2015
2
2
2
90
Generalized multivalued $F$weak contractions on complete metric spaces
2
2
In this paper, we introduce the notion of generalized multivalued $F$ weak contraction and we prove some fixed point theorems related to introduced contraction for multivalued mapping in complete metric spaces. Our results extend and improve the results announced by many others with less hypothesis. Also, we give some illustrative examples.
1

1
11


Hossein
Piri
Department of Mathematics, Faculty of Science, University of Bonab, P.O.Box 5551761167, Bonab, Iran.
Department of Mathematics, Faculty of Science,
Iran
hossein_piri1979@yahoo.com


Samira
Rahrovi
Department of Mathematics, Faculty of Science, University of Bonab, P.O.Box 5551761167, Bonab, Iran.
Department of Mathematics, Faculty of Science,
Iran
sarahrovi@gmail.com
Multivalued $F$ weak contraction
Fixed point
Multivalued mappings
[[1] "{O}. Acar and I. Altun, A Fixed Point Theorem for Multivalued Mappings with $delta$Distance. Abstr. Appl. Anal., 2014 (2014), Article ID 497092, 5 pages. ##[2] "{O}. Acar, G. Durmaz and G Minak, Generalized multivalued Fcontractions on complete metric spaces. Bull. Iranian Math. Soc., 40 (2014) 14691478. ##[3] R.P. Agarwal, D. O'Regan and N. Shahzad, Fixed point theory for generalized contractive maps of MeirKeeler type, Math. Nachr., 276 (2004) 322. ##[4] I. Altun, G. Minak and H. Dau{u}g, Multivalued Fcontractions on complete metric space, J. Convex Anal., Accepted. ##[5] S. Banach, Sur les op'{e}rations dans les ensembles abstraits et leur application aux equations itegrales, Fund. Math., 3 (1922) 133181. ##[6] V. Berinde, On the approximation of fixed points of weak contractive mappings, Carpathian J. Math., 19 (2003) 722. ##[7] V. Berinde, Iterative Approximation of Fixed Points, SpringerVerlag, Berlin, 2007. ##[8] D.W. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20 (1969) 458464. ##[9] L.B. '{C}iri'{c}, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc., 45 (1974) 267273. ##[10] W. S. Du, Some new results and generalizations in metric fixed point theory, Nonlinear Anal., 73 (2010) 14391446. ##[11] G.E. Hardy and T. D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull., 16 (1973) 201206. ##[12] J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc., 62 (1977) 344348. ##[13] G. Minak, A. Helvac and I. Altun, '{C}iri'{c} Type Generalized Fcontractions on CompleteMetric Spaces and Fixed Point Results., Filomat 28 (2014) 11431151. ##[14] SB. Nadler, Multivalued contraction mappings, Pac. J. Math., 30 (1969) 475488. ##[15] H. Piri and P. Kumam, Some fixed point theorems concerning Fcontraction in complete metric spaces, Fixed Point Theory Appl., 2014, 2014:210 doi:10.1186/168718122014210. ##[16] S. Reich, Kannan's fixed point theorem, Boll. Un. Mat. Ital., (4) 4 (1971) 111. ##[17] D. Wardowski and N. Van Dung, Fixed points of fweak contractions on complete metric spaces, Demonstratio Math., 1 (2014) 146155 ##[18] D. Wardowski, Fixed point theory of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl., 2012, Article ID 94 (2012).##]
Some new properties of fuzzy strongly ${{g}^{*}}$closed sets and $delta {{g}^{*}}$closed sets in fuzzy topological spaces
2
2
In this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$closed sets is introduced and its properties are investigated. Moreover, we study some more properties of this type of closed spaces.
1

13
21


Hamidreza
Moradi
Young Researchers and Elite Club‎, ‎Mashhad Branch‎, ‎Islamic Azad University‎, ‎Mashhad‎, ‎Iran
Young Researchers and Elite Club‎,
Iran
hrmoradi@mshdiau.ac.ir


