]>
2008
1
4
ISSN 2008-1898
50
COMMENT ON AND A CHARACTERIZATION OF THE CONCEPT OF COMPLETE RESIDUATED LATTICE
COMMENT ON AND A CHARACTERIZATION OF THE CONCEPT OF COMPLETE RESIDUATED LATTICE
en
en
We prove that some properties of the definition of complete residuated lattice [2,4] can be derived from the other properties. Furthermore we
prove that the concept of strictly two-sided commutative quantale [1,3] and
the concept of complete residuated lattice are equivalent notions.
203
205
FATHEI M.
ZEYADA
Center of Mathematics and Theoretical Computer Sciences Assiut, Egypt
M. A.
ABD-ALLAH
Department of Mathematics, Faculty of Science, Al Azhar University, Assiut, Egypt
Complete residuated lattice
Quantale
Complete MV-algebra.
Article.1.pdf
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[1]
U. Höhle , Characterization of L-topologies by L-valued neighborhoods, in: U. Höhle, S.E.Rodabaugh (Eds.), The Handbooks of Fuzzy Sets Series, Kluwer ACademic Publishers, Dordrecht, 3 (1999), 389-432
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J. Pavelka, On fuzzy logic II, Z. Math. Logic Gvundlagen Math., 25 (1979), 119-134
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K. I. Rosenthal, Quantales and their applications, Pitman Research Notes in Mathematics 234(Longman, Burnt Mill, Harlow )., (1990)
##[4]
M. S. Ying, Fuzzifying topology based on complete residuated lattice-valued logic (I), Fuzzy Sets and Systems , 56 (1993), 337-373
]
EXISTENCE AND UNIQUENESS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS
EXISTENCE AND UNIQUENESS OF FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL BOUNDARY CONDITIONS
en
en
In this article, the recently developed monotonous iterative method
is used to investigate fractional differential equations involving Riemann-Liouville
differential operators with integral boundary conditions. The existence and
uniqueness of solutions are obtained.
206
212
TAIGE
WANG
Department of Applied Mathematics, Donghua University, Shanghai 201620, China.
FENG
XIE
Department of Applied Mathematics, Donghua University, Shanghai 201620, China.
Fractional differential equations
integral boundary condition
monotonous iterative method.
Article.2.pdf
[
[1]
J. H. He, Nonlinear oscillation with fractional derivative and its applications, International Conference on Vibrating Engineering, , Dalian, China, (1998), 288-291
##[2]
J. H. He, Some applications of nonlinear fractional differential equations and their approximations, Bull. Sci. Technol., 15 (1999), 86-90
##[3]
J. H. He , Approximate analytical solution for seepage flow with fractional derivatives in porous media, Computer Methods in Applied Mechanics and Engineering , 167 (1998), 57-68
##[4]
J. H. He, X. H. Wu, Variational iteration method: New development and applications, Computers & Mathematics with Applications , 54 (2007), 881-894
##[5]
T. Jankwoski, Differential equations with integral boundary conditions, Journal of Computational and Applied Mathematic, 147 (2002), 1-8
##[6]
V. Lakshmikantham, A. S. Vatsala , Basic theory of fractional differential equation, Nonlinear Anal. TMA, 69 (2008), 2677-2682
##[7]
V. Lakshmikantham, A. S. Vatsala, General uniqueness and monotone iterative technique for fractional differential equations, Appl. Math. Lett., 21 (2008), 828-834
##[8]
V. Lakshmikantham, A. S. Vatsala, Theory of fractional differential inequalities and applications, Communications in Applied Analysis., 11 (2007), 395-402
##[9]
S. Momani, Z. Odibat , Numerical comparison of methods for solving linear differential equations of fractional order, Chaos Solitons & Fractals, 31 (2007), 1248-1255
##[10]
Z. Odibat, S. Momani, Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order, Chaos Solitons & Fractals , 36 (2008), 167-174
##[11]
Z. Odibat, S. Momani, Application of variational iteration method to nonlinear differential equations of fractional order, International Journal of Nonlinear Sciences and Numerical Simulation, 7 (2006), 27-34
##[12]
Z. Odibat, Solitary solutions for the nonlinear dispersive K(m,n) equations with fractional time derivatives, Physics Letters , A 370 (2007), 295-301
##[13]
I. Podlubny , Fractional Differential Equations , Academic Press, San Diego (1999)
##[14]
S. G. Samko, A. A. Kilbas, O. I. Marichev , Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach, New York (1993)
##[15]
Q. Wang, Homotopy perturbation method for fractional KdV-Burgers equation, Chaos Solitons & Fractals , 35 (2008), 843-850
]
ON 2-STRONG HOMOMORPHISMS AND 2-NORMED HYPERSETS IN HYPERVECTOR SPACES
ON 2-STRONG HOMOMORPHISMS AND 2-NORMED HYPERSETS IN HYPERVECTOR SPACES
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en
In this paper the notion of a 2-normed hyperset in hypervector
spaces is introduced. Also we construct some special 2-normed hypersets
of strong homomorphisms over hypervector spaces. Among other results we
consider 2-strong homomorphisms and investigate some of their properties.
