]>
2010
3
2
ISSN 2008-1898
78
GENERALIZED CONTRACTIONS AND COMMON FIXED POINT THEOREMS CONCERNING DISTANCE
GENERALIZED CONTRACTIONS AND COMMON FIXED POINT THEOREMS CONCERNING DISTANCE
en
en
In this paper we consider the generalized distance, present a generalization of
Ćirić's generalized contraction fixed point theorems on a complete metric space and investigate a common fixed point theorem about a sequence of mappings concerning generalized
distance.
78
86
A. BAGHERI
VAKILABAD
Dept. of Math.
Islamic Azad University, Science and Research Branch
Iran
S. MANSOUR
VAEZPOUR
Dept. of Math.
Amirkabir University of Technology
Iran
vaez@aut.ac.ir
Common fixed point
\(\tau\)-distance
generalized contraction.
Article.1.pdf
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[1]
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A. Azam, M. Arshad , Kannan fixed point theorem on generalized metric spaces, J. of Nonlinear Science and Applications, 1(1) (2008), 45-48
##[3]
O. Kada, T. Suzuki, W. Takahashi, Nonconvex Minimization theorems and fixed point theorems in complete metric spaces, Math. Japon, 44 (1996), 381-391
##[4]
D. Mihet, On Kannan fixed point principle in generalized metric spaces, J. of Nonlinear Science and Applications, 2(2) (2009), 92-96
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I. R. Sarma, J. M. Rao, S. S. Rao, Contractions over generalized metric spaces , J. of Nonlinear Science and Applications, 2(3) (2009), 180-182
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T. Suzuki, Several fixed point theorems concerning \(\tau\)-distance, Fixed Point Theory and Applications, 3 (2004), 195-209
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L. B. Ćirić, Generalized contractions and fixed-point theorems, Publ. Inst. Math. (Beograd)(N.S.), 12(26) (1971), 19-26
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L. B. Ćirić, On a family of contractive maps and fixed-points, Publ. Inst. Math. (Beograd)(N.S.), 17(31) (1974), 45-51
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L. B. Ćirić, A generalization of Banbch's contractions principle, Proc. Amer. Math. Soc, 45 (1974), 267-273
]
SOME FIXED POINT THEOREMS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS
SOME FIXED POINT THEOREMS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS
en
en
For a subset \(K\) of a metric space \((X, d)\) and \(x \in X\), the set
\(P_K(x) = \{y \in K : d(x, y) = d(x;K) \equiv \inf\{d(x, k) : k \in K\}\}\) is called the set of
best \(K\) -approximant to \(x\). An element \(g_\circ \in K\) is said to be a best simultaneous
approximation of the pair \(y_1, y_2 \in X\) if
\[\max\{d(y_1, g_\circ), d(y_2, g_\circ)\} = \inf_{g\in K}
\max\{d(y_1, g), d(y_2, g)\}.\]
Some results on \(T\)-invariant points for a set of best simultaneous approximation
to a pair of points \(y_1, y_2\) in a convex metric space \((X, d)\) have been proved by
imposing conditions on \(K\) and the self mapping \(T\) on \(K\) . For self mappings \(T\)
and \(S\) on \(K\) , results are also proved on both \(T\)- and \(S\)- invariant points for a set
of best simultaneous approximation. The results proved in the paper generalize
and extend some of the results of \(P\). Vijayaraju [Indian J. Pure Appl. Math.
24(1993) 21-26]. Some results on best \(K\) -approximant are also deduced.
87
95
T. D.
NARANG
Department of Mathematics
Guru Nanak Dev University
India
tdnarang1948@yahoo.co.in
SUMIT
CHANDOK
School of Mathematics and Computer Applications
Thapar University
India
chansok.s@gmail.com;sumit.chandok@thapar.edu
Best approximation
fixed point
nonexpansive
R-weakly commuting
R-subweakly commuting
asymptotically nonexpansive and uniformly asymptotically regular maps.