Anahid
Kamali
Department of Mathematics, Khaje Nasir Toosi University of Technology, Tehran, Iran.
Department of Mathematics, Khaje Nasir Toosi
Iran
ana.kamali.gh@gmail.com


Balwinder
Singh
Department of Mathematics‎, ‎P‎. ‎M‎. ‎Thevar College‎, ‎Usilampatti‎, ‎Madurai Dt‎, ‎Tamil Nadu‎, ‎India
Department of Mathematics‎, ‎P&
Iran
singhba.a@gmail.com
Fuzzy topological spaces
Fuzzy generalized closed sets
Fuzzy ${{g}^{*}}$closed sets
Fuzzy strongly ${{g}^{*}}$closed sets
[[1] K. K. Azad, On fuzzy semi continuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl., 82 (1) (1981) 1432. ##[2] G. Balasubramanian, On fuzzypreseparation axiom, Bull., Calcutta Math Soc., 90 (6) (1998) 427434. ##[3] G. Balasubramanian, and V. Chandrasekar, Totally fuzzy semi continuous functions, Bull. Calcutta Mat Soc., 92 (4) (2000) 305312. ##[4] G. Balasubramanian and P. Sundaram, On some generalization of fuzzy continuous functions, Fuzzy Sets and Systems., 86 (1) (1997) 93100. ##[5] S.S. Benchalli and G.P. Siddapur, Fuzzy ${{g}^{*}}$precontinuous maps in fuzzy topological spaces, Int. Jou. Comp. Appl., 16 (2) (2011) 1215. ##[6] C. L. Chang, Fuzzy topological spaces, J. Math Anal Appl., 24 (1968) 182190. ##[7] W. Dunham, A new closure operator for non$T_1$ topologies, Kyungpook Math. J., {22} (1982), 5560. ##[8] N. Levine, Generalized closed sets in topology, Rend. Circ. Mat. Palermo., {19} (2) (1970), 8996. ##[9] M. E. ElShafei and A. Zakari, $theta $generalized closed sets in fuzzy topological spaces, The Arabian Journal for Science and Engineering., 31 (2A) (2006) 197206. ##[10] H. Maki, Generalized $Lambda $sets and the associated closure operator, Special Issue in Commemoration of Prof. Kazusada Ikeda’s Retirement 1. Oct (1986), 139146. ##[11] H.R. Moradi, Bounded and semi bounded inverse theorems in fuzzy normed spaces, International Journal of Fuzzy System Applications., 4 (2) (2015) 4755. ##[12] H.R. Moradi, Characterization of fuzzy complete normed space and fuzzy $b$complete set, Sahand Communications in Mathematical Analysis., {1} (2) (2014) 6575. ##[13] S. Murugesan and P. Thangavelu, Fuzzy presemiclosed sets, Bull. Malays, Math Sci. Soc., 31 (2) (2008) 223232. ##[14] R. Parimelazhagan and V. S. Pillai, Strongly $g$closed sets in topological spaces, Int. Jou. Of Math. Analy., 6 (30) (2012) 14811489. ##[15] P.M. Pu and Y.M. Liu, Fuzzy topology I. neighbourhood structure of a fuzzy point and Mooresmith convergence, J. Math Anal Appl., 76 (2) (1980) 571599. ##[16] R.K. Saraf, G. Navalagi and M. Khanna, On fuzzy semipregeneralized closed sets, Bull. Malays. Math Sci. Soc., 28 (1) (2005) 1930. ##[17] R.K. Saraf and M. Khanna, On $gs$closed set in fuzzy topology, J. Indian Acad. Math., 25 (1) (2003) 133143. ##[18] S.S. Thakur and S. Sing, On fuzzy semipre open sets and fuzzy semipre continuity, Fuzzy Sets and Systems., 98 (3) (1998) 383391. ##[19] M.K.R.S. Veerakumar, Between closed sets and gclosed sets, Mem. Fac. Sci. Kochi Univ. Ser. A. Math., 17 (21) (2000) 119. ##[20] T.H. Yalvac, Semiinterior and semiclosure of a fuzzy set, J.Math. Anal. Appl., 132 (2) (1988) 356364. ##[21] L.A. Zadeh, Fuzzy sets, Inform and Control., 8 (1965) 338353.##]
Abstract structure of partial function $*$algebras over semidirect product of locally compact groups
2
2
This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$function spaces over semidirect product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism. Let $G_tau=Hltimes_tau K$ be the semidirect product of $H$ and $K$ with respect to $tau$. We define left and right $tau$convolution on $L^1(G_tau)$ and we show that, with respect to each of them, the function space $L^1(G_tau)$ is a Banach algebra. We define $tau$convolution as a linear combination of the left and right $tau$convolution and we show that the $tau$convolution is commutative if and only if $K$ is abelian. We prove that there is a $tau$involution on $L^1(G_tau)$ such that with respect to the $tau$involution and $tau$convolution, $L^1(G_tau)$ is a nonassociative Banach $*$algebra. It is also shown that when $K$ is abelian, the $tau$involution and $tau$convolution make $L^1(G_tau)$ into a Jordan Banach $*$algebra. Finally, we also present the generalized notation of $tau$convolution for other $L^p$spaces with $p>1$.
1

