A simulation for a selective model will be discussed. At the end, we will demonstrate applications of three real data sets to show the flexibility and potential of the new class of distributions.
{"title":"Generalized inverse Lindley power series distributions: modeling and simulation","authors":"S. Alkarni","doi":"10.22436/JNSA.012.12.03","DOIUrl":"https://doi.org/10.22436/JNSA.012.12.03","url":null,"abstract":"In this paper, we introduce a new generalization of a class of inverse Lindley distributions called the generalized inverse Lindley power series (GILPS) distribution. This class of distributions is obtained by compounding the generalized class of inverse Lindley distributions with the power series family of distributions. The GILPS contains several lifetime subclasses such as inverse Lindley power series, two parameters inverse Lindley power series, and inverse power Lindley power series distributions. It can generate many statistical distributions such as the inverse power Lindley Poisson distribution, the inverse power Lindley geometric distribution, the inverse power Lindley logarithmic distribution, and the inverse power Lindley binomial distribution. The proposed class has flexibility in the sense that it can generate new lifetime distributions as well as some existing distributions. For the proposed class, several properties are derived such as hazard rate function, limiting behavior, quantile function, moments, moments generating function, and distributions of order statistics. The method of maximum likelihood estimation can be used to estimate the model parameters of this new class. A simulation for a selective model will be discussed. At the end, we will demonstrate applications of three real data sets to show the flexibility and potential of the new class of distributions.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"39 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91167319","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 investigate a class of nonlinear Langevin equation involving one fractional order α ∈ (0, 1] with three-point boundary conditions. By the Banach contraction principle and Krasnoselskii’s fixed point theorem, the existence and uniqueness results of solutions are obtained. Two examples are given to show the applicability of our main results.
{"title":"Langevin equation involving one fractional order with three-point boundary conditions","authors":"A. Salem, F. Alzahrani, Lamya Almaghamsi","doi":"10.22436/JNSA.012.12.02","DOIUrl":"https://doi.org/10.22436/JNSA.012.12.02","url":null,"abstract":"In this paper, we investigate a class of nonlinear Langevin equation involving one fractional order α ∈ (0, 1] with three-point boundary conditions. By the Banach contraction principle and Krasnoselskii’s fixed point theorem, the existence and uniqueness results of solutions are obtained. Two examples are given to show the applicability of our main results.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"41 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84282969","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":"Stability analysis of a tritrophic model with stage structure in the prey population","authors":"G. Blé, M. A. Dela-Rosa, I. Loreto-Hernández","doi":"10.22436/JNSA.012.12.01","DOIUrl":"https://doi.org/10.22436/JNSA.012.12.01","url":null,"abstract":"","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77065747","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, a nonconvex vector optimization problem with both inequality and equality constraints is considered. The functions constituting it are not necessarily differentiable, but they are E-differentiable. The so-called E-Fritz John necessary optimality conditions and the so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-differentiable multiobjective programming problems with both inequality and equality constraints. Further, the sufficient optimality conditions are derived for such nonconvex nonsmooth vector optimization problems under (generalized) E-convexity. The so-called vector E-Wolfe dual problem is defined for the considered E-differentiable multiobjective programming problem with both inequality and equality constraints and several dual theorems are established also under (generalized) E-convexity hypotheses.
{"title":"E-optimality conditions and Wolfe E-duality for E-differentiable vector optimization problems with inequality and equality constraints","authors":"T. Antczak, Najeeb Abdulaleem","doi":"10.22436/JNSA.012.11.06","DOIUrl":"https://doi.org/10.22436/JNSA.012.11.06","url":null,"abstract":"In this paper, a nonconvex vector optimization problem with both inequality and equality constraints is considered. The functions constituting it are not necessarily differentiable, but they are E-differentiable. The so-called E-Fritz John necessary optimality conditions and the so-called E-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered E-differentiable multiobjective programming problems with both inequality and equality constraints. Further, the sufficient optimality conditions are derived for such nonconvex nonsmooth vector optimization problems under (generalized) E-convexity. The so-called vector E-Wolfe dual problem is defined for the considered E-differentiable multiobjective programming problem with both inequality and equality constraints and several dual theorems are established also under (generalized) E-convexity hypotheses.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"315 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79701275","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 demonstrate that the results presented in the paper [B. Bin-Mohsin, M. A. Noor, K. I. Noor, S. Iftikhar, J. Nonlinear. Sci. Appl., 11 (2018),1070–1076] are not true in general. Moreover, we give some new notions, which could be applied in type problems as in [B. Bin-Mohsin, M. A. Noor, K. I. Noor, S. Iftikhar, J. Nonlinear. Sci. Appl., 11 (2018), 1070–1076].