Article.2.pdf
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]
COMPATIBILITY OF TYPE P IN MODIFIED INTUITIONISTIC FUZZY METRIC SPACE
COMPATIBILITY OF TYPE P IN MODIFIED INTUITIONISTIC FUZZY METRIC SPACE
en
en
The object of this paper is to establish unique common fixed point theorems
for four self maps satisfying a new contractive condition in a modified intuitionistic fuzzy
metric space through compatibility of type (P). A generalization of a result of D Turkoglu
et al [J. Apply. Math. Computing (2006)] in the setting of a modified intuitionistic fuzzy
metric space follows from them. Modified intuitionistic fuzzy version of Grabiec contraction
Principle has also been established. All the results presented in this paper are new. Examples
have been constructed in support of the main results of this paper.
96
109
SHOBHA
JAIN
Quantum School of Technology
India
shobajain1@yahoo.com
SHISHIR
JAIN
Shri Vaishnav Institute of Technology and Science
India
jainshishir11@rediffmail.com
LAL BAHADUR
JAIN
Retd. Principal, Govt. Arts and Commerce College
India
lalbahdurjain11@yahoo.com
Modified intuitionistic fuzzy metric space
common fixed points
compatible maps of type (P)
weak compatible maps
t-norm
t-conorm.
Article.3.pdf
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[1]
H. Abidi, Y. J. Cho, D. O. Regan, R. Saadati, Common fixed point in L-fuzzy metric spaces, Applied Mathematics and Computation , 182 (2006), 820-828
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Shobha Jain, Shishir Jain, Lal Bahadur, r-r'contraction in Modified Intuitionistic fuzzy metric space , Kochi Journal of Mathematics , 4 (2009), 87-100
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G. Jungck , Commuting maps and fixed points, Amer. Math. monthly , 83 (1976), 261-263
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G. Jungck, Compatible mappings and common fixed point, Internat. Journal of Math. Math. Sci., 9 (1986), 771-779
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S. Kutukcu, A common fixed point theorem for a sequence of self maps in intuitionistic fuzzy metric spaces, Commun. Korean Math. Soc. , 21 (2006), 679-687
##[15]
J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals , 22 (2004), 1039-1046
##[16]
R. Saadati, J. H. Park, On the intuitionistic fuzzy topolodical spaces, Chaos Solitons and Fractals , 27 (2006), 331-44
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R. Saadati, S. Sedghi, N. Shobhe, Modified Intuitionistic Fuzzy metric spaces and fixed point theorems, Choas Fractal and Solitions, ( in press), -
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B. Singh, Shishir Jain, Fixed point theorem for six self-maps in fuzzy metric space, The Journal of Fuzzy Mathematics , 14 (2006), 231-243
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]
APPROXIMATION OF MIXED TYPE FUNCTIONAL EQUATIONS IN pBANACH SPACES
APPROXIMATION OF MIXED TYPE FUNCTIONAL EQUATIONS IN pBANACH SPACES
en
en
In this paper, we investigate the generalized Hyers-Ulam stability
of the functional equation
\[\sum^n _{i=1} f(x_i - \frac{1}{ n} \sum^n _{j=1} x_j) = \sum^n _{i=1} f(x_i) - nf( \frac{1}{ n} \sum^n_{ i=1} x_i)\quad (n \geq 2)\]
in p-Banach spaces.
110
122
S.
ZOLFAGHARI
Department of Mathematics
Semnan University
Iran
somaye.zolfaghari@gmail.com
Generalized Hyers-Ulam stability
Additive and Quadratic function
p-Banach spaces.