23
44


Arash
Ghaani Farashahi
Numerical Harmonic Analysis Group (NuHAG), Faculty of Mathematics,
University of Vienna, OskarMorgensternPlatz 1, A1090 Wien, Vienna, Austria.
Numerical Harmonic Analysis Group (NuHAG),
Iran
arash.ghaani.farashahi@univie.ac.at


Rajab Ali
KamyabiGol
Department of Pure Mathematics, Ferdowsi University of Mashhad,
Center of Excellence in Analysis on Algebraic Structures (CEAAS), P. O. Box 115991775, Mashhad, Iran.
Department of Pure Mathematics, Ferdowsi
Iran
kamyabi@ferdowsi.ac.ir
Semidirect products of groups
Left $tau$convolution ($tau_l$convolution)
Right $tau$convolution ($tau_r$convolution)
$tau$convolution
$tau$involution
$tau$approximate identity
[[1] A.A. Arejamaal, The continuous Zak transform and generalized Gabor frames, Mediterr. J. Math. 10 (2013), No. 1, 353365.##[2] A.A. Arejamaal and A. Ghaani Farashahi, Zak transform for semidirect product of locally compact groups, Anal. Math. Phys. 3 (2013), No. 3, 263276.##[3] A.A. Arejamaal and R.A. KamyabiGol, On the square integrability of quasi regular representation on semidirect product groups, J. Geom. Anal. 19 (2009), No. 3, 541552.##[4] A.A. Arejamaal and R.A. KamyabiGol, On construction of coherent states associated with semidirect products, Int. J. Wavelets Multiresolut. Inf. Process. 6 (2008), No. 5, 749759.##[5] W.R. Bloom and H. Heyer, Harmonic Analysis of Probability Measures on Hypergroups, de Gruyter Studies in Mathematics, 20, Walter de Gruyter (1995).##[6] G. Chirikjian and A. Kyatkin, Engineering Applications of Noncommutative Harmonic Analysis With Emphasis on Rotation and Motion Groups, Boca Raton, FL: CRC Press. xxii, 2001.##[7] A. Derighetti, Convolution operators on groups, Lecture Notes of the Unione Matematica Italiana, 11. Springer, Heidelberg; UMI, Bologna, 2011. xii+171 pp. ISBN: 9783642206559.##[8] J. Dixmier, CAlgebras, NorthHolland and Publishing company, 1977.##[9] J. Fell and R. Doran, Representations of Algebras, Locally Compact Groups,mand Banach Algebraic Bundles, Pure and Applied Mathematics, Vol. 1, Academic Press, 1998.##[10] J. Fell and R. Doran, Representations of Algebras, Locally Compact Groups, and Banach Algebraic Bundles, Pure and Applied Mathematics, Vol. 2, Academic Press, 1998.##[11] G.B. Folland, A course in Abstract Harmonic Analysis, CRC press, 1995.##[12] A. Ghaani Farashahi, Continuous partial Gabor transform for semidirect productm of locally compact groups, Bull. Malays. Math. Sci. Soc. 38 (2015), No. 2, 779803.##[13] A. Ghaani Farashahi, A unied group theoretical method for the partial Fourier analysis on semidirect product of locally compact groups, Results Math. 67 (2015), No. 12, 235251.##[14] A. Ghaani Farashahi, Cyclic wave packet transform on nite Abelian groups of prime order, Int. J. Wavelets Multiresolut. Inf. Process. 12 (2014), No. 6, 1450041, 14 pp.##[15] A. Ghaani Farashahi, Generalized WeylHeisenberg (GWH) groups, Anal. Math. Phys. 4 (2014), No. 3, 187197.##[16] A. Ghaani Farashahi, Convolution and involution on function spaces of homogeneous spaces, Bull. Malays. Math. Sci. Soc., (2) 36 (2013), No. 4, 11091122.##[17] A. Ghaani Farashahi, Abstract NonCommutative Harmonic Analysis of Coherent State Transforms, Ferdowsi University of Mashhad (FUM) (2012) PhD Thesis.##18. A. Ghaani Farashahi and M. MohammadPour, A unied theoretical harmonic analysis approach to the cyclic wavelet transform (CWT) for periodic signals of prime dimensions, Sahand Commun. Math. Anal. Vol. 1, No. 2, 117 (2014).##[19] A. Ghaani Farashahi and R.A. KamyabiGol, Frames and homogeneous spaces, J. Sci. Islam. Repub. Iran., 22 (2011), No. 4, 355361, 372.##[20] S. Helgason, Dierential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, San Francisco, London, 1978.##[21] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, Vol 2, 1970.##[22] E. Hewitt and K.A. Ross, Absrtact Harmonic Analysis, Vol 1, 1963.##[23] G. Hochschild, The Structure of Lie Groups, Hpoldenday, San Francisco, 1965.##[24] R.I. Jewett, Spaces with an abstract convolution of measures, Advances in Math., 18 (1975), 1101.##[25] R.A. KamyabiGol and N. Tavallaei, Wavelet transforms via generalized quasiregular representations, Appl. Comput. Harmon. Anal., 26 (2009), No. 3, 291 300.##[26] V. Kisil, Calculus of operators: covariant transform and relative convolutions, Banach J. Math. Anal. 8 (2014), No. 2, 156184.##[27] V. Kisil, Geometry of Mobius transformations. Elliptic, parabolic and hyperbolic actions of SL2(R), Imperial College Press, London, 2012.##[28] V. Kisil, Relative convolutions. I. Properties and applications, Adv. Math. 147 (1999), No. 1, 3573.##[29] V. Kisil, Connection between twosided and onesided convolution type operators on noncommutative groups, Integral Equations Operator Theory 22 (1995), No. 3, 317332.##[30] H. Reiter and J.D. Stegeman, Classical Harmonic Analysis, 2nd Ed, Oxford University Press, New York, 2000.##]
Generalized concept of $J$basis
2
2
A generalization of Schauder basis associated with the concept of generalized analytic functions is introduced. Corresponding concepts of density, completeness, biorthogonality and basicity are defined. Also, corresponding concept of the space of coefficients is introduced. Under certain conditions for the corresponding operators, some properties of the space of coefficients and basicity criterion are considered.
1

