]>
2014
7
1
ISSN 2008-1898
68
Fixed points for Geraghty-Contractions in partial metric spaces
Fixed points for Geraghty-Contractions in partial metric spaces
en
en
We establish some fixed point theorems for mappings satisfying Geraghty-type contractive conditions in the
setting of partial metric spaces and ordered partial metric spaces. Presented theorems extend and generalize
many existing results in the literature. Examples are given showing that these results are proper extensions
of the existing ones.
1
10
Vincenzo La
Rosa
Dipartimento di Matematica e Informatica
Universita degli Studi di Palermo
Italy
vincenzo.larosa@math.unipa.it
Pasquale
Vetro
Dipartimento di Matematica e Informatica
Universita degli Studi di Palermo
Italy
vetro@math.unipa.it
Coincidence point
partial metric space
ordered partial metric space
Geraghty-type contractive condition
fixed point.
Article.1.pdf
[
[1]
T. Abdeljawad, E. Karapinar, K. Tas , A generalized contraction principle with control functions on partial metric spaces, Comput. Math. Appl., 63 (2012), 716-719
##[2]
I. Altun, A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl., Article ID 508730, doi:10.1155/2011/508730. , 2011 (2011), 1-10
##[3]
I. Altun, F. Sola, H. Simsek , Generalized contractions on partial metric spaces, Topology Appl., 157 (2010), 2778-2785
##[4]
A. Amini-Harandi, H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal., 72 (2010), 2238-2242
##[5]
H. Aydi , Fixed point theorems for generalized weakly contractive condition in ordered partial metric spaces, J. Nonlinear Anal. Optimization: Theory and Applications, 2 (2011), 33-48
##[6]
H. Aydi , Common fixed point results for mappings satisfying (\(\psi,\phi\))-weak contractions in ordered partial metric spaces, Int. J. Math. Stat. , 12 (2012), 53-64
##[7]
H. Aydi, M. Abbas, C. Vetro, Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces, Topology Appl., 159 (2012), 3234-3242
##[8]
V. Berinde, F. Vetro, Common fixed points of mappings satisfying implicit contractive conditions, Fixed Point Theory Appl., 2012:105 (2012)
##[9]
M. A. Bukatin, J. S. Scott, Towards computing distances between programs via Scott domains, in: Logical Foundations of Computer Science, Lecture Notes in Computer Science (eds. S. Adian and A. Nerode), Springer (Berlin), 1234 (1997), 33-43
##[10]
M. A. Bukatin, S.Y. Shorina, Partial metrics and co-continuous valuations, in: Foundations of Software Science and Computation Structures, Lecture Notes in Computer Science (ed. M. Nivat), Springer (Berlin),, 1378 (1998), 33-43
##[11]
K. P. Chi, E. Karapinar, T. D. Thanh , A generalized contraction principle in partial metric spaces, Math. Comput. Modelling, 55 (2012), 1673-1681
##[12]
Lj. B. Ćirić, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc., 45 (1974), 267-273
##[13]
Lj. Ćirić, B. Samet, H. Aydi, C. Vetro, Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput., 218 (2011), 2398-2406
##[14]
Lj. Ćirić, On contraction type mappings , Math. Balkanica, 1 (1971), 52-57
##[15]
C. Di Bari, P. Vetro , Fixed points for weak \(\varphi\)-contractions on partial metric spaces, Int. J. of Engineering, Contemporary Mathematics and Sciences, 1 (2011), 5-13
##[16]
C. Di Bari, Z. Kadelburg, H. Nashine, S. Radenović, Common fixed points of g-quasicontractions and related mappings in 0-complete partial metric spaces, Fixed Point Theory Appl., 2012:113 (2012)
##[17]
D. Dukić, Z. Kadelburg, S. Radenović, Fixed points of Geraghty-type mappings in various generalized metric spaces, Abstr. Appl. Anal., Article ID 561245, 2011 (2011), 1-13
##[18]
M. Geraghty , On contractive mappings, Proc. Am. Math. Soc., 40 (1973), 604-608
##[19]
R. Heckmann, Approximation of metric spaces by partial metric spaces, Appl. Categ. Structures, 7 (1999), 71-83
##[20]
