]>
2010
3
3
ISSN 2008-1898
76
FUZZY MINIMAL SEPARATION AXIOMS
FUZZY MINIMAL SEPARATION AXIOMS
en
en
In this paper, we deal with some separation axioms in the context
of fuzzy minimal structures.
157
163
M.
ALIMOHAMMADY
Department of Mathematics, Faculty of Basic Sciences
University of Mazandaran
Iran
amohsen@umz.ac.ir
E.
EKICI
Department of Mathematics
Canakkale Onsekiz Mart University
Turkey
eekici@comu.edu.tr
S.
JAFARI
Department of Economics
Copenhagen University
Denmark
jafari@stofanet.dk
M.
ROOHI
Department of Mathematics, Faculty of Basic Sciences
University of Mazandaran
Iran
mehdi.roohi@gmail.com
Fuzzy sets
fuzzy topology
fuzzy separation axiom.
Article.1.pdf
[
[1]
M. Alimohammady, S. Jafari, M. Roohi, Fuzzy minimal connected sets, Bull. Kerala Math. Assoc., 5 (2008), 1-15
##[2]
M. Alimohammady, M. Roohi , Compactness in fuzzy minimal spaces, Chaos, Solitons & Fractals, 28 (2006), 906-912
##[3]
M. Alimohammady, M. Roohi, Fuzzy minimal structure and fuzzy minimal vector spaces, Chaos, Solitons & Fractals, 27 (2006), 599-605
##[4]
M. Alimohammady, M. Roohi , Fuzzy transfer minimal closed multifunctions, Ital. J. Pure Appl. Math., 22 (2007), 67-74
##[5]
M. Alimohammady, M. Roohi, Fuzzy Um sets and fuzzy (U;m)-continuous functions, Chaos, Solitons, & Fractals , 28 (2006), 20-25
##[6]
M. Alimohammady, M. Roohi, \(\Lambda_m\)-Set in fuzzy minimal space , Journal of Basic Science, 3 (2006), 11-17
##[7]
M. Alimohammady, M. Roohi, Separation of fuzzy sets in fuzzy minimal spaces, Chaos, Solitons & Fractals, 31 (2007), 155-161
##[8]
A. Azam, M. Arshad, I. Beg , Common fixed point theorems in cone metric spaces, J. Nonlinear Sci. Appl., 2 (2009), 204-213
##[9]
B. Ghosh , Semi-continuous and semi-closed mappings and semi-connectedness in fuzzy setting, Fuzzy sets syst. , 35 (1990), 345-355
##[10]
I. M. Hanafy, \(\beta S^*\)-compactness in L-fuzzy topological spaces, J. Nonlinear Sci. Appl., 2 (2009), 27-37
##[11]
S. Jafari, K. Viswanathan, M. Rajamani, S. Krishnaprakash, On decomposition of fuzzy A-continuity, J. Nonlinear Sci. Appl., 1 (2008), 236-240
##[12]
P. Pao-Ming, L. Ying-Ming, Fuzzy topology I. neighborhood structure of a fuzzy point and and Moore-Smith convergence, J. Math. Anal. Appl. , 76 (1980), 571-599
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P. Pao-Ming, L. Ying-Ming , Fuzzy Topology II. Product and quotient spaces, J. Math. Anal. Appl., 77 (1980), 20-37
##[14]
L. A. Zadeh, Fuzzy sets, Inf. control, 8 (1965), 338-353
]
REDUCTION OF AN OPERATOR EQUATION IN TO AN EQUIVALENT BIFURCATION EQUATION THROUGH SCHAUDERS FIXED POINT THEOREM
REDUCTION OF AN OPERATOR EQUATION IN TO AN EQUIVALENT BIFURCATION EQUATION THROUGH SCHAUDERS FIXED POINT THEOREM
en
en
In this paper we deal with the Nonlinear Coupled Ordinary Differential Equations(Nonlinear CODE). A Multipoint Boundary Value Problem(MBVP) associated with these Nonlinear Equations is defined as an Operator Equation. This equation(infinite dimensional) is reduced to an Equivalent
Bifurcation Equation(finite dimensional) using Schauder's Fixed Point Theorem. This Bifurcation Equation being on a finite dimensional space can be
easily solved by using standard approximation techniques.