45
59


Tofig
Najafov
Nakhchivan State University, University campus, AZ7012 Nakhchivan,
Azerbaijan.
Nakhchivan State University, University campus,
Iran
department2011@mail.ru
$J$completeness
$J$biorthogonality
$J$basicity
The space of coefficients
[[1] L. Bers, Theory of pseudoanalytic functions, Lecture Notes, New York University, 1953.##[2] L. Bers, F. John, and M. Schechter, Partial dierential equations, Lectures in Applied Mathematics III. Interscience Publishers, New York, 1964.##[3] B.T. Bilalov, Bases and tensor product, Trans. of NAS of Az., XXV(4) (2005), 1520.##[4] A.V. Bitsadze, Boundary value problems for second order elliptic equations, Moscow, Nauka, 1966, 204 p.##[5] O. Christensen, An introduction to frames and Riesz bases, Springer, 2002.##[6] A. Douglis, A function theoretical approach to elliptic systems of equations in two variables, Comm. Pure Math., VI (1953) 259289.##[7] H.G. Feichtinger and K.H. Grochenig, Banach spaces related to integrable group representations and their atomic decompositions, Part II. Monatshefte fur Mathematik, 108(23) (1989), 129148.##[8] S.A. Gabov and A.G. Sveshnikov, Linear problems of the theory of nonstationary internal waves, M., Nauka, 1990.##[9] K.H. Grochenig, Describing functions: atomic decompositions versus frames, Monatshefte fur Mathematik, 112(1) (1991), 142.##[10] Ch. Heil, A Basis Theory Primer, Springer, 2011.##[11] G.N. Hile, Elliptic systems in the plane with order terms and constant coecients, Comm. in Part. Di. Equat., 3(10) (1978), 949977.##[12] Yu.D. Pletner, Representation of solutions of the twodimensional gravitationalgyroscopic wave equation by generalized Taylor and Laurent series, Zh. Vychisl. Mat. Mat. Fiz., 30(11) (1990), 17281740.##[13] Yu.D. Pletner, Representation of the solutions of twodimensional analogues of the Sobolev equation by generalized Taylor and Laurent series, Comput. Math. Math. Phys., 32(1) (1992), 5160.##[14] A. Rahimi, Frames and Their Generalizations in Hilbert and Banach Spaces, Lambert Academic Publishing. 2011.##[15] I. Singer, Bases in Banach spaces, v.2, Springer, 1981.##[16] I. Singer, Bases in Banach spaces, v. 1, Springer, 1970.##[17] A.P. Soldatov, Secondorder elliptic systems in the halfplane, Izvestiya: Mathematics, 70(6) (2006), 161192.##[18] A.P. Soldatov, A function theorety method in elliptic problems in the plane, II. The piecewise smooth case, Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 56(3) (1992), 566604.##[19] A.P. Soldatov, A function theory method in boundary value problems in the plane, I. The smooth case, Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 55(5) (1991), 10701100.##[20] A.P. Soldatov, Boundary properties of integrals of Cauchy type, Dierential Equations, 26(1) (1990), 116120.##[21] A.P. Soldatov, Highorder ellipticsystems, Dierential Equations, 25(1) (1989), 109115.##[22] A.G. Sveshnikov, A.B. Al'shin, M.O. Korpusov, and Yu.D. Pletner, Linear and nonlinear equations of Sobolev type, Fizmatlit, Moscow, 2007.##[23] I.N. Vekua, New methods of solution of elliptic equations, Moscow, Gostekhizdat, 1948.##[24] I.N. Vekua, Generalized Analytic Functions, Moscow, Fizmatqiz, 1959.##[25] R.M. Young, An Introduction to Nonharmonic Fourier series, Springer, 1980.##]
A note on "Generalized bivariate copulas and their properties"
2
2
In 2004, Rodr'{i}guezLallena and '{U}bedaFlores have introduced a class of bivariate copulas which generalizes some known families such as the FarlieGumbelMorgenstern distributions. In 2006, Dolati and '{U}bedaFlores presented multivariate generalizations of this class. Then in 2011, Kim et al. generalized Rodr'{i}guezLallena and '{U}bedaFlores' study to any given copula family. But there are some inaccuracies in the study by Kim et al. We mean to consider the interval for the parameter proposed by Kim et al. and show that it is inaccurate.
1

