International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111420180310Some reverse Hölder inequalities with Specht's ratio on time scales444455http://dx.doi.org/10.22436/jnsa.011.04.01ENA. A. El-DeebDepartment of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, EgyptH. A. ElsennaryDepartment of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt \(\&\) Department of Mathematics, Faculty of Engineering, Sinai University, El Arish (45615), North Sinai, EgyptWing-Sum CheungDepartment of Mathematics, The University of Hong Kong, Pokfulam Road, Hong KongIn this article, we investigate some new reverse Hölder-type inequalities
on an arbitrary time scale via the diamond-\(\alpha\) 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.http://isr-publications.com/jnsa/6866/download-some-reverse-holder-inequalities-with-spechts-ratio-on-time-scalesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111420180310Stability of pathogen dynamics models with viral and cellular infections and immune impairment456468http://dx.doi.org/10.22436/jnsa.011.04.02ENA. M. ElaiwDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi ArabiaA. A. RaezahDepartment of Mathematics, Faculty of Science, King Khalid University, P. O. Box 25145, Abha 61466, Saudi ArabiaB. S. AlofiDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi ArabiaWe 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 \(\mathcal{R}_{0}\), 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. http://isr-publications.com/jnsa/6867/download-stability-of-pathogen-dynamics-models-with-viral-and-cellular-infections-and-immune-impairmentInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111420180313Properties of hyperholomorphic functions and integrals for commutative-quaternionic valued functions469476http://dx.doi.org/10.22436/jnsa.011.04.03ENJi Eun KimDepartment of Mathematics, Dongguk University, Gyeongju, Republic of KoreaWe give representations and properties of a hyperholomorphic function with values in commutative-quaternions. We first consider expressions of commutative-quaternions. Also, we investigate the results of derivatives and integrations for a hyperholomorphic function of commutative-quaternionic variables in Clifford analysis.http://isr-publications.com/jnsa/6873/download-properties-of-hyperholomorphic-functions-and-integrals-for-commutative-quaternionic-valued-functionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111420180316Dynamics of the fuzzy difference equation \(z_n =\max\{\frac{ 1}{ z_{n-m}} , \frac{\alpha_n }{z_{n-r} }\}\)477485http://dx.doi.org/10.22436/jnsa.011.04.04ENTaixiang SunGuangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, Guangxi Univresity of Finance and Economics, Nanning, 530003, ChinaHongjian XiGuangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, Guangxi Univresity of Finance and Economics, Nanning, 530003, ChinaGuangwang SuGuangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, Guangxi Univresity of Finance and Economics, Nanning, 530003, ChinaBin QinGuangxi Key Laboratory Cultivation Base of Cross-border E-commerce Intelligent Information Processing, Guangxi Univresity of Finance and Economics, Nanning, 530003, ChinaIn this paper, we study the eventual periodicity of the following
fuzzy max-type difference equation
\[z_n=\max\{\frac{1}{z_{n-m}},\frac{\alpha_n}{z_{n-r}}\},\ \
n=0,1,\ldots,\] where \(\{\alpha_n\}_{n\geq 0}\) is a periodic
sequence of positive fuzzy numbers and the initial values
\(z_{-d},z_{-d+1},\ldots,z_{-1}\)
are positive fuzzy numbers with
\(d=\max\{m,r\}\). We show that if
\(\max(\mbox{supp}\ \alpha_n)<1\), then every positive solution of
this equation is eventually periodic with period \(2m\). http://isr-publications.com/jnsa/6887/download-dynamics-of-the-fuzzy-difference-equation-z-n-maxfrac-1-z-n-m-fracalpha-n-z-n-rInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111420180316Hitting probabilities for non-convex lattice486489http://dx.doi.org/10.22436/jnsa.011.04.05ENG. CaristiDepartment of Economics, University of Messina, via dei Verdi, 75 98122, Messina, ItalyM. PettineoDepartment of Mathematics, University of Palermo, via Archirafi, 34-Palermo, ItalyA.PuglisiDepartment of Economics, University of Messina, via dei Verdi, 75 98122, Messina, ItalyIn this paper, we consider three lattices with cells represented in Figures 1,
