This paper is concerned with the higher order nonlinear neutral differential equation [a(t)(x(t) + b(t)x(τ(t))) ′](n−1) + f(t, x(g1(t)), . . . , x(gk(t))) = c(t), t > t0. By dint of the Leray-Schauder nonlinear alternative, Rothe fixed point theorem and some new techniques, we prove the existence of uncountably many bounded positive solutions for the equation. Several nontrivial examples are given to illustrate the applications and advantages of the results presented in this paper.
{"title":"A higher order nonlinear neutral differential equation","authors":"G. Jiang, Weiling Sun, Z. An, Liangshi Zhao","doi":"10.22436/JNSA.012.10.06","DOIUrl":"https://doi.org/10.22436/JNSA.012.10.06","url":null,"abstract":"This paper is concerned with the higher order nonlinear neutral differential equation [a(t)(x(t) + b(t)x(τ(t))) ′](n−1) + f(t, x(g1(t)), . . . , x(gk(t))) = c(t), t > t0. By dint of the Leray-Schauder nonlinear alternative, Rothe fixed point theorem and some new techniques, we prove the existence of uncountably many bounded positive solutions for the equation. Several nontrivial examples are given to illustrate the applications and advantages of the results presented in this paper.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75099597","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 aim of this paper is to define Θβ = { v ∈ J u : Θ($(u, v)) ≤ [Θ($(u,J u))]β } and establish some new fixed point theorems in the setting of left K-complete T1-quasi metric space. Our theorems generalize, extend, and unify several results of literature.
{"title":"Fixed point theorems for Θ-contractions in left K-complete T1-quasi metric space","authors":"Durdana Lateef, Jamshaid Ahmad","doi":"10.22436/JNSA.012.10.05","DOIUrl":"https://doi.org/10.22436/JNSA.012.10.05","url":null,"abstract":"The aim of this paper is to define Θβ = { v ∈ J u : Θ($(u, v)) ≤ [Θ($(u,J u))]β } and establish some new fixed point theorems in the setting of left K-complete T1-quasi metric space. Our theorems generalize, extend, and unify several results of literature.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85069592","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 proves the existence of a unique common fixed point of two self mappings defined on complete cone quasi metric space C with respect to Banach algebra, consequently in particular, it proves the existence of only one fixed point of a generalized cyclic Banach algebra contraction and a cyclic Banach algebra Kannan type mappings with respect to a couple of non empty subsets (A,B) of a complete cone quasi metric space C. These existences extend the fixed point results of the attached references and then generalized the corresponding classical results in usual Banach spaces as well.
{"title":"Common fixed point of generalized cyclic Banach algebra contractions and Banach algebra Kannan types of mappings on cone quasi metric spaces","authors":"Sahar Mohamed Ali Abou Bakr","doi":"10.22436/JNSA.012.10.03","DOIUrl":"https://doi.org/10.22436/JNSA.012.10.03","url":null,"abstract":"This paper proves the existence of a unique common fixed point of two self mappings defined on complete cone quasi metric space C with respect to Banach algebra, consequently in particular, it proves the existence of only one fixed point of a generalized cyclic Banach algebra contraction and a cyclic Banach algebra Kannan type mappings with respect to a couple of non empty subsets (A,B) of a complete cone quasi metric space C. These existences extend the fixed point results of the attached references and then generalized the corresponding classical results in usual Banach spaces as well.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85398803","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 objective of this work is to modify two hybrid projection algorithm. First, we prove the strongly convergence to common fixed points of a sequence {xn} generated by the hybrid projection algorithm of two asymptotically nonexpansive mappings, second, we prove the strongly convergence of a sequence {xn} generated by the hybrid projection algorithm of two asymptotically nonexpansive semigroups. Our main results extend and improve the results of Dong et al. [Q.-L. Dong, S. N. He, Y. J. Cho, Fixed Point Theory Appl., 2015 (2015), 12 pages].
{"title":"Hybrid iterative methods for two asymptotically nonexpansive semigroups in Hilbert spaces","authors":"I. Inchan","doi":"10.22436/JNSA.012.10.01","DOIUrl":"https://doi.org/10.22436/JNSA.012.10.01","url":null,"abstract":"The main objective of this work is to modify two hybrid projection algorithm. First, we prove the strongly convergence to common fixed points of a sequence {xn} generated by the hybrid projection algorithm of two asymptotically nonexpansive mappings, second, we prove the strongly convergence of a sequence {xn} generated by the hybrid projection algorithm of two asymptotically nonexpansive semigroups. Our main results extend and improve the results of Dong et al. [Q.-L. Dong, S. N. He, Y. J. Cho, Fixed Point Theory Appl., 2015 (2015), 12 pages].","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"4 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89882904","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}
Our main objective is to study the real fixed points and singular values of a two-parameter family of transcendental meromorphic functions gλ,n(z) = λ z (bz−1)n , λ ∈ R{0}, z ∈ C{0}, n ∈ N{1}, b > 0, b 6= 1 in the present paper which obtains from generating function of the unified generalized Apostol-type polynomials. The real fixed points of gλ,n(x), x ∈ R {0} with their stability are found for n odd and n even. It is shown that gλ,n(z) has infinite number of singular values. Further, it is seen that some critical values of gλ,n(z) lie in the closure of the disk and other lie in the exterior of the disk with center at the origin.
