In this paper, we deal with a stochastic differential equation with fast oscillating coefficients and with respect to a Brownian motion and a Poisson random measure. The large deviation principle of solution is established, and the effect of the highly nonlinear and locally periodic coefficients is stated. Moreover, we derive an explicit expression for the action functional when the viscosity parameter ε is of order 1 while the homogenization parameter δε tends to zero.
{"title":"On a Wiener-Poisson equation with rapidly fluctuating coefficients: application to large deviations","authors":"A. Coulibaly, M. Allaya","doi":"10.22436/JNSA.014.06.06","DOIUrl":"https://doi.org/10.22436/JNSA.014.06.06","url":null,"abstract":"In this paper, we deal with a stochastic differential equation with fast oscillating coefficients and with respect to a Brownian motion and a Poisson random measure. The large deviation principle of solution is established, and the effect of the highly nonlinear and locally periodic coefficients is stated. Moreover, we derive an explicit expression for the action functional when the viscosity parameter ε is of order 1 while the homogenization parameter δε tends to zero.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"22 1","pages":"440-451"},"PeriodicalIF":0.0,"publicationDate":"2021-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73779544","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 introduce a hybrid iteration involving inertial-term for split equilibrium problem and fixed point for a finite family of asymptotically strictly pseudocontractive mappings. We prove that the sequence converges strongly to a solution of split equilibrium problem and a common fixed point of a finite family of asymptotically strictly pseudocontractive mappings. The results proved extend and improve recent results of Chang et al. [S. S. Chang, H. W. J. Lee, C. K. Chan, L. Wang, L. J. Qin, Appl. Math. Comput., 219 (2013), 10416–10424], Dewangan et al. [R. Dewangan, B. S. Thakur, M. Postolache, J. Inequal. Appl., 2014 (2014), 11 pages], and many others.
在本文中，我们引入了一种包含分裂平衡问题的惯性项和有限族的不动点的混合迭代。证明了该序列强收敛于分裂平衡问题的解和有限族的渐近严格伪压缩映射的一个公共不动点。结果证明，扩展和改进了Chang等人最近的研究结果。张淑娟，李宏杰，陈家强，王丽娟，秦丽娟，李志强。数学。第一版。王晓明，王晓明，王晓明，等。生物信息学研究进展[j] .生物信息学学报，2013,29(2):416 - 424。德旺根，B. S. Thakur, M. Postolache, J.不等式。达成。(2014(2014)， 11页)等。
{"title":"Iterative solution of split equilibrium and fixed point problems in real Hilbert spaces","authors":"J. N. Ezeora, P. Jackreece","doi":"10.22436/JNSA.014.05.06","DOIUrl":"https://doi.org/10.22436/JNSA.014.05.06","url":null,"abstract":"In this article, we introduce a hybrid iteration involving inertial-term for split equilibrium problem and fixed point for a finite family of asymptotically strictly pseudocontractive mappings. We prove that the sequence converges strongly to a solution of split equilibrium problem and a common fixed point of a finite family of asymptotically strictly pseudocontractive mappings. The results proved extend and improve recent results of Chang et al. [S. S. Chang, H. W. J. Lee, C. K. Chan, L. Wang, L. J. Qin, Appl. Math. Comput., 219 (2013), 10416–10424], Dewangan et al. [R. Dewangan, B. S. Thakur, M. Postolache, J. Inequal. Appl., 2014 (2014), 11 pages], and many others.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"41 1","pages":"359-371"},"PeriodicalIF":0.0,"publicationDate":"2021-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87284074","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 consider the following quasilinear Choquard equation with critical nonlinearity { −4u+ V(x)u− u4u2 = (Iα ∗ |u|p)|u|p−2u+ u2(2 )−2u, x ∈ RN, u > 0, x ∈ RN, where Iα is a Riesz potential, 0 < α < N, and N+α N < p < N+α N−2 , with 2 ∗ = 2N N−2 . Under suitable assumption on V , we research the existence of positive ground state solutions of above equations. Moreover, we consider the ground state solution of the equation (1.4). Our work supplements many existing partial results in the literature.
