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2012
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A Numerical Approach of a Family of Smoluchowskis Equations by Use of Adomian Decomposition Method
A Numerical Approach of a Family of Smoluchowskis Equations by Use of Adomian Decomposition Method
en
en
The Smoluchowski's equation as a partial differential equation models the diffusion and binary coagulation of a large collection of tiny particles. The mass parameter, indexed either by positive integers, or positive real’s, corresponds to the discrete or continuous form of the equations. In this article, we try to use the Adomian's decomposition method (ADM) to approximate the solution of the homogeneous Smolochowski's equation with different kernels. Some test problems have been included to show the accuracy of the method.
514
522
Mohammad Reza
Yaghouti
Marzie
Malzoumati
Haman
Deilami
Adomian's decomposition method
the homogeneous Smoluchowski's equation.
Article.1.pdf
[
[1]
G. Adomian, A review of the decomposition method in applied mathematics, J. Math. Anal. Appl., 135 (1998), 501-544
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G. Adomian, Solving frontier problems of physics: the decomposition method, Kluwer Academic Publishers, Boston (1994)
##[3]
J. Biazar, S. M. Shafiof, A simple algorithm for calculating Adomian polynomials, Int. J. Contemp. Math. Sciences, 2 (2007), 975-982
##[4]
Y. Cherruault, G. Adomian, Decomposition methods: a new proof of convergence, Math. Comput. Modeling, 18 (1993), 103-106
##[5]
Y. Cherruault, Convergence of Adomian's method, Kybernetics, 18 (1989), 31-38
##[6]
D. Kaya, I. E. Inan, A convergence analysis of the ADM and an application, Applied Mathematics and Computation, 161 (2005), 1015-1025
##[7]
F. Filbet, P. Laurencot, Numerical simulation of the Smoluchowski coagulation equation, SIAM J. Sci. Comput., 25 (2004), 2004-2028
##[8]
A. Hammond, F. Rezakhanlou, The kinetic limit of a system of coagulating Brownian particles, Archive for Relation Mechanics and Analysis, 185 (2007), 1-67
##[9]
A. Hammond, F. Rezakhanlou, Kinetic limit for a system of coagulating planar Brownian particles, J. Stat. Phys., 123 (2006), 997-1040
##[10]
H. Heidarzadeh, M. Mashinchi Joubari, R. Asghari, Application Of Adomian Decomposition Method To Nonlinear Heat Transfer Equation, J. Math. Comp. Sci., 4 (2012), 436-447
##[11]
Y. C. Jiao, Y. Yamamoto, C. Dong, Y. Hao, An after treatment technique for improving the accuracy of Adomian's decomposition method, Comp. Math. Appl., 43 (2000), 783-798
##[12]
F. Leyvraz, H. R. Tschudi, Singularities in the kinetics of coagulation processes, J. Phys. A., 14 (1981), 3389-3405
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M. Ranjbar, H. Adibi, M. Lakestani, Equilibrium Fluctuations for a Model of Coagulating-Fragmenting Planar Brownian Particles, Commun. Math. Phys., 296 (2010), 769-826
##[14]
A. M. Wazwaz, The decomposition method for approximate solution of the Goursat problem, Applied Mathematics and Computation, Vol. 69, 299--311 (1994)
##[15]
A. M. Wazwaz, A reliable modification of Adomian decomposition method, Appl. Math. Comput., 102 (1999), 77-86
##[16]
A. M. Wazwaz, A new algorithm for calculating Adomian polynomials for nonlinear operators, Appl. Math. Comput., 111 (2000), 53-69
]
Counterexamples in Analysis
Counterexamples in Analysis
en
en
The counterexamples are used for better comprehension of underlying concept in a theorem or definition. This paper is about the counterexamples in Mathematical Analysis, that we construct them to be apparently correct statements by a few change in the conditions of a valid proposition. Our aim in this paper is to present how the counterexamples help to boost the level of understanding of mathematical Analysis concepts.
