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2009
2
1
ISSN 2008-1898
69
REMARKS ON REMOTAL SETS IN VETOR VALUED FUNCTION SPACES
REMARKS ON REMOTAL SETS IN VETOR VALUED FUNCTION SPACES
en
en
Let \(X\) be a Banach space and \(E\) be a closed bounded subset of \(X\).
For \(x \in X\) we set \(D(x,E) = \sup\{\| x − e \|: e \in E\}\). The set \(E\) is called remotal
in \(X\) if for any \(x \in X\), there exists \(e \in E\) such that \(D(x,E) = \| x − e \|\) . It is
the object of this paper to give new results on remotal sets in \(L^p(I,X)\), and to
simplify the proofs of some results in [5].
1
10
M.
SABABHEH
Department of Science and Humanities, Princess Sumaya University For Technology, Al Jubaiha, Amman 11941, Jordan.
R.
KHALIL
Department of Mathematics, Jordan University, Al Jubaiha, Amman 11942, Jordan.
Remotal sets
Approximation theory in Banach spaces.
Article.1.pdf
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[1]
E. Asplund, Farthest points in reflexive locally uniformly rotund Banach spaces, Israel J. Math. , 4 (1966), 213-216
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M. Baronti, P. Papini, Remotal sets revisited, Taiwanese J. Math., 5 (2001), 357-373
##[3]
A. Boszany, A remark on uniquely remotal sets in C(K,X) , Period.Math.Hungar, 12 (1981), 11-14
##[4]
E. Cheney, W. Light , Lecture notes in Mathematics, Springer-Verlag Berlin Heidelberg, (1985)
##[5]
R. Khalil, Sh. Al-Sharif, Remotal sets in vector valued function spaces, Scientiae Mathematicae Japonica, 63, No, 3 (2006), 433-441
##[6]
S. Rolewicz, Functional analysis and control theory, D.Reidel publishing company, ( 1986.)
]
LOCAL CONVERGENCE ANALYSIS OF INEXACT NEWTON-LIKE METHODS
LOCAL CONVERGENCE ANALYSIS OF INEXACT NEWTON-LIKE METHODS
en
en
We provide a local convergence analysis of inexact Newton–like
methods in a Banach space setting under flexible majorant conditions. By
introducing center–Lipschitz–type condition, we provide (under the same computational
cost) a convergence analysis with the following advantages over earlier
work [9]: finer error bounds on the distances involved, and a larger radius
of convergence.
Special cases and applications are also provided in this study.
11
18
IOANNIS K.
ARGYROS
Cameron university, Department of Mathematics Sciences, Lawton, OK 73505, USA.
SAID
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–like method
Banach space
Majorant conditions
Local convergence.
Article.2.pdf
[
[1]
I. K. Argyros, Relation between forcing sequences and inexact Newton iterates in Banach space, Computing, 63 (1999), 134-144
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I. K. Argyros, Forcing sequences and inexact Newton iterates in Banach space, Appl. Math. Lett. , 13 (2000), 69-75
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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)
##[6]
I. K. Argyros, On the semilocal convergence of inexact Newton methods in Banach spaces, J. Comput. Appl. Math. in press, (doi:10.1016/j.cam.2008.10.005. ), -
##[7]
J. Chen, W. Li , Convergence behaviour of inexact Newton methods under weak Lipschitz condition, J. Comput. Appl. Math. , 191 (2006), 143-164
##[8]
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
##[9]
O. P. Ferreira, M. L. N. Goncalves, Local convergence analysis of inexact Newton–like methods under majorant condition, preprint, http://arxiv.org/abs/0807.3903?context=math.OC., (document), -
##[10]
X. Guo, On semilocal convergence of inexact Newton methods, J. Comput. Math., 25 (2007), 231-242
##[11]
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)
##[13]
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
##[15]
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
]
A RELATED FIXED POINT THEOREM IN TWO FUZZY METRIC SPACES
A RELATED FIXED POINT THEOREM IN TWO FUZZY METRIC SPACES
en
en
We prove a related fixed point theorem for two mappings in two
fuzzy metric spaces using an implicit relation which gives fuzzy versions of
theorems of [1], [2] and [10].