61
64


Vadoud
Najjari
Young Researchers and Elite Club, Maragheh branch, Islamic Azad University, Maragheh, Iran.
Young Researchers and Elite Club, Maragheh
Iran
fnajjary@yahoo.com


Asghar
Rahimi
Department of Mathematics, University of Maragheh, P.O.Box 55181
83111, Maragheh, Iran.
Department of Mathematics, University of
Iran
rahimi@maragheh.ac.ir
Absolutely continuous functions
Bivariate distributions
Copulas
[[1] T. Bacig'{a}l, R. Mesiar, V. Najjari, Generators of copulas and aggregation, Information Sciences, 306 (2015) 8187. ##[2] T. Bacig'{a}l, V. Najjari, R. Mesiar, H. Bal, Additive generators of copulas, Fuzzy Sets and Systems, 264 (2015) 4250. ##[3] H. Bal, V. Najjari, Archimedean copulas family via hyperbolic generator, Gazi University Journal of Science, 26(2): (2013) 195200. ##[4] H. Bekrizadeh, G. A. Parham. M. R. Zadkarmi, The New Generalization of FarlieâGumbelâMorgenstern Copulas, Applied Mathematical Sciences, 6(71) (2012) 35273533. ##[5] H. Bekrizadeh, G. A. Parham. M. R. Zadkarmi, A new class of positive dependent bivariate copula and its properties, Proc. of the 2nd Workshop on Copula and its Applications, (2012) 1221. ##[6] A. Dolati, M. '{U}bedaFlores, Some new parametric families of multivarite copulas, International Mathematical Forum, 1 (2006) 1725. ##[7] J. M. Kim, E. A. Sungur, T. Choi, T. Y. Heo, Generalized bivariate copulas and their properties, Model Assisted Statistics and Applications, 6 (2011) 127136. ##[8] R. Mesiar, J. Komorn'{i}k, M. Komorn'{i}kov'{a}, On some construction methods for bivariate copulas, Advances in Intelligent Systems and Computing, 228 (2013) 3945. ##[9] R. Mesiar, V. Najjari, New families of symmetric/asymmetric copulas, Fuzzy Sets and Systems, 252 (2014) 99110. ##[10] V. Najjari., T. Bacig'{a}l., H. Bal., An Archimedean Copula Family with Hyperbolic Cotangent Generator, International Journal of Uncertainty, Fuzziness and KnowledgeBased Systems, 22(5): (2014) 761768. ##[11] R. B. Nelsen, An Introduction to copulas, Springer, New York, (Second edition), 2006. ##[12] J. A. Rodr'{i}guezLallena, M. '{U}bedaFlores, A new class of bivariate copulas, Statistics and Probability Letters, 66 (2004) 315325. ##[13] S. T. c{S}ahin Tekin, V. Najjari, H. H. "{O}rkc"{u}, Simulation study on copulas, Sahand Communications in Mathematical Analysis, 1(2) (2014) 5563.##]
Fixed point theorems for $alpha$contractive mappings
2
2
In this paper we prove existence the common fixed point with different conditions for $alphapsi$contractive mappings. And generalize weakly Zamfirescu map in to modified weakly Zamfirescu map.
1