523
526
S. Alireza
Jalili
Narges Khatoon
Tohidi
Counterexamples
Topological Space
Convergence
Divergence.
Article.2.pdf
[
[1]
P. Alexandrov, H. Hopf, Topologie, Springer, Berlin (1935)
##[2]
S. Banach , Theorie des operations lineaires, Instytut Matematyczny Polskiej Akademi Nauk, Germany (1932)
##[3]
N. Dunford, J. Schwartz, Linear operators, Interscience publishers, New York (1958)
##[4]
B. R. Gelbaum, J. M. H. Olmsted, Counterexamples in Analysis, Dover Holden-Day, Inc., 2003 (2003), -
##[5]
F. Hausdorff, Mengenlehre, Dover Publications, New York (1944)
##[6]
J. Mason, S. Klymchuk, Using counter-examples in calculus, World Scientific, New York (2009)
##[7]
M. I. A. Othman, A. M. S. Mahdy, Differential Transformation Method and Variation Iteration Method for Cauchy Reaction-diffusion Problems, The Journal of Mathematics and Computer Science, 1 (2010), 61-75
##[8]
J. Rashidinia, A. Tahmasebi, Taylor Series Method For The System Of Linear Volterra Integro-differential Equations, J. Math. Computer Sci., 4 (2012), 331-343
]
The Block Aor Iterative Methods for Solving Fuzzy Linear Systems
The Block Aor Iterative Methods for Solving Fuzzy Linear Systems
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en
In this article the block AOR Iterative methods are used for solving fuzzy linear systems. The convergence of the methods and functional relationship between eigenvalues in block AOR is investigated.
527
535
H.
Saberi Najafi
S. A.
Edalatpanah
Fuzzy linear system (FLS)
AOR method
Block AOR
Eigenvalue.
Article.3.pdf
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[1]
J. J. Buckley, Y. Qu, Solving fuzzy equations: a new solution concept, Fuzzy Sets and Systems, 39 (1991), 291-301
##[2]
M. Dehghan, B. Hashemi, Iterative solution of fuzzy linear systems, Appl. Math. Comput., 175 (2006), 645-674
##[3]
S. A. Edalatpanah, The preconditioning AOR method for solving linear equation systems with iterative methods, Dissertation, Lahijan Branch, Islamic Azad University (2008)
##[4]
M. Friedman, M. Ming, A . Kandel, Fuzzy linear systems, Fuzzy Sets and Systems, 96 (1998), 201-209
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M. Ma, M. Friedman, A. Kandel, Duality infuzzy linear systems, Fuzzy Sets and Systems, 109 (2000), 55-58
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A. Hadjidimos, Accelerated overrelaxation method, Math. Comput., 32 (1978), 149-157
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H. Minc, Nonnegative Matrices, John Wiley & Sons, New York (1998)
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S. X. Miao, B. Zheng, K. Wang, Block SOR methods for fuzzy linear systems, J. Appl. Math. Comput., 26 (2008), 201-218
##[9]
S. H. Nasseri, F. Zahmatkesh, Huang method for solving fully fuzzy linear system, The Journal of Mathematics and Computer Science, 1 (2010), 1-5
##[10]
S. H. Nasseri, M. Gholami, Linear System of Equations with Trapezoidal Fuzzy Numbers, The Journal of Mathematics and Computer Science, 3 (2011), 71-79
##[11]
H. Saberi Najafi, S. Kord Rostami, S. A. Edalatpanah, The Convergence Analysis Of Preconditioned AOR Method For M-, H-Matrices, Journal of Applied Mathematics IAUL, 5 (2008), 29-38
##[12]
H. Saberi Najafi, S. A. Edalatpanah, Fast Iterative Method-FIM.Application to the Convection- Diffusion Equation, Journal of Information and Computing Science, 6 (2011), 303-313
##[13]
H. Saberi Najafi , F. Ramezani Sasemasi, S. Sabouri Roudkoli, S. Fazeli Nodehi, Comparison of two methods for solving fuzzy differential equations based on Euler method and Zadeh’s extension, The Journal of Mathematics and Computer Science, 2 (2011), 295-306
##[14]
H. Saberi Najafi, S. A. Edalatpanah, Some Improvements In Preconditioned Modified Accelerated Overrelaxation (PMAOR) Method For Solving Linear Systems, Journal of Information and Computing Science, 6 (2011), 15-22
##[15]
H. Saberi Najafi, S. A. Edalatpanah, On the convergence regions of generalized accelerated overrelaxation method for linear complementarity problems, Journal of Optimization Theory and Applications, Vol. 156, 859--866 (2013)
