]>
2022
25
2
105
Solution and intuitionistic fuzzy stability of 3-dimensional cubic functional equation: using two different methods
Solution and intuitionistic fuzzy stability of 3-dimensional cubic functional equation: using two different methods
en
en
In this article, we adopt fixed point method and direct method to find the solution and Intuitionistic fuzzy stability of 3-dimensional cubic functional equation
\begin{eqnarray*} g(2u_{1} + u_{2} + u_{3}) &=& 3g(u_{1} + u_{2} + u_{3}) + g( - u_{1} + u_{2} + u_{3}) + 2g(u_{1} + u_{2})+ 2g(u_{1} + u_{3}) -6g(u_{1} - u_{2}) -6g(u_{1} - u_{3}) \\& &\quad- 3g( u_{2} + u_{3}) + 2g(2u_{1} - u_{2}) + 2g(2u_{1} - u_{3}) - 18g(u_{1}) -6g( u_{2}) -6g(u_{3}).\end{eqnarray*}
103
114
Jyotsana
Jakhar
Department of Mathematics
M.D. University
India
dahiya.jyotsana.j@gmail.com
Renu
Chugh
Department of Mathematics
M.D. University
India
chugh.r1@gmail.com
Jagjeet
Jakhar
Department of Mathematics
Central University of Haryana
India
jagjeet@cuh.ac.in
Functional equations
intuitionistic fuzzy Banach space
fixed point method
direct method
Article.1.pdf
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Explicit Halpern-type iterative algorithm for solving equilibrium problems with applications
Explicit Halpern-type iterative algorithm for solving equilibrium problems with applications
en
en
A number of iterative algorithms have been established to solve equilibrium problems, and one of the most effective methods is a two-step extragradient method. The main objective of this study is to introduce a modified algorithm that is constructed around two methods; Halpern-type method and extragradient method with a new size rule to solve the equilibrium problems accompanied with pseudo-monotone and Lipschitz-type continuous bi-function in a real Hilbert space. Using certain mild conditions on the bi-function, as well as certain conditions on the iterative control parameters, proves a strong convergence theorem. The proposed algorithm uses a monotonic step size rule depending on local bi-function information. The main results are also used to solve variational inequalities and fixed-point problems. The numerical behavior of the proposed algorithm on different test problems is provided compared to other existing algorithms.
115
132
Kanikar
Muangchoo
Faculty of Science and Technology
Rajamangala University of Technology Phra Nakhon (RMUTP)
Thailand
kanikar.m@rmutp.ac.th
Equilibrium problem
Lipschitz-type continuity
strong convergence
fixed point problem
variational inequality problem
Article.2.pdf
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]
Modified subgradient extragradient method to solve variational inequalities
Modified subgradient extragradient method to solve variational inequalities
en
en
In this paper, we introduce a new method to solve pseudomonotone variational inequalities with the Lipschitz condition in a real Hilbert space. This problem is a general mathematical problem in the sense that it unifies a number of the mathematical problems as a particular case, such as the optimization problems, the equilibrium problems, the fixed point problems, the saddle point problems and Nash equilibrium point problems. The new method is constructed around two methods: the extragradient method and the inertial method. The proposed method uses a new stepsize rule based on local operator information rather than its Lipschitz constant or any other line search method. The proposed method does not require any knowledge of the Lipschitz constant of an operator. The strong convergence of the proposed method is well-established. Finally, we conduct a number of numerical experiments to determine the performance and superiority of the proposed method.