本文考虑了具有临界非线性{−4u+ V(x)u−u4u2 = (Iα∗|u|p)|u|p−2u+ u2(2)−2u, x∈RN, u > 0, x∈RN的拟线性Choquard方程，其中Iα是Riesz势，0 < α < N，且N+α N < p < N+α N−2，且2∗= 2N N−2。在适当的V假设下，研究了上述方程正基态解的存在性。此外，我们考虑方程(1.4)的基态解。我们的工作补充了文献中许多现有的部分结果。
{"title":"Ground state solutions for a class of quasilinear Choquard equation with critical growth","authors":"Liuyang Shao, Haibo Chen, Yingmin Wang","doi":"10.22436/JNSA.014.06.02","DOIUrl":"https://doi.org/10.22436/JNSA.014.06.02","url":null,"abstract":"In this paper, we consider the following quasilinear Choquard equation with critical nonlinearity { −4u+ V(x)u− u4u2 = (Iα ∗ |u|p)|u|p−2u+ u2(2 )−2u, x ∈ RN, u > 0, x ∈ RN, where Iα is a Riesz potential, 0 < α < N, and N+α N < p < N+α N−2 , with 2 ∗ = 2N N−2 . Under suitable assumption on V , we research the existence of positive ground state solutions of above equations. Moreover, we consider the ground state solution of the equation (1.4). Our work supplements many existing partial results in the literature.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"14 1","pages":"390-399"},"PeriodicalIF":0.0,"publicationDate":"2021-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87292886","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 study, we tried to construct I-statistically pre-Cauchy on triple sequences via Orlicz functions φ̃. We prove that for triple sequences, I-statistical φ̃-convergence implies I-statistical pre-Cauchy condition and examine some main properties of these concepts.
在本研究中，我们尝试利用Orlicz函数φ o构造三组序列上的i -统计前柯西。我们证明了对于三组序列，i -统计φ n -收敛意味着i -统计预柯西条件，并检验了这些概念的一些主要性质。
{"title":"Generalized statistically pre-Cauchy triple sequences via Orlicz functions","authors":"M. Huban","doi":"10.22436/JNSA.014.06.04","DOIUrl":"https://doi.org/10.22436/JNSA.014.06.04","url":null,"abstract":"In this study, we tried to construct I-statistically pre-Cauchy on triple sequences via Orlicz functions φ̃. We prove that for triple sequences, I-statistical φ̃-convergence implies I-statistical pre-Cauchy condition and examine some main properties of these concepts.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"27 1","pages":"414-422"},"PeriodicalIF":0.0,"publicationDate":"2021-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73580190","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}
P. Y. Dousseh, C. Ainamon, C. Miwadinou, A. V. Monwanou, J. Chabi-Orou
Synchronization of chaotic dynamical systems with fractional order is receiving great attention in recent literature because of its applications in a variety of fields including optics, secure communications of analog and digital signals, and cryptographic systems. In this paper, chaos control of a new financial system, and chaos synchronization between two identical financial systems, and non-identical financial systems with integer and fractional order are investigated. Chaos control is based on a linear feedback controller for stabilizing chaos to unstable equilibrium. In addition, chaos synchronization, not only between two identical new chaotic financial systems, but also between the new financial system and an another financial system given in the literature is realized by using active control technique. The synchronization is done for integer and fractional order in each case. It is shown that chaotic behavior can be controlled easily to any unstable equilibrium point of the new financial system. Also, it is observed that synchronization is enhanced when the fractional order increases and approximates to one. Numerical simulations are used to verify the proposed methods.