19
24
ABDELKRIM
ALIOUCHE
Department of Mathematics, University of Larbi Ben M’ Hidi, Oum-El-Bouaghi, 04000, Algeria.
FAYCEL
MERGHADI
Department of Mathematics, University of Tebessa, 12000, Algeria.
AHCENE
DJOUDI
Université de Annaba, Faculté des sciences, Département de mathématiques, B. P. 12, 23000, Annaba, Algérie
Fuzzy metric space
implicit relation
sequentially compact fuzzy metric space
related fixed point.
Article.3.pdf
[
[1]
A. Aliouche, B. Fisher, Fixed point theorems for mappings satisfying implicit relation on two complete and compact metric spaces, Applied Mathematics and Mechanics, 27 (9) (2006), 1217-1222
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B. Fisher , Fixed point on two metric spaces, Glasnik Mat., 16 (36) (1981), 333-337
##[3]
A. George, P. Veeramani, On some result in fuzzy metric space, Fuzzy Sets Syst., 64 (1994), 395-399
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M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Syst., 27 (1988), 385-389
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I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11 (1975), 326-334
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V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstratio Math., 32 (1999), 157-163
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K. P. R. Rao, N. Srinivasa Rao T. Ranga Rao, J. Rajendra Prasad, Fixed and related fixed point theorems in sequentially compact fuzzy metric spaces , Int. Journal of Math. Analysis, 2 (2008), 1353-1359
##[8]
K. P. R. Rao, Abdelkrim Aliouche, G. Ravi Babu, Related Fixed Point Theorems in Fuzzy Metric Spaces, The Journal of Nonlinear Sciences and its Application, 1 (3) (2008), 194-202
##[9]
B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 313-334
##[10]
M. Telci, Fixed points on two complete and compact metric spaces, Applied Mathematics and Mechanics, 22 (5) (2001), 564-568
##[11]
L. A. Zadeh , Fuzzy sets, Inform and Control, 8 (1965), 338-353
]
A NOTE ON THE A CONTRACTION THEOREM IN MENGER PROBABILISTIC METRIC SPACES
A NOTE ON THE A CONTRACTION THEOREM IN MENGER PROBABILISTIC METRIC SPACES
en
en
25
26
S.
SHAKERI
Article.4.pdf
[
]
\(\beta S^*\)-COMPACTNESS IN L-FUZZY TOPOLOGICAL SPACES
\(\beta S^*\)-COMPACTNESS IN L-FUZZY TOPOLOGICAL SPACES
en
en
In this paper, the notion of \(\beta S^*\)−compactness is introduced in
L−fuzzy topological spaces based on \(S^*\)−compactness. A \(\beta S^*\)−compactness
L-fuzzy set is \(S^*\)−compactness and also \(\beta \)−compactness. Some of its properties
are discussed. We give some characterizations of \(\beta S^*\)−compactness in
terms of pre-open, regular open and semi-open L−fuzzy set. It is proved that
\(\beta S^*\)−compactness is a good extension of \(\beta \)−compactness in general topology.
Also, we investigated the preservation theorems of \(\beta S^*\)−compactness under
some types of continuity.
27
37
I. M.
HANAFY
Department of Mathematics, Faculty of Education, Suez Canal University, El-Arish, Egypt
L−fuzzy topological spaces
fuzzy \(\beta S^*\)−compactness
local \(\beta S^*\)−compactness
\(\beta_a\) − cover
\(Q_a\) − cover.