164
178
PALLAV KUMAR
BARUAH
Department of Mathematics and Computer Science
Sri Sathya Sai University
India
baruahpk@sssu.edu.in
B V K
BHARADWAJ
Department of Mathematics and Computer Science
Sri Sathya Sai University
India
bvkbharadwaj@sssu.edu.in
M
VENKATESULU
Department of Mathematics and Computer Applications
Kalasalingam University
India
venkatesulum 2000@yahoo.co.in
Coupled Differential Operator
Nonlinear Operator
Hilbert Space.
Article.2.pdf
[
[1]
A. Aliouche, Common Fixed Point Theorems for Hybrid Mappings Satysfying Generalised Contractive Conditions, Journal of Nonlinear Sciences and Applications, 2 (2009), 136-145
##[2]
A. Azam, M. Arshad, I. Beg, Common Fixed Point Theorems in cone Metric Spaces , Journal of Nonlinear Sciences and Applications, 1 (2009), 204-213
##[3]
L. Cesari, Functional analysis and Galerkin's Method, Mich. Math J., 11 (1964), 385-359
##[4]
L. Cesari, R. Kannan , Functional analysis and nonlinear differential equations, Contributions to differential equations, vol 1, No 2, Interscience, Newyork (1956)
##[5]
P. C. Das, M. Venkatesulu, An Alternative Method for Boundary Value Problems with Ordinary Differential Equations , Riv. Math. Univ. Parma, 4 (1983), 15-25
##[6]
P. C. Das, M. Venkatesulu, An Existential Analysis for a Nonlinear Differential Equation with Nonlinear Multipoint Boundary Conditions via the alternative mathod, Att. Sem. Mat. Fis.Univ, Modena, XXXII , (1983), 287-307
##[7]
P. C. Das, M. Venkatesulu, An Existential Analysis for a Multipoint Boundary Value Problem via Alternative Method, Riv. Math. Univ. Parma, 4 (1984), 183-193
##[8]
L. Kantarovich, Functional Analysis and Applied Mathematics, Uspehi Mat.Nauk, 3 (1948), 89-185
##[9]
J. Locker , Functional Analysis and Two Point Differential operators, Longman scientific and Technical, Harlow (1986)
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J. Locker, An existential analysis for nonlinear boundary value problems, SIAM J. Appl. Math., 19 (1970), 109-207
##[11]
P. K. Baruah, B. V. K. Bharadwaj, M. Venkatesulu, Characterization of Maximal, Minimal and Inverse Operators and an Existence Theorem for Coupled Ordinary Differential Operator, International Journal of Mathematics and Analysis, 1 (2009), 25-56
##[12]
P. K. Baruah, B. V. K. Bharadwaj, M. Venkatesulu, Green's Matrix for Linear Coupled Ordinary Differential Operator, International Journal of Mathematics and Analysis, 1(1) (2009), 57-82
##[13]
R. Ali Khan, N. Ahmad Asif, Positive Solutions for a Class of Singular Two Point Boundary Value Problems, Journal of Nonlinear Sciences and Applications, 2 (2009), 126-135
##[14]
S. Sinha, O. P. Mishra, J. Dhar, Study of a prey-predator dynamics under the simultaneous effectof toxicant and disease, The Journal of Nonlinear Sciences and Applications, 1 (2008), 36-44
##[15]
M. Venkatesulu, P. K. Baruah, A. Prabu, A Existence theorem for IVPs of Coupled Ordinary Differential Equations, International Journal of Differential Equations and Applications, 10 (2005), 435-447
]
COUPLED FIXED POINTS OF SET VALUED MAPPINGS IN PARTIALLY ORDERED METRIC SPACES
COUPLED FIXED POINTS OF SET VALUED MAPPINGS IN PARTIALLY ORDERED METRIC SPACES
en
en
Let \((X,\preceq)\) be a partially ordered set and \(d\) be a metric on \(X\)
such that \((X, d)\) is a complete metric space. Let \(F : X \times X \rightsquigarrow X\) be a mixed
monotone set valued mapping. We obtain sufficient conditions for the existence
of a coupled fixed point of \(F\).
179
185
ISMAT
BEG
Centre for Advanced Studies in Mathematics
Lahore University of Management Sciences
Pakistan
ibeg@lums.edu.pk
ASMA RAS
BUTT
Centre for Advanced Studies in Mathematics
Lahore University of Management Sciences
Pakistan
asmar@lums.edu.pk
Coupled fixed point
partially ordered set
metric space
set valued mapping.
