]>
2009
2
2
ISSN 2008-1898
74
SOME PROPERTIES OF B-CONVEXITY
SOME PROPERTIES OF B-CONVEXITY
en
en
In this paper, we give a characteristic of B-convexity structures
of finite dimensional B-spaces: if a finite dimensional B-space has the weak
selection property then its B-convexity structure satisfies H-condition. We
also get some relationships among B-convexity structures, selection property
and fixed point property. We show that in a compact convex subset of a finite
dimensional B-space satisfying H-condition the weak selection property implies
the fixed point property.
71
77
HONGMIN
SUO
School of Mathematics and Computer Science, GuiZhou University for Nationalities , 550025, Guiyang, Guizhou, China.
B-Convexity
continuous selection
fixed point
KKM-maping.
Article.1.pdf
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]
STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF STRICT PSEUDO-CONTRACTION MAPPINGS
STRONG CONVERGENCE THEOREMS FOR EQUILIBRIUM PROBLEMS AND FIXED POINT PROBLEMS OF STRICT PSEUDO-CONTRACTION MAPPINGS
en
en
The purpose of this paper is to introduce an iterative scheme
for finding a common element of the set of solutions of an equilibrium problem
and the set of fixed points of a k−strict pseudo-contraction non-self mapping in
Hilbert space. By the viscosity approximation algorithms, under suitable conditions
, some strong convergence theorems for approximating to this common
elements are proved. The results presented in the paper extend and improve
some recent results of Marino and Xu [G.Marino,H.K.Xu, Weak and strong
convergence theorems for k−strict pseudo-contractions in Hilbert spaces, J.
Math. Anal. Appl. 329 (2007) 336–349], Zhou [H.Zhou, Convergence theorems
of fixed Points for k−strict pseudo-contractions in Hilbert spaces, Nonlinear
Anal. 69 (2008) 456–462], Takahashi and Takahashi [S. Takahashi, W. Takahashi,
Viscosity approximation methods for equilibrium problems and fixed
point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506–
515], Ceng,Homidan,etc [L. C. Ceng, S.A.Homidan, Q.H.Ansari, J. C. Yao, An
iterative scheme for equilibrium problems and fixed point problems of strict
pseudo-contraction mappings, J. Comput. Appl. Math. 223 (2009) 967–974].
78
91
LIANG CAI
ZHAO
Department of Mathematics, Yibin University, Yibin, Sichuan 644000, China
SHIH-SEN
CHANG
Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China
Equilibrium problem
strict pseudo-contraction mapping
fixed point
strong convergence theorem.
Article.2.pdf
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L. C. Ceng, S. A.Homidan, Q. H. Ansari, J. C. Yao, An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction mappings, J. Comput. Appl. Math., 223 (2009), 967-974
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G. Marino, H. K. Xu, Weak and strong convergence theorems for k−strict pseudocontractions in Hilbert spaces, J. Math. Anal. Appl., 329 (2007), 336-349
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A. Tada, W. Takahashi, Strong convergence theorem for an equilibrium problem and a nonexpansive mapping, in: W. Takahashi, T. Tanaka(Eds.), Nonlinear Analysis and Convex Analysis, 609–617, Yokohama Publishers, Yokohama (2006)
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S. Takahashi, W. Takahashi , Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl., 331 (2007), 506-515
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W. Takahashi, M. Toyoda, Weak convergence theorems for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl., 118 (2003), 417-428
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H. Zhou , Convergence theorems of fixed Points for k−strict pseudo-contractions in Hilbert spaces, Nonlinear Anal., 69 (2008), 456-462
]
ON KANNAN FIXED POINT PRINCIPLE IN GENERALIZED METRIC SPACES
ON KANNAN FIXED POINT PRINCIPLE IN GENERALIZED METRIC SPACES
en
en
The concept of a generalized metric space, where the triangle
inequality has been replaced by a more general one involving four points, has
been recently introduced by Branciari. Subsequently, some classical metric
fixed point theorems have been transferred to such a space. The aim of this
note is to show that Kannan's fixed point theorem in a generalized metric space
is a consequence of the Banach contraction principle in a metric space.
92
96
Dorel
Miheţ
West University of Timişoara, Bv. V. Parvan 4, 300223, Timişoara, Romania.
Generalized metric space
T-orbitally complete
Fixed point.