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H. Saberi Najafi, S. A. Edalatpanah, An Improved Model for Iterative Algorithms in Fuzzy Linear Systems, Computational Mathematics and Modeling, Vol. 24, 433--451 (2013)
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H. Saberi Najafi, S. A. Edalatpanah, Preconditioning Strategy to Solve Fuzzy Linear Systems (FLS), International Review of Fuzzy Mathematics, Vol. 7, 65--80 (2012)
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R. S. Varga, Matrix Iterative Analysis, Springer Science & Business Media, Berlin (2000)
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A. K. Yeyios, A necessary condition for the convergence of the accelerated overrelaxation (AOR) method, J. Comput. Appl. Math., 26 (1989), 371-373
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L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353
]
Ranking Decision Making Units by Compromise Programming
Ranking Decision Making Units by Compromise Programming
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en
Data envelopment analysis (DEA) is a very useful management and decision tool. The ranking of decision making units (DMU) has become an important component in the decision process. In this paper we developed a new method for measuring the efficiency score of Decision-Making Units (DMUs) by using compromise programming. The proposed method calculates distance to the ideal for each DMU. The DMU with shorter distance to the ideal has better efficiency. A numerical example is provided to illustrate the application of the proposed DEA model.
536
541
Majid
Darehmiraki
Zahra
Behdani
Data envelopment analysis
Ideal decision making (IDMU)
Compromise programming
Article.4.pdf
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[1]
P. Anderson, N. C. Petersen, A pdrocedure for ranking efficient units in data envelopment analysis, Management science, 39 (1993), 1261-1264
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A. Charnes, W. W. Cooper, E. Rhodes, Measuring the efficiency of decision making units, Eur. J. Oper. Res., 2 (1978), 429-444
##[3]
F. Hosseinzadeh Lotfi, G. R. Jahanshahloo, A. Memariani, A method for finding common set of weights by multiple objective Programming in data envelopment analysis, Southwest journal of pure and applied mathematics, 1 (2000), 44-54
##[4]
C. Kao, Weight determination for consistently ranking alternatives in multiple criteria decision analysis, Applied Mathematical Modelling, 34 (2010), 1779-1787
##[5]
S. Mehrabian, M. R. Alirezaee, G. R. Jahanshahloo, A complete efficiency ranking of decision making units in data envelopment analysis, Computational optimization and applications, 14 (1999), 261-266
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G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, M. Sanei, Review of ranking models in dataenvelopment analysis, Applied mathematical sciences, 2 (2008), 1431-1448
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G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, N. Shoja, G. Tohidi, S. Razavian, Ranking using norm in data envelopment analysis, Applied mathematics and computational, 153 (2004), 215-224
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G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, F. Rezai Balf, H. Zhiani Rezai, D. Akbarian, Ranking efficient DMUs using tchebycheff norm, Working Paper, Iran (2004)
##[9]
G. R. Jahanshahloo, M. Sanei, F. Hosseinzadeh Lotfi, N. Shoja, Using the gradient line for ranking DMUs in DEA, Applied mathematics and computation, 151 (2004), 209-219
##[10]
G. R. Jahanshahloo, M. Sanei, N. Shoja, Modified ranking models, using the concept of advantage in data envelopment analysis, Working paper, Iran (2004)
##[11]
G. R. Jahanshahloo, F. Hosseinzadeh Lotfi, F. Rezai Balf, H. Zhiani Rezai, Using Monte Carlo method for ranking efficient DMUs, Aplied Mathematic and Computation, 162 (2005), 371-379
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M. S. Saati, M. Zarafat Angiz, G. R. Jahanshahloo, A model for ranking decision making units in data envelopment analysis, Recrca operative, Vol. 31 (2001)