D. Ilić, V. Pavlović, V. Rakočević, Some new extensions of Banach's contraction principle to partial metric space, Appl. Math. Lett., 24 (2011), 1326-1330
##[21]
E. Karapinar, Weak \(\phi\)-contraction on partial metric spaces, J. Comput. Anal. Appl., 14 (2012), 206-210
##[22]
E. Karapinar , A note on common fixed point theorems in partial metric spaces, Miskolc Math. Notes, 12 (2011), 185-191
##[23]
E. Karapinar, I. M. Erhan, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24 (2011), 1900-1904
##[24]
E. Karapinar, U. Yuksel , Some common fixed point theorems in partial metric spaces, J. Appl. Math., Article ID 263621 , 2011 (2011), 1-17
##[25]
R. D. Kopperman, S. G. Matthews, H. Pajoohesh, What do partial metrics represent? , Notes distributed at the 19th Summer Conference on Topology and its Applications, University of CapeTown (2004)
##[26]
H. P. A. Kunzi, H. Pajoohesh, M. P. Schellekens, Partial quasi-metrics, Theoret. Comput. Sci. , 365 (2006), 237-246
##[27]
S. G. Matthews , Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., 728 (1994), 183-197
##[28]
S. J. O'Neill , Partial metrics, valuations and domain theory, in: Proc. 11th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., 806 (1996), 304-315
##[29]
J. J. Nieto, R. Rodríguez-López , Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order , 22 (2005), 223-239
##[30]
J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) , 23 (2007), 2205-2212
##[31]
J. J. Nieto, R. L. Pouso, R. Rodríguez-López , Fixed point theorems in ordered abstract spaces , Proc. Amer. Math. Soc., 132 (2007), 2505-2517
##[32]
S. Oltra, O. Valero, Banach's fixed point theorem for partial metric spaces , Rend. Istit. Mat. Univ. Trieste, 36 (2004), 17-26
##[33]
D. Paesano, P. Vetro, Suzuki's type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911-920
##[34]
A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2003), 1435-1443
##[35]
S. Reich, Some remarks concerning contraction mappings , Canad. Math. Bull. , 14 (1971), 121-124
##[36]
S. Romaguera, Fixed point theorems for generalized contractions on partial metric spaces, Topology Appl., 159 (2012), 194-199
##[37]
S. Romaguera, Matkowski's type theorems for generalized contractions on (ordered) partial metric spaces, Appl. Gen. Topol., 12 (2011), 213-220
##[38]
S. Romaguera, M. Schellekens, Duality and quasi-normability for complexity space , Appl. Gen. Topol., 3 (2002), 91-112
##[39]
S. Romaguera, M. Schellekens , Partial metric monoids and semivaluation spaces, Topology Appl., 153 (2005), 948-962
##[40]
B. Samet, C. Vetro, P. Vetro , Fixed point theorems for \(\alpha-\psi\)-contractive type mappings , Nonlinear Anal., 75 (2012), 2154-2165
##[41]
M. P. Schellekens, A characterization of partial metrizability: domains are quantifiable, Theoret. Comput. Sci., 305 (2003), 409-432
##[42]
M. P. Schellekens, The correspondence between partial metrics and semivaluations, Theoret. Comput. Sci. , 315 (2004), 135-149
##[43]
T. Suzuki , A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc., 136 (2008), 1861-1869
##[44]
F. Vetro, S. Radenović, Nonlinear \(\psi\) -quasi-contractions of Ćirić-type in partial metric spaces, Appl. Math. Comput., 219 (2012), 1594-1600
]
Convergence and stability analysis of modified backward time centered space approach for non-dimensionalizing parabolic equation
Convergence and stability analysis of modified backward time centered space approach for non-dimensionalizing parabolic equation
en
en
The present paper is motivated by the desire to obtain the numerical solution of the heat equation. A
finite-difference schemes is introduced to obtain the solution. The convergence and stability analysis of the
proposed approach is discussed and compared.
11
17
Khosro
Sayevand
Faculty of Mathematical Sciences
Malayer University
Iran
ksayehvand@malayeru.ac.ir
Convergence analysis
Finite-difference schemes
Heat equation
Stability.