65
72
حجت
افشاری
Hojjat
Afshari
Faculty of Basic Science, University of Bonab, P.O.Box 5551761167, Bonab, Iran.
Faculty of Basic Science, University of Bonab,
Iran
hojat.afshari@yahoo.com
مجتبی
سجادمنش
Mojtaba
Sajjadmanesh
Faculty of Basic Science, University of Bonab, P.O.Box 5551761167, Bonab, Iran.
Faculty of Basic Science, University of Bonab,
Iran
s.sajjadmanesh@azaruniv.edu
$alpha$contractive map
Modified weakly Zamfirescu map
Fixed point
[[1] D. ArizaRuiza, A. JimenezMelado, A continuation method for weakly Kannan maps, fixed point theory and applications, (2010), Art. Id 321594, 12pp.##[2] D. ArizaRuiza, A. JimenezMelado, Genaro Lopezacedo, A fixed point theorem for weakly Zamfirescu mappings, Nonlinear analysis (2010).##[3] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fund. Math., 3 (1922) 133181.##[4] S. K. Chatterjea, Fixedpoint theorems, C. R. Acad. Bulgare Sci., 25 (1972) 727730.##[5] J. Dugundji, A. Granas, Weakly contractive maps and elementary domain invariance theorem, Bull. Soc. Math. Greece (N. S) 19, No.1 (1978) 141151.##[6] R. Kannan, Some results on fixed points, Bull Calcutta Math. Soc., 60 (1968), 7176.##[7] B. Samet, C. Vetro, P. Vetro, Fixedpoint theorems for αΨcotractive type mappings, Nonlinear Analysis (2011), .##[8] T. Zamfirescu, Fixedpoint theorems in metric spacesArch. Math., 23 (1972), 292298.##]
A tensor product approach to the abstract partial fourier transforms over semidirect product groups
2
2
In this article, by using a partial on locally compact semidirect product groups, we present a compatible extension of the Fourier transform. As a consequence, we extend the fundamental theorems of Abelian Fourier transform to nonAbelian case.
1

73
81


Ali akbar
Arefijammal
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.
Department of Mathematics and Computer Sciences,
Iran
arefijamaal@gmail.com


Fahimeh
Arabyani Neyshaburi
Department of Mathematics and Computer Sciences, Hakim Sabzevari University, Sabzevar, Iran.
Department of Mathematics and Computer Sciences,
Iran
arabyanif@hsu.ac.ir
Partial Fourier transform
Locally compact groups
Semidirect product groups
Artial dual groups
[[1] S.T. Ali, J.P. Antoine, and J.P. Gazeau, Coherent States, Wavelets and Their Generalizations, SpringerVerlag, New York, 2000.##[2] A. Arejamaal, The continuous Zak transform and generalized Gabor frames, Mediterr. J. Math. 10 (2013) 353365.##[3] A. Arejamaal and R.A. KamyabiGol, On the square integrability of quasi regular representation on semidirect product groups, J. Geom. Anal. 19 (2009) No. 3, 541552. ##[4] G.S. Chirikjian and A.B. Kyatkin, Engineering applications of noncommutative harmonic analysis. With emphasis on rotation and motion groups, CRC Press, 2001.