International Scientific Research PublicationsJournal of Mathematics and Computer Science(JMCS) ISSN 2008-949X17320170713Strong convergence of modified viscosity implicit approximation methods for asymptotically nonexpansive mappings in complete CAT(0) spaces345354http://dx.doi.org/10.22436/jmcs.017.03.01ENNuttapolPakkaranangDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.PoomKumamDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.Yeol JeChoDepartment of Mathematics Education and the RINS, Gyeongsang National University, Jinju 660-701, Korea.PlernSaiparaDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.AnantachaiPadcharoenDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand.ChatupholKhaofongDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand. In this paper, we introduce a modified viscosity implicit iteration for asymptotically nonexpansive mappings in complete
CAT(0) spaces. Under suitable conditions, we prove some strong convergence to a fixed point of an asymptotically nonexpansive
mapping in a such space which is also the solution of variational inequality. Moreover, we illustrate some numerical example
of our main results. Our results extend and improve some recent result of Yao et al. [Y.-H. Yao, N. Shahzad, Y.-C. Liou, Fixed
Point Theory Appl., 2015 (2015), 15 pages] and Xu et al. [H.-K. Xu, M. A. Alghamdi, N. Shahzad, Fixed Point Theory Appl.,
2015 (2015), 12 pages].
http://www.isr-publications.com/jmcs/4456/download-strong-convergence-of-modified-viscosity-implicit-approximation-methods-for-asymptotically-nonexpansive-mappings-in-complete-cat0-spacesInternational Scientific Research PublicationsJournal of Mathematics and Computer Science(JMCS) ISSN 2008-949X17320170717A combination of curve fitting algorithms to collect a few training samples for function approximation355364http://dx.doi.org/10.22436/jmcs.017.03.02ENSaeedParsaDepartment of Computer Engineering, Iran University of Science and Technology, Narmak, Tehran, 16844, Iran.Mohammad HadiAlaeiyanDepartment of Computer Engineering, Iran University of Science and Technology, Narmak, Tehran, 16844, Iran. The aim of this paper is to approximate the numerical result of executing a program/function with a number of input
parameters and a single output value with a small number of training points. Curve fitting methods are preferred to nondeterministic
methods such as neural network and fuzzing system methods, because they can provide relatively more accurate
results with the less amount of member in the training dataset. However, curve fitting methods themselves are most often
function specific and do not provide a general solution to the problem. These methods are most often targeted at fitting specific
functions to their training dataset. To provide a general curve fitting method, in this paper, the use of a combination of Lagrange,
Spline, and trigonometric interpolation methods are suggested. The Lagrange method fits polynomial functions of degree N to
its training values. In order to improve the resultant fitted polynomial our combinatorial method combines Lagrange with the
polynomial resulted from the Spline method. If the absolute error of the actual value and the predicted value of a function are
not desired, the trigonometric interpolation methods that fit trigonometric functions can be applied. Our experiments with a
number of benchmark examples demonstrate the relatively high accuracy of our combinational fitting method.
http://www.isr-publications.com/jmcs/4533/download-a-combination-of-curve-fitting-algorithms-to-collect-a-few-training-samples-for-function-approximationInternational Scientific Research PublicationsJournal of Mathematics and Computer Science(JMCS) ISSN 2008-949X17320160718The effect of perturbations on the circular restricted four-body problem with variable masses365377http://dx.doi.org/10.22436/jmcs.017.03.03ENAbdullah A.AnsariCollege of Science at Al-Zulfi, Majmaah University, KSA.Ziyad A.AlhussainCollege of Science at Al-Zulfi, Majmaah University, KSA.RabahKellilCollege of Science at Al-Zulfi, Majmaah University, KSA. This paper presents a new investigation of the circular restricted four body problem under the effect of any variation in
coriolis and centrifugal forces. Here, masses of all the bodies vary with time. This has been done by considering one of the
primaries as oblate body and all the primaries are placed at the vertices of a triangle. Due to the oblateness, the triangular configuration
becomes an isosceles triangular configuration which was an equilateral triangle in the classical case. After evaluating
the equations of motion, we have determined the equilibrium points, the surfaces of the motion, the time series and the basins of
attraction of the infinitesimal body. We note that, when we increase both the coriolis and centrifugal forces, the curves, surfaces
of motion, and the basins of attraction are shrinking except when we fix the centrifugal force and increase the value of coriolis
force, the curves are expanding and the equilibrium points are away from the origin. The behavior of the surfaces of motion
and the basins of attraction in the last case (fixing the centrifugal force and increasing the value of coriolis force) will be studied
next. In all the present study, we found that all the equilibrium points are unstable.
http://www.isr-publications.com/jmcs/4693/download-the-effect-of-perturbations-on-the-circular-restricted-four-body-problem-with-variable-massesInternational Scientific Research PublicationsJournal of Mathematics and Computer Science(JMCS) ISSN 2008-949X17320170719An eighth order frozen Jacobian iterative method for solving nonlinear IVPs and BVPs378399http://dx.doi.org/10.22436/jmcs.017.03.04ENDina AbdullahAlrehailiDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.Dalal AdnanAl-MaturiDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.SalemAl-AidarousDepartment of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.FayyazAhmadDipartimento di Scienza e Alta Tecnologia, Universita dell’Insubria, Via Valleggio 11, Como 22100, Italy. A frozen Jacobian iterative method is proposed for solving systems of nonlinear equations. In particular, we are interested in
solving the systems of nonlinear equations associated with initial value problems (IVPs) and boundary value problems (BVPs).