213
223
P.
RAJA
Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Hafez Ave., P. O. Box 15914, Tehran, Iran. Fax: +98-21-66497930.
S. M.
VAEZPOUR
Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Hafez Ave., P. O. Box 15914, Tehran, Iran. Fax: +98-21-66497930.
invex set
invex set
Hypervector space
Strong homomorphism.
Article.3.pdf
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[1]
S. Gähler, Linear 2-normierte Rume, Math. Nachr. , 28 (1964), 1-43
##[2]
Z. Lewandowska , Linear operators on generalized 2-normed spaces, Bull. Math. Soc. Sci. Math. Roumanie, 42 (1999), 353-368
##[3]
Z. Lewandowska , On 2-normed sets, Glasnik Matematicki, 38(58) (2003), 99-110
##[4]
Z. Lewandowska, Bounded 2-linear operators on 2-normed sets, Glasnik Matematicki, 39(59) (2004), 301-312
##[5]
C. S. Lin, On strictly convex and strictly 2-convex 2-normed spaces, Math. Nachr, 149 (1990), 149-154
##[6]
A. Misiak, n-inner product spaces, Math. Nachr., 140 (1989), 299-319
##[7]
P. Raja, S. M. Vaezpour, Normed Hypervector Spaces, , 2 (2007), 35-44
##[8]
P. Raja, S. M. Vaezpour, Strong Homomorphisms and Linear Functionals in Normed Hypervector Spaces, , (submitted), -
##[9]
P. Raja, S. M. Vaezpour , Convexity in Normed Hypervector Spaces, Ital. J. Pure Appl. Math., 28 (2011), 7-16
##[10]
M. Scafati Tallini , A-ipermoduli e spazi ipervettoriali, Rivisita di Mat. Pura e Appl., Univ. Udine, 3 (1988), 39-48
##[11]
A. White, 2-Banach spaces, Math. Nachr. , 42 (1969), 43-60
]
NEW SOLITONS AND PERIODIC SOLUTIONS FOR THEKADOMTSEV-PETVIASHVILI EQUATION
NEW SOLITONS AND PERIODIC SOLUTIONS FOR THEKADOMTSEV-PETVIASHVILI EQUATION
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en
In this paper, the sine-cosine, the standard tanh and the extended tanh methods has been used to obtain solutions of the Kadomstev-
Petviashvili(KP) equation. New solitons solutions and periodic solutions are
formally derived. The change of parameters, that will drastically change characteristics of the equation, is examined.
224
229
A.
BORHANIFAR
Department of Mathematics, University of Mohaghegh Ardabili,Ardabil, Iran.
H.
JAFARI
Department of Mathematics and Computer science, University of Mazandaran,P. O. BOX 47416-95447 Babolsar, Iran.
S. A.
KARIMI
Department of Mathematics, University of Mohaghegh Ardabili,Ardabil, Iran.
The sine-cosine method
The standard tanh and the extended tanh methods
The Kadomtsev-Petviashvili equation.
Article.4.pdf
[
[1]
W. Malfliet, W . Hereman, The tanh method: I Exact solution of nonlinear evolution and wave equation , Phys. Scr., 54 (1996), 563-568
##[2]
W. Malfliet, W . Hereman, The tanh method: II Perturbation technique for conservative system, Phys. Scr., 54 (1996), 569-575
##[3]
A. M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema, Rotterdam (2002)
##[4]
A. M. Wazwaz, Dustinct variants of the KdV equation with compact and noncompact structures, Appl. Math. Comput., 150 (2004), 365-377
##[5]
A. M. Wazwaz, Variants of the generalized KdV eauation with compact and noncompact structures, Comput. Math. Appl., 47 (2004), 583-591
##[6]
A. M. Wazwaz, An analytical study of the compactons structures in a class of nonlinear dispersive equation, Math Comput Simulation, 63(1) (2003), 35-44
##[7]
A. M. Wazwaz, A computational approachto soliton solutions of the Kadomtsev-Petviashili equation, Comput. Math. Appl., 123(2) (2001), 205-217
##[8]
A. M. Wazwaz, The extended tenh method for Zhakharov-Kkuznetsov (ZK) equation, the modified ZK equation and its generalized forms, Communications in Nonlinear Science and Numerical Simulation, 13(6) (2008), 1039-1047
##[9]
A. M. Wazwaz, Multiple-front solutions for the Burgers-Kadomtsev-petviashvili equation, Applied Mathematics and Computation, 200 (2008), 437-443
]
FUZZY NONLINEAR OPTIMIZATION
FUZZY NONLINEAR OPTIMIZATION
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en
In this paper, we define a fuzzy version of the quadratic optimization problem and then give a method to solve these problems by using linear
ranking functions. The method will be discussed in details.