Article.3.pdf
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M. Akram, A. Siddiqui , A fixed point theorem for A-contractions on a class of generalized metric spaces, Korean J. Math. Sciences, 10 (2) (2003), 1-5
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A. Azam, M. Arshad , Kannan fixed point theorem on generalized metric spaces, J. Nonlinear Sci. Appl. , 1 (1) (2008), 45-48
##[3]
A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (1-2) (2000), 31-37
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P. Das, A fixed point theorem on a class of generalized metric spaces, Korean J. Math. Sc., 9 (1) (2002), 29-33
##[6]
P. Das, L. K. Dey, A fixed point theorem in a eneralized metric space, Soochow Journal of Mathematics , 33 (1) (2007), 33-39
##[7]
B. K. Lahiri, P. Das, Fixed point of a Ljubomir Ćirić's quasi-contraction mapping in a generalized metric space, Publ. Math. Debrecen, 61 (3-4) (2002), 589-594
##[8]
R. Kannan, Some results on fixed points, Bull. Cal. Math. Soc., 60 (1968), 71-76
##[9]
D. N. Sarknel, Banach's fixed point theorem implies Kannan's, Bull. Cal. Math. Soc., 91 (2) (1999), 143-144
]
EXISTENCES AND BOUNDARY BEHAVIOR OF BOUNDARY BLOW-UP SOLUTIONS TO QUASILINEAR ELLIPTIC SYSTEMS WITH SINGULAR WEIGHTS
EXISTENCES AND BOUNDARY BEHAVIOR OF BOUNDARY BLOW-UP SOLUTIONS TO QUASILINEAR ELLIPTIC SYSTEMS WITH SINGULAR WEIGHTS
en
en
Using the method of explosive sub and supper solution, the existence
and boundary behavior of positive boundary blow up solutions for some
quasilinear elliptic systems with singular weight function are obtained under
more extensive conditions.
97
104
QIAOYU
TIAN
Department of Mathematics Hezuo Minorities Teacher College, Hezuo Gansu , 747000. P. R. China
SHUIBO
HUANG
Department of Mathematics Hezuo Minorities Teacher College, Hezuo Gansu , 747000. P. R. China
Quasilinear elliptic systems
Boundary blow up
Explosive sub- and super-solution.
Article.4.pdf
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J. García-Melián, Large solutions for an elliptic system of quasilinear equations, J. Differential Equations. , 245 (2008), 3735-3752
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S. Huang, Q. Tian, C. Mu, Asymptotic behavior of large solution to elliptic equation of Bieberbach-Rademacher type with convection terms, Appl. Math. Comput. , 210 (2009), 284-293
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S. Huang, Q. Tian, C. Mu , The prospers of boundary blow-up solutions to elliptic systems of competitive type with singular weights, Chinese J. Engrg Math. (in Chinese), (2009), -
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H. Li, M. Wang, Existence and uniqueness of positive solutions to the boundary blow-up problem for an elliptic system, J. Differential Equations. , 234 (2007), 246-266
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C. Liu, D. Yang, Existence of large solutions for a quasilinear elliptic problem via explosive sub-supersolutions, Appl. Math. Comput, 199 (2008), 414-424
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C. Mu, S. Huang, Q. Tian, L. Liu, Large solutions for an elliptic system of competitive type: Existence, uniqueness and asymptotic behavior, Nonlinear Anal., (2009)
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L. Wei, M. Wang, Existence and estimate of large solutions for an elliptic system, Nonlinear Anal., 70 (2009), 1096-1104
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M. Wang, L. Wei, Existence and boundary blow-up rates of solutions for boundary blow-up elliptic systems, Nonlinear Anal. , (2009)
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Z. Wu , D. Yang, Existence of boundary blow-up solutions for a class of quasilinear elliptic systems with critical case, Appl Math Comput., 198 (2008), 574-581
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D.Yang, Z. Wu, Existence of boundary blow-up solutions for a class of quasilinear elliptic systems with subcritical case, Commun.Pure. Appl. Anal. , 6 (2007), 531-540
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D. Yang, Existence of entire explosive positive radial solutions for a class of quasilinear elliptic systems, J. Math. Anal. Appl. , 288 (2003), 768-783
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Z. Zhang, Existence of large solutions for a semilinear elliptic problem via explosive subsupersolutions, Electron J. Differential Equations. , 2 (2006), 1-8
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]
INTUITIONISTIC FUZZY STABILITY OF JENSEN TYPE MAPPING
INTUITIONISTIC FUZZY STABILITY OF JENSEN TYPE MAPPING
en
en
In this paper we prove result for Jensen type mapping in the setting
of intuitionistic fuzzy normed spaces. We generalize a Hyers-Ulam stability result
in the framework of classical normed spaces.
105
112
S.
SHAKERI
Department of Mathematics, Islamic Azad University-Ayatollah Amoli branch, Amol P.O. Box 678, Iran
Stability
Jensen type mapping
intuitionistic fuzzy normed space.