Article.5.pdf
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A. I. Aggour, On some applications of lattices, Ph. D. Thesis, Al-Azhar Univ., Cairo, Egypt (1998)
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Ganesan Balasubramanian , On fuzzy \(\beta \)−compact spaces and fuzzy \(\beta \)− extremally disconnected spaces, Kybernetika [cybernetics], 33 (1997), 271-277
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D. S. Zhao, The N−compactness in L−fuzzy topological spaces , J. Math. Anal. Appl., 128 (1987), 46-70
]
ON THE POSITIVE AND NEGATIVE SOLUTIONS OF LAPLACIAN BVP WITH NEUMANN BOUNDARY CONDITIONS
ON THE POSITIVE AND NEGATIVE SOLUTIONS OF LAPLACIAN BVP WITH NEUMANN BOUNDARY CONDITIONS
en
en
In this paper, we consider the following Neumann boundary value
problem
\[
\begin{cases}
-u''(x) = u^3(x) - \lambda|u(x)|,\quad x \in (0, 1),\\
u'(0) = 0 = u'(1),
\end{cases}
\]
where \(\lambda\in \mathbb{R}\) is parameter. We study the positive and negative solutions of this
problem with respect to a parameter \(\rho \) (i.e. \(u(0) = \rho\)) in all \(\mathbb{R}^*\). By using a
quadrature method, we obtain our results. Also we provide some details about
the solutions that are obtained.
38
45
G. A.
AFROUZI
Department of Mathematics, Faculty of Basic Sciences, Mazandaran University, Babolsar, Iran
M. KHALEGHY
MOGHADDAM
Department of Basic Sciences, Faculty of Agriculture Engineering, Sari Agricultural Sciences and Natural Resources University, Sari, Iran.
J.
MOHAMMADPOUR
Department of Mathematics, Islamic Azad Univercitiy Ghaemshahr Branch, P.O. Box163, Ghaemshahr, Iran.
M.
ZAMENI
Department of Mathematics, Islamic Azad Univercitiy Ghaemshahr Branch, P.O. Box163, Ghaemshahr, Iran.
Positive and negative solutions
Interior critical points
Quadrature method
Neumann boundary condition
Laplacian problem.
Article.6.pdf
[
[1]
I. Addou, On the number of solutions for boundary-value problems with jumping nonlinearities, Ph.D. Thesis, Universit´e des Sciences et de la Technologie Houari Boumedienne, Algiers, Algeria (2000)
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G. A. Afruzi, M. Khaleghy Moghadaam, Existence and multiplicity results for a class of p-Laplacian problems with Neumann-Robin boundary conditions, Chaos, Solitons & Fractals, 30 (2006), 967-973
##[3]
G. A. Afrouzi, M. Khalehghy Moghaddam, Nonnegative solution Curves of Semipositone Problems With Dirichlet Boundary conditions, Nonlinear Analysis, Theory, methods, and Applications, 61 (2005), 485-489
##[4]
F. Ammar–Khodja, Une revue et quelques compléments sur la détermination du nombre des solutions de certains problémes elliptiques semi–linéaires, Thése Doctorat 3é Cycle, Université Pierre et Marie Curie,I, Paris V (1983)
##[5]
V. Anuradha, C. Maya, R. Shivaji, Positive solutions for a class of nonlinear boundary value problems with Neumann–Robin boundary conditions, J. Math. Anal. Appl. , 236 (1999), 94-124
##[6]
A. Castro, R. Shivaji, Nonnegative solutions for a class non-positone problems, Proc. Roy. Soc. Edinburgh, Sect. A , 108 (1988), 291-302
##[7]
M. Guedda, L. Veron , Bifurcation phenomena associated to the p-Laplacian operator, Trans. Amer. Math. Soc. , 310 (1988), 419-431
##[8]
R. A. Khan, N. A. Asif, Positive solutions for a class of singular two point boundary value problems, J. Nonlinear Sci. Appl., 2 (2009), 126-135
##[9]
A. R. Miciano, R. Shivaji, Multiple positive solutions for a class of semipositone Neumann two point boundary value problems, J. Math. Anal. Appl. , 178 (1993), 102-115
]
ON THE DEFINITION OF FUZZY HILBERT SPACES AND ITS APPLICATION
ON THE DEFINITION OF FUZZY HILBERT SPACES AND ITS APPLICATION
en
en
In this paper we introduce the notion of fuzzy Hilbert spaces and
deduce the fuzzy version of Riesz representation theorem. Also we prove some
results in fixed point theory and utilize the results to study the existence and
uniqueness of solution of Uryson's integral equation.