Article.2.pdf
[
[1]
W. A. Day, Extension of a property of the heat equation to linear thermoelasticity and other theories, Quart. Appl. Math. , 40 (1982), 319-330
##[2]
A. R. Mitchell, D. F. Griffiths , The finite difference methods in partial differential equations, Wiley, New York (1980)
##[3]
R. F. Waxming, B. J. Hyett, The modified equation approach to the stability and accuracy analysis of finite-difference methods, J. Comput. Phys., 14 (1974), 159-179
##[4]
L. Lapidus, G. F. Pinder , Numerical solution of partial differential equations in science and engineering, Wiley, New York (1982)
##[5]
C. F. Gerald, P. O. Wheatley, Applied numerical analysis, Fifth Edition, Addison-Wesley (1994)
##[6]
J. R. Cannon, S. Prez-Esteva , J. Van Der Hoek, A Galerkin procedure for the diffusion equation subject to the specification of mass, SIAM J. Num. Anal., 24 (1987), 499-515
##[7]
G. R. Habetlet, R. I. Schiffman, A finite difference method for analysing the compression of pro-viscoelasticmedia, Computing , 6 (1970), 342-348
##[8]
R. K. Miller , An integro-differential equation for rigid heat conduction equations with memory, J. Math. Anal. Appl., 66 (1978), 318-327
]
Solution and stability of a reciprocal type functional equation in several variables
Solution and stability of a reciprocal type functional equation in several variables
en
en
In this paper, we obtain the general solution and investigate the generalized Hyers-Ulam stability of a
reciprocal type functional equation in several variables of the form
\[\frac{\Pi^m_{ i=2} r(x_1 + x_i)}{\sum ^m_{i=2}[\Pi^m_{ j=2, j\neq i} r(x_1+x_j)]}=\frac{\Pi ^m _{i=1} r(x_i)}{\sum ^m_{i=2}r(x_1)[\Pi^m_{ j=2, j\neq i} r(x_j)]+ (m - 1)\Pi^m_{ i=2} r(x_i)}\]
where \(m\) is a positive integer with \(m \geq 3\).
18
27
K.
Ravi
PG & Research Department of Mathematics
Sacred Heart College
India
shckravi@yahoo.co.in
E.
Thandapani
Ramanujan Institute of Advance Study in Mathematics
University of Madras
India
ethandapani@yahoo.co.in
B.V. Senthil
Kumar
Department of Mathematics
C. Abdul Hakeem College of Engg. and Tech.
India
bvssree@yahoo.co.in
Rassias reciprocal functional equation
General reciprocal functional equations
Adjoint and difference functional equations
Article.3.pdf
[
[1]
T. Aoki , On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64-66
##[2]
Z. Gajda, On stability of additive mappings, Int. J. Math. Math. Sci., 14 (1991), 431-434
##[3]
P. Gavruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings , J. Math. Anal. Appl. , 184 (1994), 431-436
##[4]
D. H. Hyers, On the stability of the linear functional equation , Proc. Nat. Acad. Sci. U.S.A. , 27 (1941), 222-224
##[5]
J. M. Rassias, On approximation of approximately linear mappings by linear mappings, J. Funct. Anal., 6 (1982), 126-130
##[6]
J. M. Rassias , On approximation of approximately linear mappings by linear mappings, Bull. Sci. Math., 108 (1984), 445-446
##[7]
J. M. Rassias, Solution of a problem of Ulam, J. Approx.Theory, 57 (1989), 268-273
##[8]
K. Ravi, B. V. Senthil Kumar, Ulam-Gavruta-Rassias stability of Rassias Reciprocal functional equation, Global Journal of App. Math. and Math. Sci., 3 (2010), 57-79
##[9]
K. Ravi, J. M. Rassias, B. V. Senthil Kumar, Ulam stability of Generalized Reciprocal Funtional Equation in several variables, Int. J. App. Math. Stat. , 19 (2010), 1-19
##[10]
K. Ravi, J. M. Rassias, B. V. Senthil Kumar, Ulam stability of Reciprocal Difference and Adjoint Funtional Equations, The Australian J. Math. Anal.Appl., 8(1) (2011), 1-18
##[11]
K. Ravi, E. Thandapani, B. V. Senthil Kumar, Stability of reciprocal type functional equations, PanAmerican Math. Journal, 21(1) (2011), 59-70
##[12]
Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc.Amer.Math. Soc., 72 (1978), 297-300
##[13]
S. M. Ulam, A collection of mathematical problems, Interscience Publishers, Inc., New York (1960)
]
Existence and uniqueness of fixed points in modified intuitionistic fuzzy metric spaces
Existence and uniqueness of fixed points in modified intuitionistic fuzzy metric spaces
en
en
In this paper, utilizing the concept of common limit range property, we prove integral type common fixed
point theorems for two pairs of weakly compatible mappings satisfying \(\phi\)-contractive conditions in modified
intuitionistic fuzzy metric spaces. We give some examples to support the useability of our results. We
extend our results to four finite families of self mappings by using the notion of pairwise commuting.