3, and 5 and we determine the probability that a random segment of constant length
intersects a side of the lattice considered.http://isr-publications.com/jnsa/6890/download-hitting-probabilities-for-non-convex-latticeInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111420180317On certain classes of bi-univalent functions related to \(m\)-fold symmetry490499http://dx.doi.org/10.22436/jnsa.011.04.06ENSaqib HussainCOMSATS Institute of Information Technology, Abbotabad, PakistanShahid KhanDepartment of Mathematics, Riphah International University Islamabad, PakistanMuhammad Asad ZaighumDepartment of Mathematics, Riphah International University Islamabad, PakistanMaslina DarusSchool of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia 43600, Bangi, Selangor, MalaysiaIn our present investigation, we introduce two new
subclasses \(S_{\Sigma _{m}}(\alpha ,\lambda ,\mu )\) and \(S_{\Sigma
_{m}}(\beta ,\lambda ,\mu )\) 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.http://isr-publications.com/jnsa/6893/download-on-certain-classes-of-bi-univalent-functions-related-to-m-fold-symmetryInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111420180317Fourier series of finite product of Bernoulli and ordered Bell functions500515http://dx.doi.org/10.22436/jnsa.011.04.07ENTaekyun KimDepartment of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin 300160, China \(\&\) Department of Mathematics, Kwangwoon University, Seoul, 139-701, Republic of KoreaDae San KimDepartment of Mathematics, Sogang University, Seoul, 121-742, Republic of KoreaDmitry V. DolgyHanrimwon, Kwangwoon University, Seoul, 139-701, Republic of KoreaJongkyum KwonDepartment of Mathematics Education and ERI, Gyeongsang National University, Jinju, Gyeongsangnamdo, 52828, Republic of Korea In this paper, we consider three types of functions given by products of Bernoulli and ordered Bell functions and derive their Fourier series expansions. In addition, we will express each of them in terms of Bernoulli functions.http://isr-publications.com/jnsa/6894/download-fourier-series-of-finite-product-of-bernoulli-and-ordered-bell-functionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111420180319Viral dynamics of an HIV model with pulse antiretroviral therapy and adherence516528http://dx.doi.org/10.22436/jnsa.011.04.08ENYouping YangSchool of Mathematics and Statistics, Shandong Normal University, Jinan, 250014, P. R. ChinaAn immunological model of HIV-1 infection that accounts for
antiretroviral drug uptake via explicit compartments is considered.
Different from traditional methods where the drug effects is
modeled implicitly as a proportional inhibition of viral infection
and production, in this paper, it is assumed that the CD4\(^+\) T
cells can 'prey on' the antiretroviral drugs and become the cells
which cannot be infected or produce new virions. Drug dymamics is
modeled applying impulsive differential equations. The basic
reproductive number \(R_0\) is defined via the next infection
operator. It is shown that with perfect adherence the virus can be
eradicated permanently if \(R_0\) is less than unity, otherwise, the
virus can persist by applying persistent theory. The effects of
imperfect adherence are also explored. The results indicate that
even for the same degree of adherence, different adherence patterns
may lead to different therapy outcomes. In particular, for regular
dosage missing, the more dosages are consecutively missed, the worse
therapy outcomes will be. http://isr-publications.com/jnsa/6901/download-viral-dynamics-of-an-hiv-model-with-pulse-antiretroviral-therapy-and-adherenceInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111420180319Strong convergence of a new iterative algorithm for fixed points of asymptotically nonexpansive mappings529540http://dx.doi.org/10.22436/jnsa.011.04.09ENYuanheng WangDepartment of Mathematics, Zhejiang Normal University, Jinhua, ChinaJialei FengDepartment of Mathematics, Zhejiang Normal University, Jinhua, ChinaIn this paper, we investigate a new iterative implicit algorithm for fixed points of asymptotically nonexpansive mapping in Hilbert spaces. We also prove its strong convergence theorem under certain assumptions imposed on the parameters and extend some well-known results. As an application, we apply our main result to \(\mu\)-inverse strongly monotone mapping.http://isr-publications.com/jnsa/6902/download-strong-convergence-of-a-new-iterative-algorithm-for-fixed-points-of-asymptotically-nonexpansive-mappingsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111420180323On mixed complex intersection bodies541549http://dx.doi.org/10.22436/jnsa.011.04.10ENChang-Jian ZhaoDepartment of Mathematics, China Jiliang University, Hangzhou 310018, P. R. China In 2013, the mixed complex intersection bodies of