Article.5.pdf
[
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K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986), 87-96
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D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc., 57 (1951), 223-237
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G. Deschrijver, E. E. Kerre, On the relationship between some extensions of fuzzy set theory, Fuzzy Sets and Systems , 23 (2003), 227-235
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S. B. Hosseini, D. O’Regan, R. Saadati, Some results on intuitionistic fuzzy spaces, Iranian J. Fuzzy Syst, 4 (2007), 53-64
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J. M. Rassias, M. J. Rassias, On the Ulam stability of Jensen and Jensen type mappings on restricted domains, J. Math. Anal. Appl., 281 (2003), 516-524
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J. M. Rassias, M. J. Rassias, Asymptotic behavior of alternative Jensen and Jensen type junctional equations , Bull. Sci. Math. , 129 (2005), 545-558
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J. M. Rassias, Refined Hyers-Ulam approximation of approximately Jensen type mappings, Bull. Sci. Math. Bull. Sci. math., 131 (2007), 89-98
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J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 22 (2004), 1039-1046
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R. Saadati, J. H. Park , On the intuitionistic fuzzy topological spaces, Chaos, Solitons and Fractals , 27 (2006), 331-344
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R. Saadati, J. H. Park, Intuitionistic fuzzy Euclidean normed spaces, Commun. Math. Anal., 1 (2006), 85-90
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]
SEPARATION THEOREM WITH RESPECT TO SUB-TOPICAL FUNCTIONS AND ABSTRACT CONVEXITY
SEPARATION THEOREM WITH RESPECT TO SUB-TOPICAL FUNCTIONS AND ABSTRACT CONVEXITY
en
en
This paper deals with topical and sub-topical functions in a class
of ordered Banach spaces. The separation theorem for downward sets and
sub-topical functions is given. It is established some best approximation problems
by sub-topical functions and we will characterize sub-topical functions as
superimum of elementary sub-topical functions.
113
125
M.
ALIMOHAMMADY
Department of Mathematics, University of Mazandaran, Babolsar 47416 − 1468, Iran.
A.
SHAHMARI
Islamic Azad University, Ayatollah Amoli branch, Amol, Iran
Downward set
Subdifferential set
ordered Banach space
topical function
sub-topical function
separation theorem
abstract convex set.
Article.6.pdf
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[1]
M. Alimohammady, A. Shahmari , Superlinear separation on downward sets and characterization of topical functions over ordered Banach spaces, Optimization, ( to appear. ), -
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H. Mohebi , Topical functions and their properties in a class of ordered Banach spaces, J. Math. Anal. Appl., ( in press.), -
##[6]
H. Mohebi, A. M. Rubinov, Best approximation by downward sets with applications, J. Math. Anal. Appl., ( in press. ), -
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A. M. Rubinov, Abstract convexity and global optimization, Kluwer Academic Publishers , Boston , Dordrech, London (2000)
##[9]
A. M. Rubinov, I. Singer , Topical and sub-topical functions , downward sets and abstract convexity, Optimization , 50 (2001), 307-351
]
POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR TWO POINT BOUNDARY VALUE PROBLEMS
POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR TWO POINT BOUNDARY VALUE PROBLEMS
en
en
Existence of positive solution for a class of singular boundary value
problems of the type
\[−x''(t) = f(t, x(t), x'(t)),\quad t \in (0, 1)\]
\[x(0) = 0, x(1) = 0,\]
is established. The nonlinearity \(f \in C((0, 1) \times (0,\infty) \times (−\infty,\infty), (−\infty,\infty))\)
is allowed to change sign and is singular at \(t = 0, t = 1\) and/or \(x = 0\). An
example is included to show the applicability of our result.
126
135
RAHMAT ALI
KHAN
Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Campus of College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan
NASEER AHMAD
ASIF
Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Campus of College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan
Positive solutions
Singular differential equations
Dirichlet boundary conditions.
Article.7.pdf
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M. Fenga, W. Gea, Positive solutions for a class of m-point singular boundary value problems, Math. Comput. Modelling , 46 (2007), 375-383
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G. C. Yang, Existence of solutions to the third-order nonlinear differential equations arising in boundary layer theory, Appl. Math. Lett., 6 (2003), 827-832
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]
COMMON FIXED POINT THEOREMS FOR HYBRID MAPPINGS SATISFYING GENERALIZED CONTRACTIVE CONDITIONS
COMMON FIXED POINT THEOREMS FOR HYBRID MAPPINGS SATISFYING GENERALIZED CONTRACTIVE CONDITIONS
en
en
We prove common fixed point theorems in symmetric spaces for
two pairs of hybrid mappings using the concept of T−weakly and S−weakly
commuting mappings satisfying generalized contractive conditions which generalize
theorems of Aamri and El Moutawakil [J. Math. Anal. Appl., 270
(2002), 181–188.], Aamri and El Moutawakil [Appl. Math. E-notes., 3 (2003),
156–162.] and Aliouche [J. Math. Anal. Appl., 322 (2006), 796–802.].
136
145
ABDELKRIM
ALIOUCHE
Department of Mathematics, University of Larbi Ben M’Hidi, Oum-El-Bouaghi, 04000, Algeria.
Hybrid mappings
T−weakly commuting
property (E.A)
common property (E.A)
common fixed point
symmetric space.
Article.8.pdf
[
[1]
M. Aamri, D. El Moutawakil , Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl., 270 (2002), 181-188
##[2]
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