Article.4.pdf
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M. Eshaghi Gordji, H. Khodaei, C. Park, A fixed point approach to the Cauchy-Rassias stability of general Jensen type quadratic-quadratic mappings, , (To appear), -
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V. A. Faizev, Th. M. Rassias, P. K. Sahoo, The space of (\(\psi,\gamma\))-additive mappings on semigroups, Trans. Amer. Math. Soc. , 354 (11) (2002), 4455-4472
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]
STABILITY OF A GENERALIZED EULER-LAGRANGE TYPE ADDITIVE MAPPING AND HOMOMORPHISMS IN C*-ALGEBRAS II
STABILITY OF A GENERALIZED EULER-LAGRANGE TYPE ADDITIVE MAPPING AND HOMOMORPHISMS IN C*-ALGEBRAS II
en
en
Let \(X; Y\) be Banach modules over a \(C^*\)-algebra and let \(r_1,..., r_n \in \mathbb{R}\) be given. We prove the generalized Hyers-Ulam stability of the following
functional equation in Banach modules over a unital \(C^*\)-algebra:
\[\sum^n_{j=1}f(\frac{1}{2}\sum_{1\leq i\leq n;i\neq j}r_ix_i − \frac{1}{2}r_jx_j)+\sum^n_{i=1}r_if(x_i) = nf(\frac{1}{2}\sum^n_{i=1}r_ix_i) \qquad (0.1)\]
We show that if
\(\sum^n_{i=1 }r_i\neq 0; r_i \neq 0; r_j \neq 0\) for some \(1 \leq i < j \leq n\) and a
mapping \(f : X \rightarrow Y\) satisfies the functional equation (0.1) then the mapping
\(f : X \rightarrow Y\) is additive. As an application, we investigate homomorphisms in
unital \(C^*\)-algebras.
123
143
ABBAS
NAJATI
Department of Mathematics Faculty of Sciences
University of Mohaghegh Ardabili
Iran
a.nejati@yahoo.com
CHOONKIL
PARK
Department of Mathematics Research Institute for Natural Sciences
Hanyang University
South Korea
baak@hanyang.ac.kr
Generalized Hyers-Ulam stability
generalized Euler-Lagrange type additive mapping
homomorphism in \(C^*\)-algebras.
Article.5.pdf
[
[1]
M. Amyari, C. Park, M. S. Moslehian, Nearly ternary derivations , Taiwanese J. Math. , 11 (2007), 1417-1424
##[2]
T. Aoki , On the stability of the linear transformation in Banach spaces , J. Math. Soc. Japan , 2 (1950), 64-66
##[3]
P. W. Cholewa , Remarks on the stability of functional equations, Aequationes Math. , 27 (1984), 76-86
##[4]
C. Y. Chou, J.-H. Tzeng , On approximate isomorphisms between Banach ∗-algebras or C*-algebras, Taiwanese J. Math. , 10 (2006), 219-231
##[5]
S. Czerwik, On the stability of the quadratic mapping in normed spaces, Abh. Math. Sem. Univ. Hamburg , 62 (1992), 59-64
##[6]
M. Eshaghi Gordji, J. M. Rassias, N. Ghobadipour, Generalized Hyers-Ulam stability of generalized (N;K)-derivations, Abstract and Applied Analysis, Article ID 437931, 2009 (2009), 1-8
##[7]
M. Eshaghi Gordji, T. Karimi, S. Kaboli Gharetapeh, Approximately n-Jordan homomorphisms on Banach algebras, J. Inequal. Appl. Article ID 870843, 2009 (2009), 1-8
##[8]
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##[9]
Z.-X. Gao, H.-X. Cao, W.-T. Zheng, L. Xu, Generalized Hyers-Ulam-Rassias stability of functional inequalities and functional equations, J. Math. Inequal. , 3 (2009), 63-77
##[10]
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##[11]
P. Găvruta, On the stability of some functional equations, in: Stability of Mappings of Hyers-Ulam Type, Hadronic Press lnc. Palm Harbor, Florida , (1994), 93-98
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P. Găvruta, On a problem of G. Isac and Th.M. Rassias concerning the stability of mappings, J. Math. Anal. Appl. , 261 (2001), 543-553
##[13]
P. Găvruta, On the Hyers-Ulam-Rassias stability of the quadratic mappings, Nonlinear Funct. Anal. Appl. , 9 (2004), 415-428
##[14]
A. Grabiec, The generalized Hyers-Ulam stability of a class of functional equations, Publ. Math. Debrecen , 48 (1996), 217-235
##[15]
