]>
2017
17
3
91
Strong convergence of modified viscosity implicit approximation methods for asymptotically nonexpansive mappings in complete CAT(0) spaces
Strong convergence of modified viscosity implicit approximation methods for asymptotically nonexpansive mappings in complete CAT(0) spaces
en
en
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].
345
354
Nuttapol
Pakkaranang
Poom
Kumam
Yeol Je
Cho
Plern
Saipara
Anantachai
Padcharoen
Chatuphol
Khaofong
Asymptotically nonexpansive mapping
projection
viscosity
implicit iterative rule
variational inequality
CAT(0) spaces.
Article.1.pdf
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A combination of curve fitting algorithms to collect a few training samples for function approximation
A combination of curve fitting algorithms to collect a few training samples for function approximation
en
en
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.
355
364
Saeed
Parsa
Mohammad Hadi
Alaeiyan
Output function approximation
black box approximation
curve fitting
linear function approximation
nonlinear function approximation.
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]
The effect of perturbations on the circular restricted four-body problem with variable masses
The effect of perturbations on the circular restricted four-body problem with variable masses
en
en
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.
365
377
Abdullah A.
Ansari
Ziyad A.
Alhussain
Rabah
Kellil
Circular restricted four body problem
isosceles triangular configuration
coriolis and centrifugal forces
oblateness
variable mass
basins of attraction
unstable.
Article.3.pdf
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]
An eighth order frozen Jacobian iterative method for solving nonlinear IVPs and BVPs
An eighth order frozen Jacobian iterative method for solving nonlinear IVPs and BVPs
en
en
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.
378
399
Dina Abdullah
Alrehaili
Dalal Adnan
Al-Maturi
Salem
Al-Aidarous
Fayyaz
Ahmad
Frozen Jacobian iterative methods
systems of nonlinear equations
nonlinear initial-boundary value problems
Jacobi-Gauss-Lobatto quadrature
collocation method.
Article.4.pdf
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[1]
F. Ahmad, E. Tohidi, J. A. Carrasco, A parameterized multi-step Newton method for solving systems of nonlinear equations, Numer. Algorithms, 71 (2016), 631-653
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##[3]
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##[4]
A. H. Bhrawy, An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system, Appl. Math. Comput., 247 (2014), 30-46
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A. H. Bhrawy, E. H. Doha, M. A. Abdelkawy, R. A. Van Gorder, Jacobi-Gauss-Lobatto collocation method for solving nonlinear reaction-diffusion equations subject to Dirichlet boundary conditions, Appl. Math. Model., 40 (2016), 1703-1716
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M. Dehghan, F. Fakhar-Izadi, The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves, Math. Comput. Modelling, 53 (2011), 1865-1877
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E. H. Doha, A. H. Bhrawy, M. A. Abdelkawy, R. A. Van Gorder, Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1 + 1 nonlinear Schrdinger equations, J. Comput. Phys., 261 (2014), 244-255
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On the Korobov and Changhee mixed-type polynomials and numbers
On the Korobov and Changhee mixed-type polynomials and numbers
en
en
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.
400
407
Byung Moon
Kim
Jeong Gon
Lee
Lee-Chae
Jang
Sangki
Choi
Korobov polynomials
Changhee polynomials
Korobov and Changhee mixed-type polynomials.
Article.5.pdf
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D. V. Dolgiĭ, D. S. Kim, T. Kim, On Korobov polynomials of the first kind, (Russian) Mat. Sb., 208 (2017), 65-79
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D. V. Dolgy, D. S. Kim, T. Kim, S.-H. Rim, Some identities of special q-polynomials, J. Inequal. Appl., 2014 (2014 ), 1-10
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D. V. Dolgy, T. Kim, H.-I. Kwon, Identities of symmetry for the higher-order Carlitz’s degenerate q-Euler polynomials under the symmetry group of degree 3, Adv. Stud. Contemp. Math. (Kyungshang), 26 (2016), 595-600
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D. S. Kim, T. Kim, Some identities of Korobov-type polynomials associated with p-adic integrals on \(Z_p\), Adv. Difference Equ., 2015 (2015 ), 1-13
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T. Kim, D. S. Kim, A note on nonlinear Changhee differential equations, Russ. J. Math. Phys., 23 (2016), 88-92
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The Shilnikov type homoclinic orbits of perturbed cubic polynomial Moon-Rand systems
The Shilnikov type homoclinic orbits of perturbed cubic polynomial Moon-Rand systems
en
en
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.
408
419
Dandan
Xie
Yinlai
Jin
Feng
Li
Nana
Zhang
Pad´e approximant
analytic solution
Shilnikov theorem
homoclinic orbit.
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Numerical analysis of fractional order Pine wilt disease model with bilinear incident rate
Numerical analysis of fractional order Pine wilt disease model with bilinear incident rate
en
en
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.
420
428
Yongjin
Li
Fazal
Haq
Kamal
Shah
Muhammad
Shahzad
Ghaus ur
Rahman
Pine Wilt Disease
bilinear incident rate
fractional derivatives
Laplace-Adomian decomposition method
analytical solution.
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]
Jessen type functionals and exponential convexity
Jessen type functionals and exponential convexity
en
en
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.
429
436
Rishi
Naeem
Matloob
Anwar
Jessen functional
exponential convexity
mean value theorems.
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