28
41
Sunny
Chauhan
Near Nehru Training Centre
India
sun.gkv@gmail.com
Wasfi
Shatanawi
Department of Mathematics
Hashemite University
Jordan
swasfi@hu.edu.jo
Suneel
Kumar
Government Higher Secondary School
India
ksuneel_math@rediffmail.com
Stojan
Radenović
Faculty of Mechanical Engineering
University of Belgrade
Serbia
radens@beotel.net
Modified intuitionistic fuzzy metric space
weakly compatible mappings
common limit range property
fixed point.
Article.4.pdf
[
[1]
M. Aamri, D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. , 270(1) (2002), 181-188
##[2]
A. T. Atanassov , Intuitionistic fuzzy sets , Fuzzy Sets & Systems, 20 (1986), 87-96
##[3]
A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29(9) (2002), 531-536
##[4]
E. Canzoneri, P. Vetro, Fixed points for asymptotic contractions of integral Meir-Keeler type, J. Nonlinear Sci. Appl., 5(2) (2012), 126-132
##[5]
S. Chauhan, M. Imdad, B. Samet, Coincidence and Common Fixed Point Theorems in Modified Intuitionistic Fuzzy Metric Spaces, Math. Comput. Model., in press. (2013)
##[6]
S. Chauhan, B. D. Pant, S. Radenović, Common fixed point theorems for R-weakly commuting mappings with common limit in the range property, J. Indian Math. Soc., J. Indian Math. Soc. (2014), -
##[7]
Y. J. Cho, B. E. Rhoades, R. Saadati, B. Samet, W. Shatanawi , Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type, Fixed Point Theory Appl. , Vol. 2012, Article 8 (2012)
##[8]
Y. J. Cho, R. Saadati, A common fixed point theorem in intuitionistic fuzzy metric spaces, Int. J. Comput. Appl. Math., 2(1) (2007), 1-5
##[9]
G. Deschrijver, C. Cornelis, E. E. Kerre, On the representation of intuitionistic fuzzy t-norm and t-conorm, IEEE Trans. Fuzzy System, 12 (2004), 45-61
##[10]
G. Deschrijver, E. E. Kerre, On the relationship between some extensions of fuzzy set theory, Fuzzy Sets & Systems, 133 (2003), 227-235
##[11]
A. Djoudi, A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl., 329(1) (2007), 31-45
##[12]
A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets & Systems, 64 (1994), 395-399
##[13]
V. Gregori, S. Romaguera, P. Veereamani, A note on intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 28 (2006), 902-905
##[14]
M. Imdad, J. Ali , Some common fixed point theorems in fuzzy metric spaces, Math. Commun., 11 (2006), 153-163
##[15]
M. Imdad, J. Ali, M. Hasan, Common fixed point theorems in modified intuitionistic fuzzy metric spaces, Iran. J. Fuzzy Syst., 9(5) (2012), 77-92
##[16]
M. Imdad, B. D. Pant, S. Chauhan, Fixed point theorems in Menger spaces using the (CLRST ) property and applications, J. Nonlinear Anal. Optim. Theory Appl., 3(2) (2012), 225-237
##[17]
S. Jain, S. Jain, L. B. Jain, Compatibility of type (P) in modified intuitionistic fuzzy metric space, J. Nonlinear Sci. Appl., 3(2) (2010), 96-109
##[18]