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T. Sueyoshy, DEA nonparametric ranking test and index measurement: Slack-adjusted DEA and an application to Japanese agriculture cooperatives, Omega, 27 (1999), 315-326
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K. Tone, A slack-Based measure of efficiency in data envelopment Analysis, Eur. J. Oper. Res., 130 (2001), 498-509
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K. Tone, A slacks-based measure of efficiency in data envelopment analysis, Eur. J. Oper. Res., 143 (2002), 32-41
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Y.-M. Wang, Y. Luo, DEA efficiency assessment using ideal anti-ideal decision making units, Applied mathematics and computation, 173 (2006), 902-915
]
Quasilinearization and Numerical Solution of Nonlinear Volterra Integro-differential Equations
Quasilinearization and Numerical Solution of Nonlinear Volterra Integro-differential Equations
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en
When we use the projection methods in order to obtain the approximation solution of nonlinear equations, we always have some difficulties such as solving nonlinear algebraic systems. The method of generalized quasilinearization when is applied to the nonlinear integro-differential equations of Volterra type, gives two sequences of linear integro-differential equations with solutions monotonically and quadratically convergent to the solution of nonlinear equation. In this paper we employ step-by-step collocation method to solve the linear equations numerically and then approximate the solution of the nonlinear equation. In this manner we do not encounter solving nonlinear algebraic systems. Error analysis of the method is performed and to show the accuracy of the method some numerical examples are proposed.
542
553
M. N.
Rasoulizadeh
Volterra integro-differential equation
Collocation method
Quasilinearization technique.
Article.5.pdf
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[1]
R. Bellman, R. Kalaba, Quasilinearization and Nonlinear Boundary Value Problems, Elsevier, New York (1965)
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J. Jiang, A. S. Vatsala, The Quasilinearization Method in the System of Reaction Diffusion Equations, Appl. Math. Comput., 97 (1998), 223-235
##[3]
J. I. Ramos, Piecewise-quasilinearization Techniques for Singularly Perturbed Volterra Integro-differential Equations, Appl. Math. Comput., 188 (2007), 1221-1233
##[4]
B. Ahmad, A Quasilinearization Method for a Class of Integro-differential Equations with Mixed Nonlinearities, Nonlinear Anal: Real World Appl., 7 (2006), 997-1004
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S. G. Pandit, Quadratically Converging Iterative Schemes for Nonlinear Volterra Integral Equations and an Application, Journal of Applied Mathematics and Stochastic Analysis, 10 (1997), 169-178
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K. Maleknejad, E. Najafi, Numerical Solution of Nonlinear Volterra Integral Equations Using the Idea of Quasilinearization, Commun. Nonlinear. Sci. Numer. Simulat., 16 (2011), 93-100
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V. Lakshmikantham, An Extension of the Method of Quasilinearization, J. Optim. Theory Appl., 82 (1994), 315-321
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V. Lakshmikantham, N. Shahzad, J. J. Nieto, Methods of Generalized Quasilinearization for Periodic Boundary Value Problems, Nonlinear Anal., 27 (1996), 143-151
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Z. Drici, F. A. McRae, J. V. Devi, Quasilinearization for Functional Differential Equations with Retardation and Anticipation, Nonlinear Anal., 70 (2009), 1763-1775
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H. R. Erfanian, T. Mostahsan, Approximate Solution of a Class of Nonlinear Volterra Integral Equations, The Journal of Mathematics and Computer Science, 3 (2011), 278-286
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M. Bakhshi, M. Asghari-Larimi, M. Asghari-Larimi, Three-Dimensional Differential Transform Method for Solving Nonlinear Three-Dimensional Volterra Integral Equations, The Journal of Mathematics and Computer Science, 2 (2012), 246-256