{"title":"Chaos control and synchronization of a new chaotic financial system with integer and fractional order","authors":"P. Y. Dousseh, C. Ainamon, C. Miwadinou, A. V. Monwanou, J. Chabi-Orou","doi":"10.22436/JNSA.014.06.01","DOIUrl":"https://doi.org/10.22436/JNSA.014.06.01","url":null,"abstract":"Synchronization of chaotic dynamical systems with fractional order is receiving great attention in recent literature because of its applications in a variety of fields including optics, secure communications of analog and digital signals, and cryptographic systems. In this paper, chaos control of a new financial system, and chaos synchronization between two identical financial systems, and non-identical financial systems with integer and fractional order are investigated. Chaos control is based on a linear feedback controller for stabilizing chaos to unstable equilibrium. In addition, chaos synchronization, not only between two identical new chaotic financial systems, but also between the new financial system and an another financial system given in the literature is realized by using active control technique. The synchronization is done for integer and fractional order in each case. It is shown that chaotic behavior can be controlled easily to any unstable equilibrium point of the new financial system. Also, it is observed that synchronization is enhanced when the fractional order increases and approximates to one. Numerical simulations are used to verify the proposed methods.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"37 1","pages":"372-389"},"PeriodicalIF":0.0,"publicationDate":"2021-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78991922","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}
The main scenario of the present paper is to introduce certain approach of variables by setting the structural behavior of fractional inequalities. Some new structural properties will be established concerning them.
{"title":"New approach for structural behavior of variables","authors":"A. Ganie","doi":"10.22436/JNSA.014.05.05","DOIUrl":"https://doi.org/10.22436/JNSA.014.05.05","url":null,"abstract":"The main scenario of the present paper is to introduce certain approach of variables by setting the structural behavior of fractional inequalities. Some new structural properties will be established concerning them.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"1 1","pages":"351-358"},"PeriodicalIF":0.0,"publicationDate":"2021-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89335203","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}
K. Ramkumar, K. Ravikumar, D. Chalishajar, A. Anguraj
This paper is concerned with a class of impulsive stochastic partial integrodifferential equations (ISPIEs) with delays and Poisson jumps. First, using the resolvent operator technique and contraction mapping principle, we can directly prove the existence and uniqueness of the mild solution for the system mentioned above. Then we develop a new impulsive integral inequality to obtain the global, both pth moment exponential stability and almost surely exponential stability of the mild solution is established with sufficient conditions. Also, a numerical example is provided to validate the theoretical result.
{"title":"Asymptotic behavior of attracting and quasi-invariant sets of impulsive stochastic partial integrodifferential equations with delays and Poisson jumps","authors":"K. Ramkumar, K. Ravikumar, D. Chalishajar, A. Anguraj","doi":"10.22436/JNSA.014.05.04","DOIUrl":"https://doi.org/10.22436/JNSA.014.05.04","url":null,"abstract":"This paper is concerned with a class of impulsive stochastic partial integrodifferential equations (ISPIEs) with delays and Poisson jumps. First, using the resolvent operator technique and contraction mapping principle, we can directly prove the existence and uniqueness of the mild solution for the system mentioned above. Then we develop a new impulsive integral inequality to obtain the global, both pth moment exponential stability and almost surely exponential stability of the mild solution is established with sufficient conditions. Also, a numerical example is provided to validate the theoretical result.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"32 1","pages":"339-350"},"PeriodicalIF":0.0,"publicationDate":"2021-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85938641","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 the present article, we establish a link between the theory of positive linear operators and the orthogonal polynomials by defining Bernstein-Chlodowsky-Kantorovich operators based on Gould-Hopper polynomials (orthogonal polynomials) and investigate the degree of convergence of these operators for unbounded continuous functions having a polynomial growth. In this connection, the moments of the operators are derived first, and then the approximation degree of the considered operators is established by means of the complete and the partial moduli of continuity. Next, we focus on the rate of convergence of these operators for functions in a weighted space. The associated Generalized Boolean Sum (GBS) operator of the operators under study is defined, and the degree of approximation is studied with the aid of the mixed modulus of smoothness and the Lipschitz class of Bögel continuous functions.