230
235
S.H.
NASSERI
Department of Mathematics, Mazandaran University, Babolsar, Iran.
Fuzzy numbers
ranking function
quadratic programming.
Article.5.pdf
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[1]
M. Bazaraa, H. Sherali, C. M. Shetty, Nonlinear Programming: Theory and Algorithms, Third Edition, John Wiley, (2006)
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N. Mahdavi-Amiri, S. H. Nasseri , Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables, Fuzzy Sets and Systems , 158 (2007), 1961-1978
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N. Mahdavi-Amiri, S. H. Nasseri, Duality in fuzzy number linear programming by use of a certain linear ranking function, Applied Mathematics and Computation , 180 (2006), 206-216
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H. R. Maleki, M. Tata, M. Mashinchi, Linear programming with fuzzy variables, Fuzzy Sets and Systems , 109 (2000), 21-33
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]
ON DECOMPOSITION OF FUZZY A-CONTINUITY
ON DECOMPOSITION OF FUZZY A-CONTINUITY
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en
In this paper, we introduce and study the notion of fuzzy \(C\)-sets
and fuzzy \(C\)-continuity. We also prove a mapping \(f : X \rightarrow Y\) is fuzzy
\(A\)-continuous if and only if it is both fuzzy semi-continuous and fuzzy \(C\)-continuous.
236
240
S.
JAFARI
College of Vestsjaelland South Herrestrade 11 4200 Slagelse Denmark.
K.
VISWANATHAN
Post Graduate and Research Department of Mathematics N G M College Pollachi-642 001 Tamilnadu, INDIA.
M.
RAJAMANI
Post Graduate and Research Department of Mathematics N G M College Pollachi-642 001 Tamilnadu, INDIA.
S.
KRISHNAPRAKASH
Post Graduate and Research Department of Mathematics N G M College Pollachi-642 001 Tamilnadu, INDIA.
fuzzy A-set
fuzzy C-set
fuzzy A-continuity
fuzzy C-continuity.
Article.6.pdf
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K. K. Azad, On fuzzy semi-continuity, fuzzy almost continuity, J. Math. Anal. Appl., 87 (1981), 14-32
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A. S. Bin Shahana, On fuzzy strong semi-continuity and fuzzy pre-continuity, Fuzzy sets and system, 44 (1991), 303-308
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M. S. El-Naschie, On the uncertanity of cantorian geometry and the two-slit experiment, Chaos, Solitons and fractals , 9(3) (1998), 517-529
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M. S. El-Naschie, On the certification of heterotic strings, M theory and \(\varepsilon^\infty\) theory, chaos, Solitons and fractals , (2000), 2397-2408
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Y. Erguang, Y. Pengfei, On decomposition of A-continuity, Acta Math. Hunger., 110(4) (2006), 309-313
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M. Ganster, I. L. Reilly, A decomposition of continuity, Acta Math. Hunger., 56 (1990), 299-301
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M. Rajamani, M. Ambika, Another decomposition of fuzzy continuity in fuzzy topological spaces, Proc. Of Annual Conference of KMA and National Seminar on Fuzzy Mathematics and Applications, Payyanur College, Payyanur, Jan , 8-10 (2004), 41-48
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J. Tong , A decomposition of fuzzy continuity, Fuzzy Math, 7 (1987), 97-98
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L. A. Zadeh, Fuzzy sets, Inform. and Control , 8 (1965), 338-353
]
ON \(\Phi\)-FIXED POINT FOR MAPS ON UNIFORM SPACES
ON \(\Phi\)-FIXED POINT FOR MAPS ON UNIFORM SPACES
en
en
The concept of fixed point is extended to \(\Phi\)-fixed point for those
maps on uniform spaces. Two results are presented, first for single-valued maps
and second for set-valued maps.
241
243
M.