133
149
Kanikar
Muangchoo
Faculty of Science and Technology
Rajamangala University of Technology Phra Nakhon (RMUTP)
Thailand
kanikar.m@rmutp.ac.th
Variational inequality problem
subgradient extragradient-like method
strong convergence result
Lipschitz continuity
pseudomonotone mapping
Article.3.pdf
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P. N. Anh, H. T. C. Thach, J. K. Kim, Proximal-like subgradient methods for solving multi-valued variational inequalities, Nonlinear Funct. Anal. Appl., 25 (2020), 437-451
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K. Muangchoo, H. U. Rehman, P. Kumam, Two strongly convergent methods governed by pseudo-monotone bi-function in a real Hilbert space with applications, J. Appl. Math. Comput., 2021 (2021), 1-27
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H. U. Rehman, P. Kumam, A. B. Abubakar, Y. J. Cho, The extragradient algorithm with inertial effects extended to equilibrium problems, Comput. Appl. Math., 39 (2020), 1-26
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H. U. Rehman, P. Kumam, I. K. Argyros, N. A. Alreshidi, Modified proximal-like extragradient methods for two classes of equilibrium problems in Hilbert spaces with applications, Comput. Appl. Math.,, 40 (2021), 1-26
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H. U. Rehman, P. Kumam, Y. J. Cho, Y. I. Suleiman, W. Kumam, Modified Popov’s explicit iterative algorithms for solving pseudomonotone equilibrium problems, Optim. Methods Softw., 36 (2021), 82-113
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H. U. Rehman, P. Kumam, Y. J. Cho, P. Yordsorn, Weak convergence of explicit extragradient algorithms for solving equilibrium problems, J. Inequal. Appl., 2019 (2019), 1-25
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H. U. Rehman, P. Kumam, Q.-L. Dong, Y. J. Cho, A modified self-adaptive extragradient method for pseudomonotone equilibrium problem in a real Hilbert space with applications, Math. Methods Appl. Sci., 44 (2021), 3527-3547
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]
Predator-prey dynamics with Allee effect on predator species subject to intra-specific competition and nonlinear prey refuge
Predator-prey dynamics with Allee effect on predator species subject to intra-specific competition and nonlinear prey refuge
en
en
A modified version of our previously analyzed prey-predator refuge model is presented in this article by introducing Allee effect on the predator species and mutual interference among the predators. Possible number of coexistence equilibrium points are investigated with the help of prey and predator nullcline. The local stability and Hopf-bifurcation conditions are established around the coexistence equilibria. We have also discussed the nature of Hopf-bifurcation around the unique coexistence equilibrium point of the system as well. Finally, a comprehensive numerical simulation is carried out to justify our obtained analytical findings.
150
165
Hafizul
Molla
Department of Mathematics
Manbhum Mahavidyalaya
India
Sahabuddin
Sarwardi
Department of Mathematics \(\&\) Statistics
Aliah University
India
s.sarwardi@gmail.com
Mohammad
Sajid
Department of Mechanical Engineering, College of Engineering
Qassim University
Kingdom of Saudi Arabia
Ecological model
refuge
stability
Hopf-bifurcation
nature of Hopf-bifurcation
numerical simulations
Article.4.pdf
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J. Banerjee, S. K. Sasmal, R. K. Layek, Supercritical and subcritical Hopf-bifurcations in a two-delayed prey--predator system with density-dependent mortality of predator and strong Allee effect in prey, Biosystems, 180 (2019), 19-37
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S. Sarwardi, M. M. Haque, S. Hossain, Analysis of Bogdanov-Takens bifurcations in a spatiotemporal harvested-predator and prey system with Beddington-DeAngelis type response function, Nonlinear Dynam., 100 (2020), 1755-1778
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On the \(q\)-Sumudu transform with two variables and some properties
On the \(q\)-Sumudu transform with two variables and some properties
en
en
In this paper we present some properties of double \(q\)-Sumudu transform in \(q\)-calculus by using the functions of two variables.
Furthermore results on convergence, absolute convergence and convolution are discussed. At the end some examples are given to illustrate use of double \(q\)-Sumudu transform.
166
175
Artan F.
Alidema
Department of Mathematics, Faculty of Mathematical and Natural Science
University of Prishtina
Kosovo
artan.alidema@uni-pr.edu
Shkumbin V.
