]>
2020
13
3
ISSN 2008-1898
56
A new iterative algorithm for solving some nonlinear problems in Hilbert spaces
A new iterative algorithm for solving some nonlinear problems in Hilbert spaces
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en
In this paper, a new iterative algorithm for finding a common element of the set of minimizers of a convex function, the set of solutions of variational inequality problem, the set of solutions of equilibrium problems and the set of fixed points of demicontractive mappings is constructed. Convergence theorems are also proved in Hilbert spaces without any compactness assumption. Furthermore, a numerical example is given to demonstrate the implementability of our algorithm. Our theorems are significant improvements in several important recent results.
119
132
T. M. M.
Sow
Department of Mathematics
Gaston Berger University
Senegal
sowthierno89@gmail.com
Fixed points problem
convex minimization problem
equilibrium problem
variational inequality problem
Article.1.pdf
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Y. Yao, H. Zhou, Y. C. Liou, Strong convergence of modified Krasnoselskii-Mann iterative algorithm for nonexpansive mappings, J. Math. Anal. Appl. Comput., 29 (2009), 383-389
]
The extended Burr XII distribution: properties and applications
The extended Burr XII distribution: properties and applications
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en
This paper introduces a new four-parameter lifetime model called the
Marshall-Olkin generalized Burr XII (MOGBXII) distribution. We derive some
of its mathematical properties, including quantile and generating functions,
ordinary and incomplete moments, mean residual life, and mean waiting time
and order statistics. The MOGBXII density can be expressed as a linear
mixture of Burr XII densities. The maximum likelihood and least squares
methods are used to estimate the MOGBXII parameters. Simulation results are
obtained to compare the performances of the two estimation methods for both
small and large samples. We empirically illustrate the flexibility and importance of the MOGBXII distribution in modeling various types of lifetime data.
133
146
Ahmed Z.
Afify
Department of Statistics, Mathematics and Insurance
Benha University
Egypt
ahmed.afify@fcom.bu.edu.eg
Ashraf D.
Abdellatif
Department of Technological Management and Information
Higher Technological Institute
Egypt
ashraf_abdellatif@yahoo.com
Burr XII
least squares
maximum likelihood
mean residual life
moments
order statistics
Article.2.pdf
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[1]
T. H. M. Abouelmagd, S. Al-mualim, A. Z. Afify, M. Ahmad, H. Al-Mofleh, The odd Lindley Burr XII distribution with applications, Pakistan J. Statist., 34 (2018), 15-32
##[2]
T. H. M. Abouelmagd, M. S. Hamed, A. Z. Afify, The extended Burr XII distribution with variable shapes for the hazard rate, Pak. J. Stat. Oper. Res., 13 (2017), 687-698
##[3]
A. Z. Afify, G. M. Cordeiro, M. Bourguignon, E. M. Ortega, Properties of the transmuted Burr XII distribution, regression and its applications, J. Data Sci., 16 (2018), 485-510
##[4]
A. Z. Afify, G. M. Cordeiro, E. M. M. Ortega, H. M. Yousof, N. S. Butt, The four-parameter Burr XII distribution: properties, regression model, and applications, Comm. Statist. Theory Methods, 47 (2018), 2605-2624
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A. Z. Afify, G. M. Cordeiro, H. M. Yousof, A. Saboor, E. M. M. Ortega, The Marshall-Olkin additive Weibull distribution with variable shapes for the hazard rate, Hacet. J. Math. Stat., 47 (2018), 365-381
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A. Z. Afify, A. K. Suzuki, C. Zhang, M. Nassar, On threeparameter exponential distribution: properties, Bayesian and non-Bayesian estimation based on complete and censored samples, Commun. Stat. Simul. Comput., 2019 (2019), 1-21
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M. A. D. Aldahlan, A. Z. Afify, The odd exponentiated half-logistic Burr XII distribution, Pak. J. Stat. Oper. Res., 14 (2018), 305-317
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A. Y. Al-Saiari, L. A. Baharith, S. A. Mousa, Marshall--Olkin extended Burr Type XII distribution, Int. J. Statist. Prob., 3 (2014), 78-84
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I. W. Burr, Cumulative frequency functions, Ann. Math. Statistics, 13 (1942), 215-232
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A. E. Gomes, C. Q. da-Silva, G. M. Cordeiro, Two extended Burr models: Theory and practice, Comm. Statist. Theory Methods, 44 (2015), 1706-1734
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M. M. Mansour, E. M. Abd Elrazik, A. Z. Afify, M. Ahsanullah, E. Altun, The transmuted transmuted-G family: properties and applications, J. Nonlinear Sci. Appl., 12 (2019), 217-229
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]
Characteristic roots of a second order retarded functional differential equation via spectral-tau method
Characteristic roots of a second order retarded functional differential equation via spectral-tau method
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en
In this paper, we have found the solution of second-order delay differential equations of retarded type with multiple delays. As well as developing an approximation for finding characteristic roots for such delay differential equations via the method of spectral tau which depends on the basis mixed Fourier basis or shifted Chebyshev polynomials.