Article.3.pdf
[
[1]
I. Beg, Random fixed points of increasing compact maps, Archivum Mathematicum , 37 (2001), 329-332
##[2]
I. Beg, A. Azam, Fixed points of asymptotically regular multivalued mappings, J. Austral. Math. Soc. (Series-A) , 53(3) (1992), 313-326
##[3]
I. Beg, A. R. Butt, Fixed point for set valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal. , 71 (2009), 3699-3704
##[4]
I. Beg, A. R. Butt , Fixed points for weakly compatible mappings satisfying an implicit relation in partially ordered metric spaces, Carpathian J. Math. , 25 (2009), 1-12
##[5]
I. Beg, A. R. Butt, Common fixed point for generalized set valued contractions satisfying an implicit relation in partially ordered metric spaces, Mathematical Communications, 15 (2010), 65-76
##[6]
I. Beg, A. Latif, R. Ali, A. Azam, Coupled fixed points of mixed monotone operators on probabilistic Banach spaces, Archivum Mathematicum , 37 (2001), 1-8
##[7]
T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393
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J. Harjani, K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal. , 71 (2009), 3403-3410
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J. Harjani, K. Sadarangani, Generalized contractions in partially ordered mtric spaces and applications to ordinary differential equations, Nonlinear Anal. doi:10.1016/j.na.2009.08.003, in press (2009)
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D. Klim, D. Wardowski , Fixed point theorems for set-valued contractions in complete metric spaces, J. Math. Anal. Appl., 334 (2007), 132-139
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J. J. Nieto, R. L. Pouso, R. Rodríguez-López, Fixed point theorems in ordered abstract spaces, Proc. Amer. Math. Soc., 135 (2007), 2505-2517
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J. J. Nieto, R. Rodríguez-López, Contractive mapping theorms in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239
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J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta. Math. Sinica, (English Ser.), 23 (2007), 2205-2212
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D. O'Regan, A. Petrusel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341 (2008), 1241-1252
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A. Petrusel, I. A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc., 134 (2005), 411-418
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A. C. M. Ran, M. C. B. Reurings, A fixed point theorm in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443
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S. Reich, Fixed points of contractive functions, Boll. Unione. Mat. Ital., 4 (1972), 26-42
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Y. Wu, New fixed point theorems and applications of mixed monotone operator, J. Math. Anal. Appl., 341 (2008), 883-893
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Z. Zhitao, New fixed point theorems of mixed monotone operators and applications, J. Math. Anal. Appl., 204 (1996), 307-319
]
COMMENTS ON THE PAPER BY GORDJI AND BAGHANI ENTITLED - A GENERALIZATION OF NADLERS FIXED POINT THEOREM
COMMENTS ON THE PAPER BY GORDJI AND BAGHANI ENTITLED - A GENERALIZATION OF NADLERS FIXED POINT THEOREM
en
en
We point out that the theorem of the paper listed in the title is a
known result.
186
187
B. E.
RHOADES
Department of Mathematics
Indiana University
USA
rhoades@indiana.edu
fixed points
multivalued maps.
Article.4.pdf
[
[1]
M. E. Gordji, H. Baghani, A generalization of Nadler's fixed point theorem, J. Nonlinear Sci. and Appl., 3 (2010), 1148-151
##[2]
G. Garegnani, S. Massa, Multi-valued mappings of congtractive type, Ist. Lombardo Accad. Sci. Rend A, 112 (1978), 283-288
##[3]
K. Iseki , Multi-valued contraction mappings in complete metric spaces, Rend. Sem. Mat. Univ. Padova, 53 (1975), 15-19
##[4]
S. N. Mishra, A note on common fixed points of multivalued mappings in uniform space, Math. Sem. Notes, 9 (1981), 341-347
##[5]
V. Popa , A common fixed point theorem for a sequence of multifunctions, Studia Univ. Babes-Bolyai Math., 24 (1979), 39-41
##[6]
V. Popa, Common fixed points for a sequence of multifunctions, Stud. Cerc. Mat. 34 (1982), 370-373. , 42 (2005), 661-670
##[7]
C. Zanco, G. Garegnani , Fixed points of somehow contractive multivalued mappings, Ist. Lombardo Accad. Sci. Lett. Rend A, 114 (1980), 138-148
]
SEVERAL DISCRETE INEQUALITIES FOR CONVEX FUNCTIONS
SEVERAL DISCRETE INEQUALITIES FOR CONVEX FUNCTIONS
en
en
In this paper, we establish some interesting discrete inequalities
involving convex functions and pose an open problem.