{"title":"Quasi-arithmetic F-convex functions and their characterization","authors":"Mirosław Adamek","doi":"10.22436/JNSA.012.11.05","DOIUrl":"https://doi.org/10.22436/JNSA.012.11.05","url":null,"abstract":"In this paper we demonstrate that the results presented in the paper [B. Bin-Mohsin, M. A. Noor, K. I. Noor, S. Iftikhar, J. Nonlinear. Sci. Appl., 11 (2018),1070–1076] are not true in general. Moreover, we give some new notions, which could be applied in type problems as in [B. Bin-Mohsin, M. A. Noor, K. I. Noor, S. Iftikhar, J. Nonlinear. Sci. Appl., 11 (2018), 1070–1076].","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"20 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75419687","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":"Fixed point theorems for generalized JS-quasi-contractions in complete partial","authors":"Panisa Lohawech, A. Kaewcharoen","doi":"10.22436/JNSA.012.11.04","DOIUrl":"https://doi.org/10.22436/JNSA.012.11.04","url":null,"abstract":"","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89982940","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":"Three-Point boundary value problems associated with first order matrix difference system-existence and uniqueness via shortest and closest Lattice vector methods","authors":"Kasi Viswanadh V Kanuri, K. Murty","doi":"10.22436/JNSA.012.11.03","DOIUrl":"https://doi.org/10.22436/JNSA.012.11.03","url":null,"abstract":"","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"111 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85073437","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}
This gives new results on stable fixed points related to several kinds of strong perturbations in references. It is shown that a strong stable set of fixed points has a robust stable property. For a robust stable fixed point set of a correspondence, in its neighborhood, there is a strong stable set for any small perturbation of the correspondence. There exists a robust stable set for a correspondence, if there is at least one fixed point for the correspondence. These generalize the corresponding results in recent references and give an application in the existence of strong stable economy equilibria.
{"title":"On stable fixed points under several kinds of strong perturbations","authors":"Q. Song, P. Luo","doi":"10.22436/JNSA.012.11.01","DOIUrl":"https://doi.org/10.22436/JNSA.012.11.01","url":null,"abstract":"This gives new results on stable fixed points related to several kinds of strong perturbations in references. It is shown that a strong stable set of fixed points has a robust stable property. For a robust stable fixed point set of a correspondence, in its neighborhood, there is a strong stable set for any small perturbation of the correspondence. There exists a robust stable set for a correspondence, if there is at least one fixed point for the correspondence. These generalize the corresponding results in recent references and give an application in the existence of strong stable economy equilibria.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"170 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74870796","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}
This paper deals with the stability of the orbits for time-dependent nearly integrable Hamiltonian systems. Under the classical non-degeneracy in KAM theory we prove that the considered system possesses quasi-effective stability. Our result generalized the works in [F. Z. Cong, J. L. Hong, H. T. Li, Dyn. Syst. Ser. B, 21 (2016), 67–80] to time-dependent system and gave a connection between KAM theorem and effective stability.
{"title":"Quasi-effective stability for time-dependent nearly integrable Hamiltonian systems","authors":"Fuzhong Cong, T. Hao, Xue Feng","doi":"10.22436/JNSA.012.11.02","DOIUrl":"https://doi.org/10.22436/JNSA.012.11.02","url":null,"abstract":"This paper deals with the stability of the orbits for time-dependent nearly integrable Hamiltonian systems. Under the classical non-degeneracy in KAM theory we prove that the considered system possesses quasi-effective stability. Our result generalized the works in [F. Z. Cong, J. L. Hong, H. T. Li, Dyn. Syst. Ser. B, 21 (2016), 67–80] to time-dependent system and gave a connection between KAM theorem and effective stability.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"64 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79066408","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 define a new operator and give a sense of distribution theory to find the Fourier transform of new operator. It was found that the Fourier transform of new operator related to the Fourier transform of ultrahyperbolic operator and Diamond operator. And we also study the convolution products kδ ∗ l and ♦kδ ∗ ♦l.
{"title":"A Fourier transform and convolution of Diamond operator","authors":"W. Satsanit","doi":"10.22436/JNSA.012.10.04","DOIUrl":"https://doi.org/10.22436/JNSA.012.10.04","url":null,"abstract":"In this paper, we define a new operator and give a sense of distribution theory to find the Fourier transform of new operator. It was found that the Fourier transform of new operator related to the Fourier transform of ultrahyperbolic operator and Diamond operator. And we also study the convolution products kδ ∗ l and ♦kδ ∗ ♦l.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91370735","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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