147
153
Habeeb Kareem
Abdullah
Department of Mathematics, Faculty of Education for Girls
University of Kufa
Iraq
habeebk.abdullah@uokufa.edu.iq
Amal Khalaf
Haydar
Department of Mathematics, Faculty of Education for Girls
University of Kufa
Iraq
amalkh.hayder@uokufa.edu.iq
Kawther Reyadh
Obead
Department of Mathematics, Faculty of Education for Girls
University of Kufa
Iraq
Linear functional-differential equations
IBVPs for linear higher-order equations
spectral theory of functional-differential operators
Article.3.pdf
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H. K. Abdullah, A. K. Haydar, K. R. Obead, Solving of third order retarded dynamical system via lambert W function and stability analysis, World Wide J. Multidisciplin. Res. Develop., 4 (2018), 105-112
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H. K. Abdullah, A. K. Haydar, K. R. Obead, Solving retarded dynamical system of nth- order and stability analysis via lambert W function, Int. J. Pure Appl. Math., 118 (2018), 2567-2584
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O. Arino, M. L. Hbid, E. A. Dads, Delay differential equations and application, Springer, The Nethelands (2006)
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J. P. Boyd, Chebyshev and Fourier Spectral Methods, Dover Publ. Inc., Mineola (2001)
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S.-T. Chen, S.-P. Hsu, H.-N. Huang, B.-Y. Yang, Time response of a scalar dynamical system with multiple delays via Lambert W functions, arXiv, 2016 (2016), 1-24
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T. Koto, Method of lines approximations of delay differential equations, Comput. Math. Appl., 48 (2004), 45-59
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T. X. Li, B. Baculíková, J. Džurina, C. H. Zhang, Oscillation of fourth-order neutral differential equations with $p$--Laplacian like operators, Bound. Value Probl., 2014 (2014), 1-9
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Q. Li, R. Wang, F. Chen, T. X. Li, Oscillation of second-order nonlinear delay differential equations with nonpositive neutral coefficients, Adv. Difference Equ., 2015 (2015), 1-7
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I. Mezo, G. Keady, Some physical applications of generalized Lambert functions, Eur. J. Phys., 37 (2016), 1-10
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C. P. Vyasarayani, S. Subhash, T. Kalmar-Nagy, Spectral approximations for characteristic roots of delay differential equations, Int. J. Dynam. Control., 2 (2014), 126-132
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P. Wahi, A. Chatterjee, Galerkin projections for delay differential equations, J. Dyn. Syst. Meas. Control., 127 (2005), 80-87
]
On the convergence of double Sumudu transform
On the convergence of double Sumudu transform
en
en
In this article, we have studied the convergence properties of double Sumudu transformation, and we presented the results in the form of theorems on convergence, absolute convergence, and uniform convergence of Double Sumudu transformation. The Double Sumudu transform of double Integral has also been discussed for integral evaluation. Finally, we have solved a Volterra integro-partial differential equation by using Double Sumudu transformation.