##[5] H.G. Dales, Banach Algebras and Automatic Continuity, London Mathematical Society Monographs 24, Clarendon Press, Oxford, 2000.##[6] J. Dixmier, C*Algebras, NorthHolland, Amsterdam, 1977.##[7] J. Fell and R. Doran, Representations of *Algebras, Locally Compact Groups, and Banach *Algebraic Bundles, Pure and Applied Mathematics, vol. 1, 1st edn. Academic Press, 1998.##[8] J. Fell and R. Doran, Representations of Algebras, Locally Compact Groups, and Banach *Algebraic Bundles, Pure and Applied Mathematics, vol. 2, 1st edn. Academic Press, 1998.##[9] G.B. Folland, A Course in Abstract Harmonic Analysis, CRC Press, Boca Raton, 1995.##[10] A. Ghaani Farashahi and R.A. KamyabiGol, Abstract structure of partial function *algebras over semidirect product of locally compact groups, Sahand. Comm. Math. Anal., to be appear, 2015, (arXiv:1201.1854).##[11] A. Ghaani Farashahi, A unied group theoretical method for the partial Fourier analysis on semidirect product of locally compact groups, Results. Math. 67 (2015) no. 12, 235251.##[12] A. Ghaani Farashahi, Continuous partial Gabor transform for semidirect product of locally compact groups, Bull. Malays. Math. Sci. Soc. 38 (2015) no. 2, 779803.##[13] A. Ghaani Farashahi, Generalized WeylHeisenberg (GWH) groups, Anal. Math. Phys. 4 (2014) no. 3, 187197.##[14] E. Hewitt and K.A. Ross, Abstract Harmonic Analysis, SpringerVerlag. Vol 2, Berlin, SpringerVerlag, 1969.##[15] K.B. Laursen, Tensor products of Banach algebras with involution, Trans. Amer. Math. Soc. 136 (1969) 467487.##[16] D. Maslen and D. Rockmore, Generalized FFTs  a survey of some recent results, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Groups and Computation, II, L. Finkelstein and W. Kantor (eds.), (1996) 18323. CMP 97:11##[17] H. Reiter and J.D. Stegeman, Classical Harmonic Analysis and Locally Compact Groups, London Math. Soc. Monographs 22, Oxford Univ. Press, 2000.##[18] D. Rockmore, Applications of generalized FFTs, DIMACS Ser. Discrete Math. Theoret. Comput. Sci., Groups and Computation, II, L. Finkelstein and W. Kantor (eds.), (1996). CMP 97:11##19. V. Runde, Lectures on Amenability, Springer, Berlin, 2002.##]
Chaotic dynamics and synchronization of fractional order PMSM system
2
2
In this paper, we investigate the chaotic behaviors of the fractionalorder permanent magnet synchronous motor (PMSM) system. The necessary condition for the existence of chaos in the fractionalorder PMSM system is deduced and an active controller is developed based on the stability theory for fractional systems. The presented control scheme is simple and flexible, and it is suitable both for design and for implementation in practice. Simulation is carried out to verify that the obtained scheme is efficient and robust for controlling the fractionalorder PMSM system.
1