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. , 27 (1941), 222-224
##[16]
D. H. Hyers, G. Isac, Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhüuser, Basel (1998)
##[17]
D. H. Hyers, G. Isac, Th. M. Rassias, On the asymptoticity aspect of Hyers-Ulam stability of mappings, Proc. Amer. Math. Soc. , 126 (1998), 425-430
##[18]
K. Jun, H. Kim, On the Hyers-Ulam stability of a difference equation, J. Comput. Anal. Appl. , 7 (2005), 397-407
##[19]
K. Jun, H. Kim, Stability problem of Ulam for generalized forms of Cauchy functional equation, J. Math. Anal. Appl. , 312 (2005), 535-547
##[20]
K. Jun, H. Kim, Stability problem for Jensen type functional equations of cubic mappings, Acta Math. Sin. (Engl. Ser.) , 22 (2006), 1781-1788
##[21]
K. Jun, H. Kim, Ulam stability problem for a mixed type of cubic and additive functional equation, Bull. Belg. Math. Soc.–Simon Stevin , 13 (2006), 271-285
##[22]
K. Jun, H. Kim, J. M. Rassias, Extended Hyers-Ulam stability for Cauchy-Jensen mappings, J. Difference Equ. Appl. , 13 (2007), 1139-1153
##[23]
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##[24]
D. Miheţ , The fixed point method for fuzzy stability of the Jensen functional equation , Fuzzy Sets and Systems , 160 (2009), 1663-1667
##[25]
A. K. Mirmostafaee, A fixed point approach to almost quartic mappings in quasi fuzzy normed spaces, Fuzzy Sets and Systems , 160 (2009), 1653-1662
##[26]
M. Mirzavaziri, M. S. Moslehian, A fixed point approach to stability of a quadratic equation, Bull. Braz. Math. Soc. , 37 (2006), 361-376
##[27]
A. Najati, Hyers-Ulam stability of an n-Apollonius type quadratic mapping, Bull. Belgian Math. Soc.–Simon Stevin , 14 (2007), 755-774
##[28]
A. Najati , On the stability of a quartic functional equation, J. Math. Anal. Appl. , 340 (2008), 569-574
##[29]
A. Najati, M. B. Moghimi, Stability of a functional equation deriving from quadratic and additive functions in quasi-Banach spaces, J. Math. Anal. Appl. , 337 (2008), 399-415
##[30]
A. Najati, C. Park, Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras associated to the Pexiderized Cauchy functional equation, J. Math. Anal. Appl. , 335 (2007), 763-778
##[31]
A. Najati, C. Park, On the stability of an n-dimensional functional equation originating from quadratic forms, Taiwanese J. Math. , 12 (2008), 1609-1624
##[32]
A. Najati, C. Park, The Pexiderized Apollonius-Jensen type additive mapping and isomorphisms between C*-algebras, J. Difference Equat. Appl. , 14 (2008), 459-479
##[33]
A. Najati, G. Zamani Eskandani, Stability of a mixed additive and cubic functional equation in quasi-Banach spaces, J. Math. Anal. Appl. , 342 (2008), 1318-1331
##[34]
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##[36]
C. Park , Universal Jensen’s equations in Banach modules over a C*-algebra and its unitary group, Acta Math. Sinica , 20 (2004), 1047-1056
##[37]
C. Park, On the Hyers-Ulam-Rassias stability of generalized quadratic mappings in Banach modules, J. Math. Anal. Appl. , 291 (2004), 214-223
##[38]
C. Park, Lie ∗-homomorphisms between Lie C*-algebras and Lie ∗-derivations on Lie C*- algebras, J. Math. Anal. Appl. , 293 (2004), 419-434
##[39]
C. Park, On the stability of the orthogonally quartic functional equation , Bull. Iranian Math. Soc. , (2005), 63-70
##[40]
C. Park, Homomorphisms between Lie JC*-algebras and Cauchy-Rassias stability of Lie JC*-algebra derivations, J. Lie Theory , 15 (2005), 393-414
##[41]
C. Park, Generalized Hyers-Ulam-Rassias stability of n-sesquilinear-quadratic mappings on Banach modules over C*-algebras, J. Comput. Appl. Math. , 180 (2005), 51-63
##[42]
C. Park, Homomorphisms between Poisson JC*-algebras, Bull. Braz. Math. Soc. , 36 (2005), 79-97