188
192
XINKUAN
CHAI
College of Mathematics and Information Science
Henan Normal University
China
chaixinkuan@gmail.com
YONGGANG
ZHAO
College of Mathematics and Information Science
Henan Normal University
China
ztyg68@tom.com
HONGXIA
DU
College of Mathematics and Information Science
Henan Normal University
China
duhongxia24@gmail.com
Qi-type inequality
discrete inequality
convex functions.
Article.5.pdf
[
[1]
M. Akkouchi , On an integral inequality of Feng Qi, Divulg. Mat., 13 (2005), 11-19
##[2]
L. Bougoffa, Notes on Qi type integral inequalities, J. Inequal. Pure and Appl. Math., 4 (2003), 1-77
##[3]
Y. Chen, J. Kimball, Note on an open problem of Feng Qi , J. Inequal. Pure and Appl. Math., 7 (2006), 1-4
##[4]
V. Csiszár, T. F. Mµori, The convexity method of proving moment-type inequalities, Statist. Probab. Lett., 66 (2004), 303-313
##[5]
W. J. Liu, Q. A. Ngô, V. N. Huy, Several interesting integral inequalities, J. Math. Inequal., 3 (2009), 201-212
##[6]
S. Mazouzi, F. Qi, On an open problem regarding an integral inequality, J. Inequal. Pure and Appl. Math., 4 (2003), 1-31
##[7]
Y. Miao, Further development of Qi-type integral inequality, J. Inequal. Pure and Appl. Math., 7 (2006), 1-144
##[8]
I. Miao, J. F. Li, Further development of an open problem, J. Inequal. Pure and Appl. Math., 9 (2008), 1-108
##[9]
I. Miao, J. F. Liu, Discrete results of Qi-type inequality, Bull. Korean Math. Soc., 46 (2009), 125-134
##[10]
I. Miao, F. Qi, A discrete version of an open problem and several answers, J. Inequal. Pure and Appl. Math., 10 (2009), 1-49
##[11]
J. Pečarić, T. Pejković, Note on Feng Qi's integral inequality, J. Inequal. Pure and Appl. Math., 5 (2004), 1-51
##[12]
T. K. Pogány, On an open problem of F. Qi, J. Inequal. Pure and Appl. Math., 3 (2002), 1-54
##[13]
F. Qi, Several integral inequalities, J. Inequal. Pure and Appl. Math., 1 (2000), 1-19
##[14]
F. Qi, A. J. Li, W. Z. Zhao, D. W. Niu, J. Cao, Extensions of several integral inequalities, JIPAM. J. Inequal. Pure and Appl. Math., 7 (2006), 1-107
##[15]
N. Towghi, Notes on integral inequalities, RGMIA Res. Rep. Coll., 4 (2001), 277-278
##[16]
K.-W. Yu, F. Qi, A short note on an integral inequality, RGMIA Res. Rep. Coll., 4 (2001), 23-25
]
SOME COMMON FIXED POINT RESULTS IN NON-NORMAL CONE METRIC SPACES
SOME COMMON FIXED POINT RESULTS IN NON-NORMAL CONE METRIC SPACES
en
en
The aim of this paper is to obtain extended variants of some
common fixed point results in cone metric spaces in the case that the underlying
cone is not normal. The first result concerns g-quasicontractions of D. Ilić and
V. Rakočević [Common fixed points for maps on cone metric space, J. Math.
Anal. Appl. 341 (2008), 876-882], and the second is concerned with Hardy-Rogers-type conditions and extends some recent results of M. Abbas, B. E.
Rhoades and T. Nazir [Common fixed points for four maps in cone metric
spaces, Appl. Math. Comput. 216 (2010), 80-86].
193
202
ZORAN
KADELBURG
Faculty of Mathematics
University of Belgrade
Serbia
kadelbur@matf.bg.ac.rs
STOJAN
RADENOVIĆ
Faculty of Mechanical Engineering
University of Belgrade
Serbia
radens@beotel.net
Common fixed point
ordered Banach space
cone metric space
normal and non-normal cone
weakly compatible mappings.