{"title":"Generalized Bernstein-Chlodowsky-Kantorovich type operators involving Gould-Hopper polynomials","authors":"P. Agrawal, Sompal Singh","doi":"10.22436/JNSA.014.05.03","DOIUrl":"https://doi.org/10.22436/JNSA.014.05.03","url":null,"abstract":"In the present article, we establish a link between the theory of positive linear operators and the orthogonal polynomials by defining Bernstein-Chlodowsky-Kantorovich operators based on Gould-Hopper polynomials (orthogonal polynomials) and investigate the degree of convergence of these operators for unbounded continuous functions having a polynomial growth. In this connection, the moments of the operators are derived first, and then the approximation degree of the considered operators is established by means of the complete and the partial moduli of continuity. Next, we focus on the rate of convergence of these operators for functions in a weighted space. The associated Generalized Boolean Sum (GBS) operator of the operators under study is defined, and the degree of approximation is studied with the aid of the mixed modulus of smoothness and the Lipschitz class of Bögel continuous functions.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"2 1","pages":"324-338"},"PeriodicalIF":0.0,"publicationDate":"2021-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88298597","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 work, we obtain the approximation properties of a new generalization of Szász-Mirakjan operators based on postquantum calculus. Firstly, for these operators, a recurrence formulation for the moments is obtained, and up to the fourth degree, the central moments are examined. Then, a local approximation result is attained. Furthermore, the degree of approximation in respect of the modulus of continuity on a finite closed set and the class of Lipschitz are computed. Next, the weighted uniform approximation on an unbounded interval is showed, and by the modulus of continuity, the order of convergence is estimated. Lastly, we proved the Voronovskaya type theorem and gave some illustrations to compare the related operators’ convergence to a certain function.
{"title":"Approximation by a new generalization of Szász-Mirakjan operators via (p,q )-calculus","authors":"R. Aslan, Aydin Izgi","doi":"10.22436/JNSA.014.05.02","DOIUrl":"https://doi.org/10.22436/JNSA.014.05.02","url":null,"abstract":"In this work, we obtain the approximation properties of a new generalization of Szász-Mirakjan operators based on postquantum calculus. Firstly, for these operators, a recurrence formulation for the moments is obtained, and up to the fourth degree, the central moments are examined. Then, a local approximation result is attained. Furthermore, the degree of approximation in respect of the modulus of continuity on a finite closed set and the class of Lipschitz are computed. Next, the weighted uniform approximation on an unbounded interval is showed, and by the modulus of continuity, the order of convergence is estimated. Lastly, we proved the Voronovskaya type theorem and gave some illustrations to compare the related operators’ convergence to a certain function.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"61 1","pages":"310-323"},"PeriodicalIF":0.0,"publicationDate":"2021-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85110008","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}
A new generalized family of models called the Exponentiated Half Logistic Odd Lindley-G (EHLOL-G) distribution is developed and presented. Some explicit expressions for the structural properties including moments, conditional moments, mean and median deviations, distribution of the order statistics, probability weighted moments and Rényi entropy are derived. We applied the maximum likelihood estimation technique to estimate the parameters of the model and a simulation study is conducted to examine the efficiency of the maximum likelihood estimators. The special case of the EHLOL-Weibull (EHLOL-W) distribution is fitted to two real data sets.
{"title":"The exponentiated half-logistic odd lindley-G family of distributions with applications","authors":"Whatmore Sengweni, B. Oluyede, B. Makubate","doi":"10.22436/JNSA.014.05.01","DOIUrl":"https://doi.org/10.22436/JNSA.014.05.01","url":null,"abstract":"A new generalized family of models called the Exponentiated Half Logistic Odd Lindley-G (EHLOL-G) distribution is developed and presented. Some explicit expressions for the structural properties including moments, conditional moments, mean and median deviations, distribution of the order statistics, probability weighted moments and Rényi entropy are derived. We applied the maximum likelihood estimation technique to estimate the parameters of the model and a simulation study is conducted to examine the efficiency of the maximum likelihood estimators. The special case of the EHLOL-Weibull (EHLOL-W) distribution is fitted to two real data sets.","PeriodicalId":22770,"journal":{"name":"The Journal of Nonlinear Sciences and Applications","volume":"59 1","pages":"287-309"},"PeriodicalIF":0.0,"publicationDate":"2021-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85251066","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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