G. Jungck, B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math., 29(3) (1998), 227-238
##[19]
Y. Li, F. Gu, Common fixed point theorem of Altman integral type mappings, J. Nonlinear Sci. Appl., 2(4) (2009), 214-218
##[20]
Y. Liu, Jun Wu, Z. Li, Common fixed points of single-valued and multivalued maps, Int. J. Math. Math. Sci., 2005 (2005), 3045-3055
##[21]
J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals, 22 (2004), 1039-1046
##[22]
K. P. R. Rao, Md. Mustaq Ali, A. Som Babu, Common fixed points for D-maps satisfying integral type condition, J. Nonlinear Sci. Appl., 3(4) (2010), 294-301
##[23]
R. Saadati, S. Sedghi, N. Shobe, Modified Intuitionistic fuzzy metric spaces and some fixed point theorems, Chaos, Solitons & Fractals, 38 (2008), 36-47
##[24]
B. Samet, C. Vetro, An integral version of Ćirić's fixed point theorem, Mediterr. J. Math., 9 (2012), 225-238
##[25]
S. Sedghi, N. Shobe, A. Aliouche, Common fixed point theorems in intuitionistic fuzzy metric spaces through conditions of integral type, Appl. Math. Inform. Sci., 2(1) (2008), 61-82
##[26]
W. Sintunavarat, S. Chauhan, P. Kumam, Some fixed point results in modified intuitionistic fuzzy metric spaces, Afrika Mat. DOI 10.1007/s13370-012-0128-0 , in press (2013)
##[27]
W. Sintunavarat, P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., Article ID 637958, 2011 (2011), 1-14
##[28]
T. Suzuki, Meir-Keeler contractions of integral type are still Meir-Keeler contractions, Int. J. Math. Math. Sci. Art. ID 39281, 2007 (2007), 1-6
##[29]
M. Tanveer, M. Imdad, D. Gopal, D. K. Patel , Common fixed point theorems in modified intuitionistic fuzzy metric spaces with common property (E.A.) , Fixed Point Theory Appl., 2012 (2012), 1-36
##[30]
C. Vetro , On Branciari's theorem for weakly compatible mappings, Appl. Math. Lett., 23(6) (2010), 700-705
##[31]
P. Vijayaraju, B. E. Rhoades, R. Mohanraj , A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Internat. J. Math. Math. Sci., 15 (2005), 2359-2364
]
Common fixed point theorems under rational contractions in complex valued metric spaces
Common fixed point theorems under rational contractions in complex valued metric spaces
en
en
In this paper, we prove some common fixed point theorems for a pair of mappings satisfying certain rational
contractions in the frame work of complex valued metric besides discussing consequences of our main results.
To illustrate our results and to distinguish them from the existing ones, we equip the paper with suitable
examples.
42
50
H. K.
Nashine
Department of Mathematics
Disha Institute of Management and Technology
India
drhknashine@gmail.com;hemantnashine@gmail.com
M.
Imdad
Department of Mathematics
Aligarh Muslim University
India
mhimdad@yahoo.co.in
M.
Hasan
Department of Mathematics
Aligarh Muslim University
India
hasan352000@gmail.com
Common fixed point
contractive type mapping
complex valued metric space.