ALIMOHAMMADY
Department of Mathematics, University of Mazandaran, Babolsar, Iran.
M.
RAMZANNEZHAD
Department of Mathematics, University of Mazandaran, Babolsar, Iran.
Uniform space
\(\Phi\)-fixed point
Single-valued
set-valued.
Article.7.pdf
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[1]
M. Alimohammady, M. Roohi, Fixed point in minimal spaces, Nonlinear Analysis:Moddeling and Control, 10/4 (2005), 305-314
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A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Sci, 29 (2002), 531-536
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H. Covitz, S. B. Nadler Jr, Multi-valued contraction mappings in generalized metric space, Israel J. Math. , 8 (1970), 5-11
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Lj. B. Ciric, Fixed point theorems in topological spaces, Fund. Math. , 87 (1975), 1-5
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A. P. Robertson, W. Robertson, Topological Vector Spaces, Cambridge University Press, (1973)
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M. A. Khamsi, W. A. Kirk, An introduction to metric spaces and fixed point theory, John Wiely.(MR1818603), New Yourk (2001)
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B. T. Sims , Fundamentals of topologics, Macmillan publishing co., Inc., New York (1976)
]
LOCAL CONVERGENCE ANALYSIS FOR A CERTAIN CLASS OF INEXACT METHODS
LOCAL CONVERGENCE ANALYSIS FOR A CERTAIN CLASS OF INEXACT METHODS
en
en
We provide a local convergence analysis for a certain class inexact
methods in a Banach space setting, in order to approximate a solution of a
nonlinear equation [6]. The assumptions involve center-Lipschitz-type and
radius-Lipschitz-type conditions [15], [8], [5]. Our results have the following
advantages (under the same computational cost): larger radii, and finer error
bounds on the distances involved than in [8], [15] in many interesting cases.
Numerical examples further validating the theoretical results are also provided in this study.
244
253
IOANNIS K.
ARGYROS
Cameron university, Department of Mathematics Sciences, Lawton, OK 73505, USA.
SAÏD
HILOUT
Poitiers university, Laboratoire de Mathématiques et Applications, Bd. Pierre et Marie Curie, Téléport 2, B.P. 30179, 86962 Futuroscope Chasseneuil Cedex, France.
Inexact Newton method
Banach space
Local convergence
Convergence radii.
Article.8.pdf
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[1]
I. K. Argyros, The theory and application of abstract polynomial equations, St.Lucie/CRC/Lewis Publ. Mathematics series, , Boca Raton, Florida, U.S.A. (1998)
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I. K. Argyros, Relation between forcing sequences and inexact Newton iterates in Banach space, Computing, 63 (1999), 131-144
##[3]
I. K. Argyros, Forcing sequences and inexact Newton iterates in Banach space, Appl. Math. Lett., 13 (2000), 77-80
##[4]
I. K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space, J. Math. Anal. Appl., 298 (2004), 374-397
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I. K. Argyros, Computational theory of iterative methods, Series: Studies in Computational Mathematics, 15, Editors: C.K. Chui and L. Wuytack, Elsevier Publ. Co., New York, USA (2007)
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I. K. Argyros, Convergence and applications of Newton-type iterations, Springer-Verlag Publ., New York (2008)
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I. K. Argyros, On the semilocal convergence of inexact Newton methods in Banach spaces, J. Comput. Appl. Math. in press, 228 (2009), 434-443
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J. Chen, W. Li , Convergence behaviour of inexact Newton methods under weak Lipschitz condition, J. Comput. Appl. Math. , 191 (2006), 143-164
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J. F. Dennis, Toward a unified convergence theory for Newton-like methods, in Nonlinear Functional Analysis and Applications (L.B. Rall, ed.), Academic Press, New York, (1971), 425-472
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X. Guo, On semilocal convergence of inexact Newton methods, J. Comput. Math. , 25 (2007), 231-242
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Z. A. Huang, Convergence of inexact Newton method, J. Zhejiang Univ. Sci. Ed. , 30 (2003), 393-396
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L. V. Kantorovich, G. P. Akilov, Functional Analysis, Pergamon Press, Oxford (1982)
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B. Morini, Convergence behaviour of inexact Newton methods, Math. Comp., 68 (1999), 1605-1613
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F. A. Potra , Sharp error bounds for a class of Newton-like methods, Libertas Mathematica., 5 (1985), 71-84
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X. H. Wang, C. Li, Convergence of Newton's method and uniqueness of the solution of equations in Banach spaces, II, Acta Math. Sin. (Engl. Ser.) , 19 (2003), 405-412
]