Article.6.pdf
[
[1]
M. Abbas, G. Jungck, Common Fixed point results of noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 418-420
##[2]
M. Abbas, B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett., 22 (2009), 511-515
##[3]
M. Abbas, B. E. Rhoades, T. Nazir, Common fixed points for four maps in cone metric spaces, Appl. Math. Comput., 216 (2010), 80-86
##[4]
Lj. B. Ćirić, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc., 45 (1974), 267-273
##[5]
K. M. Das, K. V. Naik, Common fixed point theorems for commuting maps on cone metric spaces, Proc. Amer. Math. Soc., 77 (1979), 369-373
##[6]
K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, (1985)
##[7]
L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1467-1475
##[8]
D. Ilić, V. Rakočević, Common fixed points for maps on cone metric space , J. Math. Anal. Appl., 341 (2008), 876-882
##[9]
D. Ilić, V. Rakočević, Quasi-contraction on cone metric space, Appl. Math. Lett. , 22 (2009), 728-731
##[10]
G. Jungck , Common fixed points for noncontinuous nonself maps on nonmetric spacers, Far East J. Math. Sci., 4 (1986), 199-215
##[11]
G. Jungck, S. Radenović, S. Radojević, V. Rakočević, Common fixed point theorems for qeakly compatible pairs on cone metric spaces, Fixed Point Theory Appl., Article ID 643840, doi:10.1155/2009/643840. , 2009 (2009), 1-13
##[12]
Z. Kadelburg, M. Pavlović, S. Radenović, Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces, Comput. Math. Appl., 59 (2010), 3148-3159
##[13]
Z. Kadelburg, S. Radenović, V. Rakočević, Remarks on ''Quasi-contraction on a cone metric space'', Appl. Math. Lett. , 22 (2009), 1674-1679
##[14]
Z. Kadelburg, S. Radenović, V. Rakočević, Topological vector space valued cone metric spaces and fixed point theorems, Fixed Point Theory Appl., (in press. ), -
##[15]
Sh. Rezapour, R. H. Haghi, N. Shahzad, Some notes on fixed points of quasi-contraction maps, Appl. Math. Lett., 23 (2010), 498-502
]
STABILIZABILITY OF A CLASS OF NONLINEAR SYSTEMS USING HYBRID CONTROLLERS
STABILIZABILITY OF A CLASS OF NONLINEAR SYSTEMS USING HYBRID CONTROLLERS
en
en
This paper develops hybrid control strategies for stabilizing a class
of nonlinear systems. Common Lyapunov functions and switched Lyapunov
functions are used to establish easily verifiable criteria for the stabilizability of
weakly nonlinear systems under switched and impulsive control. Three types
of controller switching rules are studied: time-dependent (synchronous), state-dependent (asynchronous) and average dwell-time satisfying. Conditions are
developed for stabilizability under arbitrary switching, as well as less strict conditions for prespecified switching rules. Examples are given, with simulations,
to illustrate the theorems developed.
203
221
XINZHI
LIU
Department of Applied Mathematics
University of Waterloo
Canada
xzliu@uwaterloo.ca;xzliu@math.uwaterloo.ca
PETER
STECHLINSKI
Department of Applied Mathematics
University of Waterloo
Canada
pstechli@math.uwaterloo.ca
Hybrid systems
Switched systems
Stabilizability
Switched control
Impulsive control
Synchronous switching
State-dependent switching
Dwell-time switching.