Makolli
Department of Mathematics, Faculty of Mechanical Engeenering
University of Prishtina
Kosovo
shkumbin.makolli@uni-pr.edu
Double \(q\)-Sumudu transform
convergence
convolution
Article.5.pdf
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]
A new trigonometrical method for solving non-linear transcendental equations
A new trigonometrical method for solving non-linear transcendental equations
en
en
This paper presents a new algorithm to find a non-zero positive real root of the transcendental equations. The proposed method is based on the combination of the inverse \(\tan(x)\) function and the Newton-Raphson method. Implementation of the proposed method in MATLAB is applied to different problems to ensure the methodâ€™s applicability. The proposed method is tested on number of numerical examples and results indicate that our methods are better and more effective as compared to well-known methods. Error calculation has been done for available existing methods and the new proposed method. The errors have been reduced rapidly and obtained the real root in less number of iterations as compared to renowned methods. Certain numerical examples are presented in this paper to show the effectiveness of the proposed method. The Convergence of the proposed method is discussed and shown that the method reduces to Newton-Raphson method that is quadratic convergent. This approach will also help to produce a non-zero real root of a given non-linear equations (transcendental, algebraic, and exponential) in the commercial package.
176
181
K.
Venkateshwarlu
Department of Freshman Engineering
Geethanjali College of Engineering and Technology
India
V. S.
Triveni
Department of Freshman Engineering
Geethanjali College of Engineering and Technology
India
G.
Mahesh
Department of Freshman Engineering
Geethanjali College of Engineering and Technology
India
gattumahesh.fe@gcet.edu.in
G.
Swapna
Department of Humanities and Sciences
Geethanjali College of Pharmacy
India
Nonlinear equation
iteration method
transcendental equations
Article.6.pdf
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]
\(\theta_s\)-open sets and \(\theta_{s}\)-continuity of maps in the product space
\(\theta_s\)-open sets and \(\theta_{s}\)-continuity of maps in the product space
en
en
In this study, the concept of \(\theta_s\)-open set is introduced. The topology formed by \(\theta_s\)-open sets is strictly finer than the topology formed by \(\theta\)-open sets but is not comparable with the topology formed by \(\omega_\theta\)-open sets. Related concepts such as \(\theta_s\)-open and \(\theta_s\)-closed functions, \(\theta_s\)-continuous function, \(\theta_s\)-connected space, and some versions of separation axioms are defined and characterized. Finally, the concept of \(\theta_s\)-continuous function from an arbitrary topological space into the product space is investigated further.
182
190
Javier A.
Hassan
Department of Mathematics \(\&\) Statistics, College of Science \(\&\) Mathematics
Mindanao State University-Iligan Institute of Technology
Philippines
javier.hassan@g.msuiit.edu.ph
Mhelmar A.
Labendia
Department of Mathematics \(\&\) Statistics, College of Science \(\&\) Mathematics
Mindanao State University-Iligan Institute of Technology
Philippines
mhelmar.labendia@g.msuiit.edu.ph
\(\theta_s\)-open
\(\theta_s\)-closed
\(\theta_s\)-connected
\(\theta_s\)-continuous
\(\theta_s\)-Hausdorff
(\theta_s\)-regular
\(\theta_s\)-normal
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Quadrature method with exponential fitting for delay differential equations having Layer behavior
Quadrature method with exponential fitting for delay differential equations having Layer behavior
en
en
In this paper, we suggest a computational method for solving delay differential equations, with one end layer, dual layer and interior layer behavior using Gaussian quadrature. The problem is initially replaced with the analogous first order neutral type delay differential equation by taking the perturbation parameter within the differentiated term. For the numerical solution with boundary layer at one endpoint, dual boundary layers and internal boundary layers, the Gaussian two-point quadrature scheme was extracted with exponential fitting. Using model examples, the suggested approach is used for various perturbation and delay parameter values. The numerical scheme is validated and supported by the comparison of maximum errors with the other results in the literature. Convergence of the method is examined. For various delay parameter values, the layer structure is depicted in graphs.
191
208
M.
Lalu
Department of Mathematics
University College of Engineering, Osmania University
India
lalunaikmudavathou@gmail.com
K.
Phaneendra
Department of Mathematics
University College of Engineering, Osmania University
India
kollojuphaneendra@yahoo.co.in
Delay differential equations
boundary layer
Gauss quadrature two point formula
dual layer
internal layer
fitting factor
Article.8.pdf
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R. Darzi, A. Neamaty, Y. Darzi, B. Mohammadzadeh, A Combined Method for the Numerical Solution of Boundary Value Problems of Second Order, J. Math. Comput. Sci., 4 (2012), 102-109
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