##[43]
C. Park , Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras, Fixed Point Theory and Applications, Art. ID 50175 (2007)
##[44]
C. Park , Generalized Hyers-Ulam-Rassias stability of quadratic functional equations: a fixed point approach, Fixed Point Theory and Applications, Art. ID 493751 (2008)
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C. Park, J. Hou, Homomorphisms between C*-algebras associated with the Trif functional equation and linear derivations on C*-algebras, J. Korean Math. Soc. , 41 (2004), 461-477
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C. Park, J. Park, Generalized Hyers-Ulam stability of an Euler-Lagrange type additive mapping, J. Difference Equat. Appl. , 12 (2006), 1277-1288
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W. Park, J. Bae, On a bi-quadratic functional equation and its stability, Nonlinear Analysis–TMA , 62 (2005), 643-654
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V. Radu , The fixed point alternative and the stability of functional equations, Fixed Point Theory , 4 (2003), 91-96
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APPLICATION OF BISHOP-PHELPS THEOREM IN THE APPROXIMATION THEORY
APPLICATION OF BISHOP-PHELPS THEOREM IN THE APPROXIMATION THEORY
en
en
In this paper we apply the Bishop-Phelps Theorem to show that
if \(X\) is a Banach space and \(G\subseteq X\) is a maximal subspace so that \(G^\perp = \{x^* \in
X^*\mid x^*(y) = 0; \forall y \in G\}\) is an L-summand in \(X^*\), then \(L^1(\Omega,G)\) is contained
in a maximal proximinal subspace of \(L^1(\Omega,X)\).
144
147
R.
ZARGHAMI
Faculty of Mathematical Sciences
University of Tabriz
Iran
zarghamir@gmail.com
Bishop-Phelps Theorem
support point
proximinality
L-projection.
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]
A GENERALIZATION OF NADLERS FIXED POINT THEOREM
A GENERALIZATION OF NADLERS FIXED POINT THEOREM
en
en
In this paper, we prove a generalization of Nadler's fixed point
theorem [S.B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math.
30 (1969) 475-487].
148
151
M. ESHAGHI
GORDJI
Department of Mathematics
Semnan University
Iran
madjid.eshaghi@gmail.com
H.
BAGHANI
Department of Mathematics
Semnan University
Iran
h.baghani@gmail.com
H.
KHODAEI
Department of Mathematics
Semnan University
Iran
khodaei.hamid.math@gmail.com
M.
RAMEZANI
Department of Mathematics
Semnan University
Iran
ramezanimaryam873@gmail.com
Hausdorff metric
Set-valued contraction
Nadler's fixed point theorem.
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]
AN EFFICIENT APPLICATIONS OF HES VARIATIONAL ITERATION METHOD BASED ON A RELIABLE MODIFICATION OF ADOMIAN ALGORITHM FOR NONLINEAR BOUNDARY VALUE PROBLEMS
AN EFFICIENT APPLICATIONS OF HES VARIATIONAL ITERATION METHOD BASED ON A RELIABLE MODIFICATION OF ADOMIAN ALGORITHM FOR NONLINEAR BOUNDARY VALUE PROBLEMS
en
en
In this paper, the He's variational iteration method (VIM) based
on a reliable modification of Adomian algorithm has been used to obtain solutions of the nonlinear boundary value problems (BVP). Comparison of the
result obtained by the present method with that obtained by Adomian method
[A. M.Wazwaz, Found Phys. Lett. 13 (2000) 493 and G. L. Liu, Modern Mathematical and Mechanics, (1995) 643 ] reveals that the present method is very
effective and convenient.
152
156
A.
GOLBABAI
School of Mathematics
Iran University of Science and Technology
Iran
golbabai@iust.ac.ir
K.
SAYEVAND
School of Mathematics
Iran University of Science and Technology
Iran
sayehvand@iust.ac.ir
Adomian polynomials
Boundary value problems
Variational iteration method.
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]