154
162
Zulfiqar
Ahmed
Department of Computer Science
GIFT University
Pakistan
dr.zulfiqar.ahmed@hotmail.com
Muhammad Imran
Idrees
Department of Mathematics
Lahore Garrison University
Pakistan
hefacademy@gmail.com
Fethi Bin Muhammad
Belgacem
Department of Mathematics, Faculty of Basic Education
PAAET
Kuwait
fbmbelgacem@gmail.com
Zahida
Perveen
Department of Mathematics
Lahore Garrison University
Pakistan
drzahida95@gmail.com
Double Sumudu transform
inverse Sumudu transform
integro-partial differential equations
Article.4.pdf
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[1]
Z. Ahmed, M. Kalim, A new transformation technique to find the analytical solution of general second order linear ordinary differential equation, Int. J. Adv. Appl. Sci., 5 (2018), 109-114
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F. B. M. Belgacem, Introducing and analysing deeper Sumudu properties, Nonlinear Stud., 13 (2006), 23-41
##[3]
F. B. M. Belgacem, Applications of Sumudu transform to indefinite periodic parabolic equations, 6th International Conference on Mathematical Problems in Engineering and Aerospace Sciences (Cambridge, U. K.), 2007 (2007), 51-60
##[4]
F. B. M. Belgacem, Sumudu applications to Maxwell's equations, PIERS Online, 5 (2009), 355-360
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F. B. M. Belgacem, Sumudu transform applications to Bessel's Functions and Equations, Appl. Math. Sci., 4 (2010), 3665-3686
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F. B. M. Belgacem, E. H. N. Al-Shemas, Towards a Sumudu based estimation of large scale disasters environmental fitness changes adversely affecting population dispersal and persistence, AIP Conference Proceedings, 2014 (2014), 1442-1449
##[7]
F. B. M. Belgacem, A. A. Karaballi, Sumudu transform fundamental properties investigations and applications, J. Appl. Math. Stoch. Anal., 2006 (2006), 1-23
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F. B. M. Belgacem, A. A. Karaballi, S. L. Kalla, Analytical investigations of the Sumudu transform and applications to integral production equations, Math. Probl. Eng., 2003 (2003), 103-118
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F. B. M. Belgacem, R. Silabarasan, A distinctive Sumudu treatment of trigonometric functions, J. Comput. Appl. Math., 312 (2017), 74-81
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F. B. M. Belgacem, R. Silambarasan, Sumudu transform of Dumont bimodular Jacobi elliptic functions for arbitrary powers, AIP Conference Proceedings, 2017 (2017), 1-13
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R. R. Dhunde, G. L. Waghmare, On Some Convergence Theorems of Double Laplace Transform, J. Infor. Math. Sci., 6 (2014), 45-54
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P. Goswami, F. B. M. Belgacem, Solving Special Fractional Differential Equations by Sumudu Transform, AIP Conference Proceedings, 2012 (2012), 111-115
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M. I. Idrees, Z. Ahmed, M. Awais, Z. Perveen, On the convergence of double Elzaki transform, Int. J. Adv. Appl. Sci., 5 (2018), 19-24
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M. Mohseni Moghadam, H. Saeedi, Application of differential transforms for solving the Volterra integro-partial differential equations, Iran. J. Sci. Technol. Trans. A Sci., 34 (2010), 59-70
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W. F. Trench, Functions defined by Improper Integrals, Trinity University (Department of Mathematics), San Antonio (2012)
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G. K. Watugala, Sumudu transform---a new integral transform to solve differential equations and control engineering problems, Math. Engrg. Indust., 6 (1998), 319-329
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D. V. Widder, Advanced Calculus, Prentice-Hall, Englewood Cliffs (1961)
]
Fixed point theorems for rational type (\(\alpha \)-\(\Theta \))-contractions in controlled metric spaces
Fixed point theorems for rational type (\(\alpha \)-\(\Theta \))-contractions in controlled metric spaces
en
en
This paper aims to define rational type (\(\alpha \)-\(\Theta \))-contraction in controlled metric space and obtain some advanced fixed
point theorems. The outcomes generalize and extend various famous results in the
literature. An example and certain consequences are presented to illustrate
the significance of established results.
163
170
Jamshaid
Ahmad
Department of Mathematics
University of Jeddah
Saudi Arabia
jkhan@uj.edu.sa
Durdana
Lateef
Department of Mathematics, College of Science
Taibah University
Kingdom of Saudi Arabia
drdurdanamaths@gmail.com
Fixed point
rational type (\(\alpha \)-\(\Theta \))-contraction
controlled metric spaces
Article.5.pdf
[
[1]
T. Abdeljawad, N. Mlaiki, H. Aydi, N. Souayah, Double Controlled Metric Type Spaces and Some Fixed Point Results, Mathematics, 6 (2018), 1-10
##[2]
J. Ahmad, A. S. Al-Rawashdeh, A. Azam, Fixed point results for $\{\alpha, \xi \}$-expansive locally contractive mappings, J. Inequal. Appl., 2014 (2014), 1-10
##[3]
J. Ahmad, A. Al-Rawashdeh, A. Azam, New fixed point theorems for generalized $F$-contractions in complete metric spaces, Fixed Point Theory Appl., 2015 (2015), 1-18
##[4]