83
90


Vajiheh
Vafaei
Faculty of Mathematical sciences, University of Tabriz, tabriz, Iran.
Faculty of Mathematical sciences, University
Iran
v_vafaei@tabrizu.ac.ir


Hossein
Kheiri
Faculty of Mathematical sciences, University of Tabriz, tabriz, Iran.
Faculty of Mathematical sciences, University
Iran
hkheiri@tabrizu.ac.ir


Mohammad
Javidi
Faculty of Mathematical sciences, University of Tabriz, tabriz, Iran.
Faculty of Mathematical sciences, University
Iran
mojavidi@yahoo.com
Permanent Magnet Synchronous Motor
Fractionalorder systems
Chaotic synchronization
[[1] K. Diethelm, The Analysis of Fractional Dierential Equations, SpringerVerlag, Berlin, 2010.##[2] K. Kemih, Control of nuclear spin generator system based on passive control, Chaos Solitons Fract., 41 (2009) 18971901.##[3] N. Laskin, Fractional market dynamics, Physica A, 287 (2000) 482492. doi:10.1016/S03784371(00)003873.##[4] J.G. Lu, Chaotic dynamics and synchronization of fractionalorder Arneodo's systems, Chaos, Solitons and Fractals, 26 (2005) 11251133.##[5] L.M. Pecora and T.L. Carroll, Synchronization of chaotic systems, Phys. Rev. Lett., 64 (1990) 821824.##[6] H. Salarieh and A. Alasty, Chaos synchronization of nonlinear gyros in presence of stochastic excitation via sliding mode control, J. Sound Vib., 313 (2008) 760771.##[7] M.S. Tavazoei and M. Haeri, Chaotic attractors in incommensurate fractional order systems, Physica D, 237 (2008) 26282637.##[8] Z. Xinghua and D. Shougang, Adaptive chaotic synchronization of permanent magnet synchronous motors with nonsmooth airgap, Control Theory and Applications, 26 (6) (2009) 661664.##]