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]
Cellular Automata Approach in Optimum Shape of Concrete Arches under Dynamic Loads
Cellular Automata Approach in Optimum Shape of Concrete Arches under Dynamic Loads
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en
Traditional methods in determination of optimum shape of structures don’t scale well. This paper discusses the application of cellular automata (CA) to study of optimum shape in concrete arches under dynamic loads by cellular automata and presents a novel approach for that. In this paper, samples of semi-circular, obtuse angel, four- centered pointed, Tudor, ogee, equilateral, catenaries, lancet and four-centered arches are modeled. Then they are analyzed and optimized under acceleration–time components of Elcentro earthquake. Using cellular automata model and provided rules, the mentioned arches are analyzed and optimized. The results of error range and time of analysis in cellular automata model and FEM software compared. According the results, in CA method, precision is less but it has less time of analysis and optimization .
554
569
Afsaneh
Banitalebi Dehkordi
Kaveh
Kumarci
optimum shape
arch
concrete
dynamic load
tensile stress
cellular automata.
Article.6.pdf
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A. Gupta, S .Taylor, J. Kirkpatrick, A. Long, I. Hogg, A Flexible Concrete Arch System, Colloquium on Concrete Research in Ireland, Ireland (2005)
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M. Baei, M. Ghassemieh, A. Goudarzi, Numerical modeling of end- plate moment connection subjected to bending and axial forces, The Journal of Mathematics and Computer Science, 463--472 (2012)
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B. O. Caglayan, K. Ozakgul, O. Tezer, Assessment of a concrete arch bridge using static and dynamic load tests, ournal of Structural Engineering and Mechanics, 41 (2012), 83-99
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K. Kumarci, A. Ziaie, Optimum Shape In Brick Masonry Arches Under Static And Dynamic Loads, International Journal Of Mathematics And Computers, 7 (2008), 171-178
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K. Kumarci, P. Khosravyan, Optimum Shape In Brick Masonry Arches Under Dynamic Loads By Cellular Automata, Journal Of Civil Engineering (IEB), 37 (2009), 73-90
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A. Yarahmadi, N. Moarefi, Implementation of Cellular Automata with non- identical rule on serial base, The journal of mathematic and computer science, 4 (2012), 264-269
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]
Investigation of the Effect of Earthquake on Concrete Minaret under Static Loads Using Genetic Programing
Investigation of the Effect of Earthquake on Concrete Minaret under Static Loads Using Genetic Programing
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en
Minarets are special structures commonly used in Islamic architectures. The seismic behaviors of minarets is quite different from that the other well known structures because of their unique structural characteristics such as slenderness, distinctive geometrical shape and support system. Post earthquake observations indicate that there is a direct relationship between site selection and overall minaret behavior and damage. This study investigates the seismic response of cylindrical concrete minarets with circular cross section under static loads using genetic programing. Using SAP 2000 software, considered minarets were analyzed. At the first phase of study, according to regulation of designing of structures against earthquake (regulation No.2800), minarets dynamic responses were determined by a hand-operated analysis. Seismic analysis were carried out considering the design spectra defined by Iran structure design codes in Naqan, Shahr-e-kord. On the base of hand-operated and SAP2000 calculations the shear base and maximum lateral displacements were estimated.
570
584
Kaveh
Kumarci
Afsaneh
Banitalebi Dehkordi
Minaret
genetic programing
static loads
modeling
SAP2000 software.