B. Alqahtani, E. Karapinar, A. Öztürk, On ($\alpha-\psi $)-$K$-contractions in the extended $b$-metric space, Filomat, 32 (2018), 5337-5345
##[5]
M. Arshad, A. Hussain, Fixed point results for generalized rational $\alpha$-Geraghty contraction, Miskolc Math. Notes, 18 (2017), 611-621
##[6]
Z. Aslam, J. Ahmad, N. Sultana, New common fixed point theorems for cyclic compatible contractions, J. Math. Anal., 8 (2017), 1-12
##[7]
A. Azam, N. Mehmood, J. Ahmad, S. Radenović, Multivalued fixed point theorems in cone $b$-metric spaces, J. Inequal. Appl., 2013 (2013), 1-9
##[8]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181
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S. Czerwik, Contraction mappings in $b$-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11
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H. P. Huang, S. Radenović, Some fixed point results of generalised Lipschitz mappings on cone b-metric spaces over Banach algebras, J. Comput. Anal. Appl., 20 (2016), 566-583
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L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476
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N. Hussain, C. Vetro, F. Vetro, Fixed point results for $\alpha$-implicit contractions with application to integral equations, Nonlinear Anal. Model. Control, 21 (2016), 362-378
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M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 1-8
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T. Kamran, M. Samreen, Q. UL Ain, A generalization of $b$-metric space and some fixed point theorems, Mathematics, 5 (2017), 1-7
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M. A. Kutbi, J. Ahmad, A. Azam, On fixed points of $\alpha-\psi$-contractive multi-valued mappings in cone metric spaces, Abst. Appl. Anal., 2013 (2013), 1-13
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N. Mlaiki, H. Aydi, N. Souayah, T. Abdeljawad, Controlled Metric Type Spaces and the Related Contraction Principle, Mathematics, 6 (2018), 1-7
##[17]
W. Onsod, T. Saleewong, J. Ahmad, A. E. Al-Mazrooei, P. Kumam, Fixed points of a $\Theta$--contraction on metric spaces with a graph, Commun. Nonlinear Anal., 2 (2016), 139-149
##[18]
A. Shoaib, P. Kumam, A. Shahzad, S. Phiangsungnoen, Q. Mahmood, Fixed point results for fuzzy mappings in a $b$-metric space, Fixed Point Theory Appl., 2018 (2018), 1-12
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D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-6
]
Global asymptotic stability of the fractional differential equations
Global asymptotic stability of the fractional differential equations
en
en
In this note, we present a global asymptotic stability criterion for the fractional differential equations in triangular form. We use the Caputo generalized fractional derivative in our investigations. In our note, we introduce a new procedure to study the global asymptotic stability of the fractional differential equations.
171
175
Ndolane
Sene
Laboratoire Lmdan, Departement de Mathematiques de la Decision
Universite Cheikh Anta Diop de Dakar
Senegal
ndolanesene@yahoo.fr
Caputo left generalized fractional derivative
fractional differential equations with input
Mittag-Leffler input stability
Article.6.pdf
[
[1]
T. Abdeljawad, F. Madjidi, F. Jarad, N. Sene, On Dynamic Systems in the Frame of Singular Function Dependent Kernel Fractional Derivatives, Mathematics, 7 (2019), 1-13
##[2]
Y. Adjabi, F. Jarad, T. Abdeljawad, On generalized fractional operators and a Gronwall type inequality with applications, Filomat, 31 (2017), 5457-5473
##[3]
A. Ben Makhlouf, Stability with respect to part of the variables of nonlinear Caputo fractional differential equations, Math. Commun., 23 (2018), 119-126
##[4]
Y. Y. Gambo, R. Ameen, F. Jarad, T. Abdeljawad, Existence and uniqueness of solutions to fractional differential equations in the frame of generalized Caputo fractional derivatives, Adv. Difference Equ., 2018 (2018), 1-13
##[5]
F. Jarad, T. Abdeljawad, A modified laplace transform for certain generalized fractional operators, Results Nonlinear Anal., 2 (2018), 88-98
##[6]
F. Jarad, E. Uğurlu, T. Abdeljawad, D. Baleanu, On a new class of fractional operators, Adv. Difference Equ., 1 (2017), 1-16
##[7]
U. N. Katugampola, New approach to a generalized fractional integral, Appl. Math. Comput., 218 (2011), 860-865
##[8]
N. Sene, Exponential form for lyapunov function and stability analysis of the fractional differential equations, J. Math. Computer Sci., 18 (2018), 388-397
##[9]
N. Sene, Lyapunov characterization of the fractional nonlinear systems with exogenous input, Fractal Fract., 2 (2018), 1-10
##[10]
N. Sene, Fractional input stability for electrical circuits described by the Riemann-Liouville and the Caputo fractional derivatives, AIMS Math., 4 (2019), 147-165
##[11]
N. Sene, Fractional input stability and its application to neural network, Discrete Contin. Dyn. Syst. Ser. S, 13 (2019), 853-865
##[12]
N. Sene, Mittag-Leffler input stability of fractional differential equations and its applications, Discrete Contin. Dyn. Syst. Ser. S, 13 (2019), 867-880
##[13]
N. Sene, Stability analysis of the generalized fractional differential equations with and without exogenous inputs, J. Nonlinear Sci. Appl., 12 (2019), 562-572
##[14]
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]