46
59
M.
GOUDARZI
Dept. of Math., Amirkabir University of Technology, Hafez Ave., P. O. Box 15914, Tehran, Iran
S. M.
VAEZPOUR
Dept. of Math., Amirkabir University of Technology, Hafez Ave., P. O. Box 15914, Tehran, Iran
Fixed point theorem
fuzzy Hilbert space
fuzzy inner product space
Riesz representation theorem
Uryson's integral equation.
Article.7.pdf
[
[1]
H. Adibi, Y. J. Cho, D. O'Regan, R. Saadati, Common fixed point theorems in \(L\)-fuzzy metric spaces, Applied Mathematics and Computation, 182 (2006), 820-828
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C. Alaca, D. Turkoglu, C. Yildiz, Fixed points in intuitionistic fuzzy meric spaces, Chaos, Solitons and Fractals, 29 (2006), 1073-1076
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C. Alsina, B. Schweizer, C. Sempi, A. Sklar, On the definition of a probabilistic inner product space, Rendiconti di Matematica, Serie VII, 17 (1997), 115-127
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K. Erich, P. M. Radko, P. Endre, Triangular norms, Dordrecht : Kluwer. , (ISBN 0-7923- 6416-3.), -
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A. George, P. Veermani, On some results in fuzzy metric spaces, Fuzzy sets and systems, 64 (1994), 395-399
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M. Goudarzi, S. M. Vaezpour, R. Saadati , On the intuitionistic fuzzy inner product spaces, Chaos, Solitons and Fractals, doi :10. 1016/j. Chaos. 2008. 04. 040. (2008)
##[11]
S. B. Hosseini, D. O;regan, R. Saadati , Some results on intuitionistic fuzzy spaces, Iranian Journal of Fuzzy Systems, 4 (2007), 53-64
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J. K. Kohli, R. Kumar, On fuzzy inner product spaces and fuzzy co-inner product spaces, Fuzzy Sets and Systems, 53 (1993), 227-232
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J. K. Kohli, R. Kumar, Linear mappings, fuzzy linear spaces, fuzzy inner product spaces and fuzzy co-inner product spaces, Bull Calcutta Math. Soc., 87 (1995), 237-246
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M. A. Krasnoselskii, Topological methods in the theory of nonlinear integral equations, Pergamon press. Oxford. Londan. New York, Paris (1964)
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J. Rodríguez-lópez, S. Romaquera, The Hausdorrf fuzzy metric on compact sets, Fuzzy Sets and Systems, 147 (2004), 273-283
##[16]
R. Saadati, S. M. Vaezpour, Some results on fuzzy Banach spaces, J. Appl. Math. and computing, 17 (2005), 475-484
##[17]
R. Saadati , A note on some results on the IF-normed spaces, Chaos, Solitons and Fractals, doi :10. 1016/j. Chaos. 2007. 11. 027. 1 1 (2007)
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B. Schweizer, A. Sklar , Probabilistic metric spaces, North Holand series in probability and applied mathematics, (1983)
##[19]
Y. Su, X. Wang, J. Gao, Riesz theorem in probabilistic inner product spaces, Int. Math. Forum., 62 (2007), 3073-3078
]
CARTESIAN PRODUCTS OF PQPM-SPACES
CARTESIAN PRODUCTS OF PQPM-SPACES
en
en
In this paper we define the concept of finite and countable Cartesian
products of PqpM-spaces and give a number of its properties. We also
study the properties of topologies of those products.
60
70
Y. J.
CHO
Department of Mathematics, Gyeongsang National University, Chinju 660- 701, Korea
M. T.
GRABIEC
Department of Operation Research, Academy of Economics, al. Niepodleg losci 10, 60-967 Poznań, Poland
A. A.
TALESHIAN
Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar 47416 − 1468, Iran.
robabilistic-quasi-metric space
topology
Cartesian products of PqpM-space
countable Cartesian products of PqpM-spaces of type \(\{k_n\}\).
Article.8.pdf
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]