Article.7.pdf
[
[1]
A. C. Altunisik, Dynamic response of masonry minarets strengthened with fiber reinforced polymer (FRP) composites, Natural Hazards and Earth System Sciences, 11 (2011), 2011-2019
##[2]
M. Baei, M. Ghassemieh, A. Goudarzi, Numerical modeling of end-plate moment connection subjected to bending and axial forces, The Journal Mathematics and Computer Science, 4 (2012), 463-472
##[3]
A. Dogangun, H. Sezen, O. Tuluk, R. Livaoglu, R. Acar, Traditional Turkish masonry monumental structures and their earthquake response, International Journal of Architectural Heritage, 3 (2007), 251-271
##[4]
A. G. El- Attar, A. M. Saleh, A. Osman, Seismic Response of a historical Mamluk style minaret, WIT Transactions on The Built Environment, 57 (2001), 745-754
##[5]
J. H. Holland, D. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Massachusetts (1989)
##[6]
J. R. Koza, Genetic programming: on the programming of computers by means of natural selection, M.I.T. Press, Cambridge (1992)
##[7]
M. Mashinchi Joubari, R. Asghari, M. Zareian Jahromy, Investigation of the dynamic behavior of periodic systems with Newton harmonic balance method, Journal of Mathematics and Computer Science, 4 (2012), 418-427
##[8]
A. Menon, C. G. Lai, G. Macchi, Seismic hazard assessment of historical site of Jam in Afghanistan and stability analysis of minaret, Journal of Earthquake Engineering, 8 (2004), 251-293
##[9]
M. Mitchell, An Introduction to Genetic Algorithms, M.I.T. Press, Cambridge (1996)
##[10]
D. J. Montana, Strongly typed genetic programing, M.I.T Press, Cambridge (2002)
##[11]
Q. N. Nguyen, X. H. Neguyen, M. O'Neill, Semantic aware crossover for genetic programing: the case for real- valued function regression, European Conference on Genetic Programming (Berlin), 2009 (2009), 292-302
##[12]
H. Sezen, R. Acar, A. Dogangun, R. Livaoglu, Dynamic analysis and seismic performance of reinforced concrete minarets, engineering structures, Engineering Structures, 30 (2008), 2253-2264
##[13]
C. A. Syrmakezis, Seismic protection of historical structures and monuments, Structural Control and Health Monitoring, 13 (2006), 958-979
##[14]
A. Ziaie, M. B. Rahnama, Calculation of Concrete Minaret Frequency by Neural Network, Journal of Environmental Science and Technology, 2 (2009), 48-55
]
A Unique Common Fixed Point Theorem for Three Mappings in G--Cone Metric Spaces
A Unique Common Fixed Point Theorem for Three Mappings in G--Cone Metric Spaces
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en
In this paper we obtain a unique common fixed point theorem for three mappings in G-cone metric spaces and obtain an extension and improvement of a theorem of I. Beg et. al. [ 1 ].
585
590
K. P. R.
Rao
K. Bhanu
Lakshmi
V. C. C.
Raju
G – cone metric space
common fixed points
symmetric space.
Article.8.pdf
[
[1]
I. Beg, M. Abbas, T. Nazir, Generalized cone metric spaces, J. Nonlinear Sci. Appl., 3 (2010), 21-31
##[2]
L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476
##[3]
S. Rezapour, R. Hamlbarani, Some notes on the paper “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 345 (2008), 719-724
##[4]
Z. Mustafa, B. Sims, A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis, 7 (2006), 289-297
##[5]
G. Jungck, S. Radenovic, S. Radojevic, V. Rakocevic, Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed point theory Appl., 2009 (2009), 1-13
##[6]
S. Jain, S. Jain, L. Bahadur, Compatibility and weak compatibility for four self maps in a cone metric space, Bulletin of Mathematical Analysis and Applications, 2 (2010), 15-24
]