Article.5.pdf
[
[1]
A. Azam, B. Fisher, M. Khan, Common Fixed Point Theorems in Complex Valued Metric Spaces, Num. Func. Anal. Opt., 32 (2011), 243-253
##[2]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133-181
##[3]
V. W. Bryant , A remark on a fixed-point theorem for iterated mappings, Amer. Math. Monthly, 75 (1968), 399-400
##[4]
M. Imdad, J. Ali, M. Tanveer, Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces, Chaos Solitons Fractals, 42 (2009), 3121-3129
##[5]
M. Imdad, Q. H. Khan, Six mapping satisfying a rational inequality, Radovi Math(Presently Sarajevo Journal), 9 (1999), 251-260
##[6]
F. Rouzkard, M. Imdad , Some common fixed point theorems on complex valued metric spaces, Comp. Math. Appls., 64 (2012), 1866-1874
##[7]
W. Sintunavarat, P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and applications, J. Inequalities Appl., 2012 (2012), 1-11
]
Proof of one open inequality
Proof of one open inequality
en
en
In this paper, one conjecture presented in the paper [V. Cîrtoaje, Proofs of Three Open Inequalities With
Power-Exponential Functions, J. Nonlinear Sci. Appl. 4 (2011) no.2, 130-137, http://www.tjnsa.com] is
proved.
51
62
Ladislav
Matejíčka
Faculty of Industrial Technologies in Puchov
Trencin University of Alexander Dubcek in Trencin
Slovakia
ladislav.matejicka@tnuni.sk
Inequality
Power-exponential functions.
Article.6.pdf
[
[1]
V. Cîrtoaje, Proofs of Three Open Inequalities With Power-Exponential Functions, J. Nonlinear Sci. Appl., 4 (2011), 130-137
]
Various symmetries in matrix theory with application to modeling dynamic systems
Various symmetries in matrix theory with application to modeling dynamic systems
en
en
In this paper, we recall centrally symmetric matrices and introduce some new kinds of symmetric matrices
such as row-wise symmetric matrices, column-wise symmetric matrices, and plus symmetric matrices. The
relations between these kinds of matrices are also presented. Furthermore, a useful result is obtained
about the types of the eigenvectors of centrally symmetric matrices leading to a limit-wise relation between
centrally symmetric matrices and plus symmetric matrices which can be applied to mathematical modeling
of dynamical systems in engineering applications.
63
69
Arya Aghili
Ashtiani
Department of Electrical and Computer Engineering
Abbaspour College of Engineering, Shahid Beheshti University
Iran
arya.aghili@gmail.com
Pandora
Raja
Department of Mathematics
Shahid Beheshti University
Iran
p_raja@sbu.ac.ir
Sayyed Kamaloddin Yadavar
Nikravesh
Department of Electrical Engineering
Amirkabir University of Technology
Iran
nikravsh@aut.ac.ir
Special symmetry
symmetric matrices
mathematical modeling.
Article.7.pdf
[
[1]
A. Aghili Ashtiani, M. B. Menhaj, Numerical Solution of Fuzzy Relational Equations Based on Smooth Fuzzy Norms, Soft Computing, 14 (2010), 545-557
##[2]
A. Cantoni, P. Butler, Elgenvalues and Elgenvectors of Symmetric Centrosymmetrlc Matrlces, Linear Algebra Appl., 13 (1976), 275-288
##[3]
C. T. Chen, Linear System Theory and Design, 4th Ed., Oxford University Press (2012)
##[4]
I. J. Good , The Inverse of a Centrosymmetric Matrix, Technometrics, 12 (1970), 925-928
##[5]
K. Hoffman, R. Kunze, Linear Algebra, second ed., Prentice-Hall, Inc. (1971)
##[6]
L. Lebtahi, O. Romero, N. Thome, Relations Between \(\{K; s+1\}\)-potent matrices and Different Classes of Complex Matrices, Linear Algebra Appl., 438 (2013), 1517-1531
##[7]
H. Li, D. Zhao, F. Dai, D. Su, On the spectral radius of a nonnegative centrosymmetric matrix, Appl. Math. Comput., 218 (2012), 4962-4966
##[8]
T. Muir, A Treatise on the Theory of Determinants, Dover (originally published 1883). , (1960)
##[9]
V. V. Prasolov, Problems and Theorems in Linear Algebra, Translations of Mathematical Monographs, No. 134 (1994)
##[10]
Z. Tian, C. Gu, The Iterative Methods for Centrosymmetric Matrices, Appl. Math. Comput., 187 (2007), 902-911
##[11]
F. Z. Zhou, L. Zhang, X. Y. Hu, Least-Square Solutions for Inverse Problems of Centrosymmetric Matrices, Computers and Mathematics with Applications, 45 (2003), 1581-1589
]