In a single instance of the proposed iterative method DEDF, we evaluate two Jacobians, one inversion of the Jacobian and four
function evaluations. The direct inversion of the Jacobian is computationally expensive, so, for a moderate size, LU factorization is
a good direct method to solve the linear system. We employed the LU factorization of the Jacobian to avoid the direct inversion.
The convergence order of the proposed iterative method is at least eight, and it is nine for some particular classes of problems.
The discretization of IVPs and BVPs is employed by using Jacobi-Gauss-Lobatto collocation (J-GL-C) method. A comparison of
J-GL-C methods is presented in order to choose best collocation method. The validity, accuracy and the efficiency of our DEDF
are shown by solving eleven IVPs and BVPs problems.
http://www.isr-publications.com/jmcs/4712/download-an-eighth-order-frozen-jacobian-iterative-method-for-solving-nonlinear-ivps-and-bvpsInternational Scientific Research PublicationsJournal of Mathematics and Computer Science(JMCS) ISSN 2008-949X17320170723On the Korobov and Changhee mixed-type polynomials and numbers400407http://dx.doi.org/10.22436/jmcs.017.03.05ENByung MoonKimDepartment of Mechanical System Engineering, Dongguk University, Gyeongju, 780-714, Korea.Jeong GonLeeDivision of Mathematics and Informational Statistics and Nanoscale Science and Technology Institute,Wonkwang University, Iksan 570-749, Republic of Korea.Lee-ChaeJangGraduate School of Education, Konkuk University, Seoul 143-701, Republic of Korea.SangkiChoiDepartment of Mathematics Education, Konkuk University, Seoul 143-701, Korea. By using the Bosonic p-adic integral, Kim et al. [D. S. Kim, T. Kim, H.-I. Kwon, J.-J. Seo, Adv. Stud. Theor. Phys., 8 (2014),
745–754] studied some identities of the Korobov and Daehee mixed-type polynomials. In this paper, by using the fermionic
p-adic integral, we define the Korobov and Changhee mixed-type polynomials and give some interesting identities of those
polynomials.
http://www.isr-publications.com/jmcs/4839/download-on-the-korobov-and-changhee-mixed-type-polynomials-and-numbersInternational Scientific Research PublicationsJournal of Mathematics and Computer Science(JMCS) ISSN 2008-949X17320170723The Shilnikov type homoclinic orbits of perturbed cubic polynomial Moon-Rand systems408419http://dx.doi.org/10.22436/jmcs.017.03.06ENDandanXieSchool of Mathematics and Statistics, Linyi University, Linyi, Shandong, 276005, P. R. China.YinlaiJinSchool of Mathematics and Statistics, Linyi University, Linyi, Shandong, 276005, P. R. China.FengLiSchool of Mathematics and Statistics, Linyi University, Linyi, Shandong, 276005, P. R. China.NanaZhangSchool of Mathematics and Statistics, Shandong Normal University, Jinan, Shandong, 250014, P. R. China. In this paper, perturbed polynomial Moon-Rand systems are considered. The Padé approximant and analytic solution in
the neighborhood of the initial value are introduced into the process of constructing the Shilnikov type homoclinic orbits for
three dimensional nonlinear dynamical systems. In order to get real bifurcation parameters, four undetermined coefficients
are introduced including three initial values about position and the value of bifurcation parameter. By the eigenvectors of its
all eigenvalues, the value of the bifurcation parameter and three initial values about position are obtained directly. And, the
analytical expressions of the Shilnikov type homoclinic orbits are achieved and the deletion errors relative to the practical system
are given. In the end, we roughly predict when the horseshoe chaos occurs.
http://www.isr-publications.com/jmcs/5094/download-the-shilnikov-type-homoclinic-orbits-of-perturbed-cubic-polynomial-moon-rand-systemsInternational Scientific Research PublicationsJournal of Mathematics and Computer Science(JMCS) ISSN 2008-949X17320170807Numerical analysis of fractional order Pine wilt disease model with bilinear incident rate420428http://dx.doi.org/10.22436/jmcs.017.03.07ENYongjinLiDepartment of Mathematics, Sun Yat-sen University, Guangzhou, China.FazalHaqDepartment of Mathematics, Hazara University Mansehra, Pakistan.KamalShahDepartment of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan.MuhammadShahzadDepartment of Mathematics, Hazara University Mansehra, Pakistan.Ghaus urRahmanDepartment of Mathematics and Statistics, University of Swat, Pakistan. This work is related to an analytical solution of a fractional order epidemic model for the spread of the Pine wilt disease with bilinear incident rate. To obtain an analytical solution
of the system of nonlinear fractional differential equations for the considered model. Laplace Adomian decomposition method (LADM) will be used. Comparison of the results have been carried out between the proposed method and that of homotopy purturbation (HPM). Numerical results show that (LADM) is very efficient and accurate for solving fractional order Pine wilt disease model.
http://www.isr-publications.com/jmcs/5198/download-numerical-analysis-of-fractional-order-pine-wilt-disease-model-with-bilinear-incident-rateInternational Scientific Research PublicationsJournal of Mathematics and Computer Science(JMCS) ISSN 2008-949X17320170825Jessen type functionals and exponential convexity429436http://dx.doi.org/10.22436/jmcs.017.03.08ENRishi NaeemSchool of Natural Sciences, National University of Sciences and Technology, Islamabad, PakistanMatloob AnwarSchool of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan In this paper, we introduce the extension of Jessen functional and
investigate logarithmic and exponential convexity. We also give mean
value theorems of Cauchy and Lagrange type. Several families of
functions are also presented related to our main results.
http://www.isr-publications.com/jmcs/5361/download-jessen-type-functionals-and-exponential-convexity