本文的主要目的是研究由统一广义阿普stoll型多项式的生成函数得到的双参数超越亚纯函数族gλ，n(z) = λ z (bz - 1)n， λ∈R{0}， z∈C{0}， n∈n {1}， b > 0, b 6= 1的实不动点和奇异值。对于n个奇数和n个偶数，求出了λ，n(x)， x∈R {0}的实不动点及其稳定性。证明了gλ，n(z)有无限个奇异值。进一步可以看出，一些临界值(λ，n(z))位于圆盘的闭合处，另一些临界值位于以原点为中心的圆盘的外部。
{"title":"Real fixed points and singular values of family of functions arising from generating function of unified generalized Apostol-type polynomials","authors":"Mohammad Sajid","doi":"10.22436/JNSA.012.09.05","DOIUrl":"https://doi.org/10.22436/JNSA.012.09.05","url":null,"abstract":"Our main objective is to study the real fixed points and singular values of a two-parameter family of transcendental meromorphic functions gλ,n(z) = λ z (bz−1)n , λ ∈ R{0}, z ∈ C{0}, n ∈ N{1}, b > 0, b 6= 1 in the present paper which obtains from generating function of the unified generalized Apostol-type polynomials. The real fixed points of gλ,n(x), x ∈ R {0} with their stability are found for n odd and n even. It is shown that gλ,n(z) has infinite number of singular values. Further, it is seen that some critical values of gλ,n(z) lie in the closure of the disk and other lie in the exterior of the disk with center at the origin.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"108 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86710822","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}
L. Alnaser, Durdana Lateef, Hoda A. Fouad, Jamshaid Ahmad
The aim of this article is to prove some coincidence and fixed point theorems of hybrid contractions involving left total relations and single-valued mappings in the setting of F-metric spaces which was first introduced by Jleli and Samet [M. Jleli, B. Samet, J. Fixed Point Theory Appl., 20 (2018), 20 pages]. Finally, an example is also presented to verify the effectiveness and applicability of our main results.
{"title":"Coincidence points of self mappings and left total relations","authors":"L. Alnaser, Durdana Lateef, Hoda A. Fouad, Jamshaid Ahmad","doi":"10.22436/JNSA.012.09.03","DOIUrl":"https://doi.org/10.22436/JNSA.012.09.03","url":null,"abstract":"The aim of this article is to prove some coincidence and fixed point theorems of hybrid contractions involving left total relations and single-valued mappings in the setting of F-metric spaces which was first introduced by Jleli and Samet [M. Jleli, B. Samet, J. Fixed Point Theory Appl., 20 (2018), 20 pages]. Finally, an example is also presented to verify the effectiveness and applicability of our main results.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"30 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87958715","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 one-dimensional reaction-diffusion domain of this study, semi-analytical solutions are used for a delayed viral infection system with logistic growth. Through an ordinary differential equations system, the Galerkin technique is believed to estimate the prevailing partial differential equations. In addition, Hopf bifurcation maps are constructed. The effect of diffusion coefficient stricture and delay on the model is comprehensively investigated, and the outcomes demonstrate that diffusion and delay can stabilize or destabilize the system. We found that, as the delay parameter values rise, the values of the Hopf bifurcations for growth and the rates of viral death are augmented, whereas the rate of production is decreased. For the growth, production, and death rates strictures, there is determination of an asymptotically unstable region and a stable region. Illustrations of the unstable and stable limit cycles, as well as the Hopf bifurcation points, are found to prove the formerly revealed outcomes in the Hopf bifurcation map. The results of the semi-analytical solutions and numerical assessments revealed that the semi-analytical solutions are highly effective.
{"title":"Semi-analytical solutions for the delayed and diffusive viral infection model with logistic growth","authors":"H. Alfifi","doi":"10.22436/JNSA.012.09.04","DOIUrl":"https://doi.org/10.22436/JNSA.012.09.04","url":null,"abstract":"In the one-dimensional reaction-diffusion domain of this study, semi-analytical solutions are used for a delayed viral infection system with logistic growth. Through an ordinary differential equations system, the Galerkin technique is believed to estimate the prevailing partial differential equations. In addition, Hopf bifurcation maps are constructed. The effect of diffusion coefficient stricture and delay on the model is comprehensively investigated, and the outcomes demonstrate that diffusion and delay can stabilize or destabilize the system. We found that, as the delay parameter values rise, the values of the Hopf bifurcations for growth and the rates of viral death are augmented, whereas the rate of production is decreased. For the growth, production, and death rates strictures, there is determination of an asymptotically unstable region and a stable region. Illustrations of the unstable and stable limit cycles, as well as the Hopf bifurcation points, are found to prove the formerly revealed outcomes in the Hopf bifurcation map. The results of the semi-analytical solutions and numerical assessments revealed that the semi-analytical solutions are highly effective.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75463908","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 discuss the existence, uniqueness and continuous dependence of solution for a non-autonomous semilinear Hilfer fractional differential equation with nonlocal conditions in the space of weighted continuous functions. By means of the Krasnoselskii’s fixed point theorem and the generalized Gronwall’s inequality, we establish the desired results.
{"title":"Continuous dependence solutions for Hilfer fractional differential equations with nonlocal conditions","authors":"M. Abbas","doi":"10.22436/JNSA.012.09.02","DOIUrl":"https://doi.org/10.22436/JNSA.012.09.02","url":null,"abstract":"We discuss the existence, uniqueness and continuous dependence of solution for a non-autonomous semilinear Hilfer fractional differential equation with nonlocal conditions in the space of weighted continuous functions. By means of the Krasnoselskii’s fixed point theorem and the generalized Gronwall’s inequality, we establish the desired results.","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"114 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77601008","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 the generalized fractional differential equations with and without exogenous inputs","authors":"N. Sene","doi":"10.22436/JNSA.012.09.01","DOIUrl":"https://doi.org/10.22436/JNSA.012.09.01","url":null,"abstract":"","PeriodicalId":48799,"journal":{"name":"Journal of Nonlinear Sciences and Applications","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89106313","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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