Article.7.pdf
[
[1]
A. Bacciotti, L. Mazzi, An invariance principle for nonlinear switched systems, Systems & Control Letters , 54 (2005), 1109-1119
##[2]
M. S. Branicky, Stability of switched and hybrid systems , Proceedings of the 33rd IEEE Conference on Decision and Control , 4 (1994), 3498-3503
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, Multiple lyapunov functions and other analysis tools for switched and hybrid systems, IEEE Transactions on Automatic Control , 43 (1998), 475-482
##[4]
J. Daafouz, P. Riedinger, C. Iung, Stability analysis and control synthesis for switched systems: A switched lyapunov function approach, IEEE Transactions on Automatic Control , 47 (2002), 1883-1887
##[5]
G. Davrazos, N. T. Koussoulas, A review of stability results for switched and hybrid systems, Proceedings of 9th Mediterranean Conference on Control and Automation, (2001)
##[6]
R. A. Decarlo, M. S. Branicky, S. Pettersson, B. Lennartson, Perspectives and results on the stability and stabilizability of hybrid systems , Proceedings of the IEEE , 88 (2000), 1069-1082
##[7]
R. J. Evans, A. V. Savkin, Hybrid dynamical systems, Birkhauser, (2002)
##[8]
Zhi-Hong Guan, D. J. Hill, Xuemin Shen, On hybrid impulsive and switching systems and application to nonlinear control, IEEE Transactions on Automatic Control , 50 (2005), 1058-1062
##[9]
Zhi-Hong Guan, D. J. Hill, Jing Yao, A hybrid impulsive and switching control strategy for synchronization of nonlinear systems and application to chua's chaotic circuit, International Journal of Bifurcation and Chaos , 16 (2006), 229-238
##[10]
J. P. Hespanha , Extending lasalle's invariance principle to switched linear systems, Proceedings of the 40th IEEE Conference on Decision and Control , (2001), 2496-2501
##[11]
, Uniform stability of switched linear systems: Extensions of lasalle's invariance principle, IEEE Transactions on Automatic Control , 49 (2004), 470-482
##[12]
J. P. Hespanha, A. S. Morse, Stability of switched systems with average dwell-time, Proceedings of the 38th IEEE Conference on Decision and Control , 3 (1999), 2655-2660
##[13]
Sehjeong Kim, S. A. Campbell, Xinzhi Liu, Stability of a class of linear switching systems with time delay, IEEE Transactions on Circuits and Systems I: Regular Papers , 53 (2006), 384-393
##[14]
Z. Li, Y. Soh, C. Wen, Switched and impulsive systems: Analysis, design, and applications, Springer-Verlag, Berlin Heielberg (2005)
##[15]
D. Liberzon, A. S. Morse, Basic problems in stability and design of switched systems, IEEE Control Systems Magazine , 19 (1999), 59-70
##[16]
Jun Liu, Xinzhi Liu, Wei-Chau Xie, On the \((h_0,h)\)-stabilization of switched nonlinear systems via state-dependent switching rule, Applied Mathematics and Computation , 217 (2010), 2067-2083
##[17]
Y. Mori, T. Mori, Y. Kuroe, A solution to the common lyapunov function problem for continuous-time systems, Proceedings of the 36th IEEE Conference on Decision and Control , 4 (1997), 3530-3531
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E. Moulay, R. Bourdais, W. Perruquetti, Stabilization of nonlinear switched systems using control lyapunov functions, Nonlinear analysis: Hybrid Systems , 1 (2007), 482-490
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K. S. Narendra, J. Balakrishnan, A common lyapunov function for stable lti systems with commuting a-matrices, IEEE Transactions on Automatic Control , 39 (1994), 2469-2471
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S. Pettersson, B. Lennartson , Stability and robustness for hybrid systems, Proceedings of the 35th IEEE Conference on Decision and Control , (1996)
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R. N. Shorten, F. O. Cairbre, P. Curran, On the dynamic instability of a class of switching system, International Journal of Control , 79 (2006), 630-635
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Robert Shorten, Fabian Wirth, Oliver Mason, Kai Wulff, Christopher King, Stability criteria for switched and hybrid systems, SIAM Review , 49 (2007), 545-592
##[23]
A. van der Schaft, H. Schumacher, An introduction to hybrid dynamical systems, Springer-Verlag, London (2000)
##[24]
Hui Ye, A. N. Michel, Ling Hou, Stability theory for hybrid dynamical systems, IEEE Transactions on Automatic Control , 43 (1998), 461-474
]
CONVERGENCE THEOREMS OF A SCHEME WITH ERRORS FOR I-ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS
CONVERGENCE THEOREMS OF A SCHEME WITH ERRORS FOR I-ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS
en
en
In this paper, we prove weak and strong convergence of the Ishikawa
iterative scheme with errors to common fixed point I-asymptotically quasi-
nonexpansive mappings in a Banach space. The results obtained in this paper
improve and generalize the corresponding results in the existing literature.
222
233
SEYIT
TEMIR
Department of Mathematics, Art and Science Faculty
Harran University
Turkey
temirseyit@harran.edu.tr
I-asymptotically quasi-nonexpansive mapping
Ishikawa iterative schemes
convergence theorems.
Article.8.pdf
[
[1]
M. K. Ghosh, L. Debnath , Convergence of Ishikawa iterates of quasi-nonexpansive mappings , J. Math. Anal. Appl. , 207 (1997), 96-103
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K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171-174
##[3]
S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147-150
##[4]
H. Y. Lan, Common fixed point iterative processes with errors for generalized asymptotically quasi-nonexpansive mappings, Computers and Math. with Applications, 52 (2006), 1403-1412
##[5]
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