star bodies was introduced. Following this, in the paper, we
establish Aleksandrov-Fenchel and Brunn-Minkowski type
inequalities for the mixed complex intersection bodies, which in
special case yield some of the recent results.http://isr-publications.com/jnsa/6930/download-on-mixed-complex-intersection-bodiesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111420180323Guaranteed cost control of exponential function projective synchronization of delayed complex dynamical networks with hybrid uncertainties asymmetric coupling delays550574http://dx.doi.org/10.22436/jnsa.011.04.11ENWajaree WeeraDepartment of Mathematics, University of Pha Yao, Pha Yao 56000, ThailandThongchai BotmartDepartment of Mathematics, Khon Kaen University, Khon Kaen 40002, ThailandPiyapong NiamsupDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandNarongsak YothaDepartment of Applied Mathematics and Statistics, Rajamangala University of Technology Isan, Nakhon Ratchasima 30000, ThailandThe problem of guaranteed cost control for exponential function projective synchronization (EFPS) for complex dynamical networks with mixed time-varying delays and hybrid uncertainties asymmetric coupling delays, composing of state coupling, time-varying delay coupling, and distributed time-varying delay coupling, is investigated. In this work, the uncertainties coupling configuration matrix need not be symmetric or irreducible. The guaranteed cost control for EFPS of delayed complex dynamical networks is considered via hybrid control with nonlinear and mixed linear feedback controls, including error linear term, time-varying delay error linear term, and distributed time-varying delay error linear term. Based on the construction of improved Lyapunov-Krasovskii functional with the technique of dealing with some integral terms, the new sufficient conditions for the existence of the optimal guaranteed cost control laws are presented in terms of linear matrix inequalities (LMIs). The obtained LMIs can be efficiently solved by standard convex optimization algorithms. Moreover, numerical examples are given to demonstrate the effectiveness of proposed guaranteed cost control for EFPS. The results in this article generalize and improve the corresponding results of the recent works. http://isr-publications.com/jnsa/6931/download-guaranteed-cost-control-of-exponential-function-projective-synchronization-of-delayed-complex-dynamical-networks-with-hybrid-uncertainties-asymmetric-coupling-delaysInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190111420180325Fourier series of sums of products of \(r\)-derangement functions575590http://dx.doi.org/10.22436/jnsa.011.04.12ENTaekyun KimDepartment of Mathematics, Kwangwoon University, Seoul 139-701, S. KoreaDae San KimDepartment of Mathematics, Sogang University, Seoul 121-742, Republic of KoreaHuck-In KwonDepartment of Mathematics, Kwangwoon University, Seoul 139-701, Republic of KoreaLee-Chae JangGraduate School of Education, Konkuk University, Seoul 143-701, Republic of KoreaA derangement is a permutation that has no fixed point and the derangement number \(d_m\) is the number of fixed point-free permutations on an \(m\) element set. A generalization of the derangement numbers are the \(r\)-derangement numbers and their natural companions are the \(r\)-derangement polynomials.
In this paper we will study three types of sums of products of \(r\)-derangement functions and find Fourier series expansions of them. In addition, we will express them in terms of Bernoulli functions. As immediate corollaries to this, we will be able to express the corresponding three types of polynomials as linear combinations of Bernoulli polynomials.http://isr-publications.com/jnsa/6935/download-fourier-series-of-sums-of-products-of-r-derangement-functions