OVIDIU T. POP. 1. Introduction. The inequality from Theorem 1 is called in the literature Bergström s inequality (see [2], [3], [4], [6]).
|
|
- Russell Lang
- 6 years ago
- Views:
Transcription
1 Journal of Mathematical Inequalities Volume 3, Number 009, 37 4 ABOUT BERGSTRÖM S INEQUALITY OVIDIU T POP Communicated by P Bullen Abstract In this paper, we generalize identity 3, from where we obtain a rafinement of inequalities and Introduction The inequality from Theorem is called in the literature Bergström s inequality see [], [3], [4], [6] THEOREM If x k R and a k > 0, k {,,,n},then x a x a x n a n x x x n a a a n, x with equality if and only if x x n a a a n The generalizationof Bergström s inequality is contained in the following theorem see [5] THEOREM If x k R and a k > 0, k {,,,n},then x x x n x x x n a i x j a i x j max a a a n a a a n a i a j By particularizations in Theorem, in paper [5] the refinements are obtained of Cauchy-Schwarz s inequality For the complex numbers, it is well-known the identity: z a z a z z a a a z a z a a a a 3 Mathematics subject classification 000: 6D5 Keywords and phrases: Bergström s inequality, Lagrange s identity, multivariate inequalities refinements c D l,zagreb Paper JMI
2 38 OVIDIU T POP true for any z,z C and any a,a R\{0} such that a a 0see[6],page 35 In the following, we note N {,,} Main results In this section we start with the generalization of identity 3 THEOREM 3 If n N, n, z,z,,z n C and a,a,,a n R\{0},such that a a a n 0,then z z z n z z z n 4 a a a n a a a n a i z j a j z i a a a n Proof We consider z k x k iy k, x k,y k R, k {,,,n} Then the member from the left from the 4 is equivalent with x y x y x ny n x x x n y y y n a a a n a a a n a a a n a a a n a a 3 a 4 a n a a 3a 4 a n a a 3 a n a nx y a a 3a 4 a n a a 3 a 4 a n a a 3 a n a n x y a a a 3 a n a a a 3 a n a a a n a nx ny n a a a n x x x x 3 x x n x n x n y y y y 3 y y n y n y n a3 a 4 a n a x a x a y a y a a a n a a a n a a 4 a 5 a n a x 3 a 3 x a y 3 a 3 y a a a n an x n a n x n a n y n a n y n a3 a 4 a n a z a z a a a n a a a n a a 4 a 5 a n a z 3 a 3 z a a a n a n z n a n z n, from where, the relation 4 results
3 ABOUT BERGSTRÖM S INEQUALITY 39 COROLLARY If n N, n, x,x,,x n R and a,a,,a n R\{0},such that a a a n 0,then x a x a x n a n x x x n a a a n 5 a i x j a j x i a a a n Proof In the identity 4 we consider z k x k R, k {,,,n} COROLLARY If n N, x, x k,y k R, k {,,,n},then x x x n y y y n 6 x y x y x n y n x i y j x j y i Proof Changing a k by y k and x k by x k y k, k {,,,n} in identity 5, we obtain identity 6 REMARK The identity from Corollary is called Lagrange s identity COROLLARY 3 If z,z,,z n C and a,a,,a n 0,, then z z z n z z z n, 7 a a a n a a a n with equality if and only if a i z j a j z i for any i, j {,,,n} Proof The inequality 7 results immediately from Theorem 3 THEOREM 4 If n N, n, z,z,,z n C and a,a,,a n R\{0} such that a a a n > 0,then z a z a z n a n a a a n with equality if and only if z z z n 0 Proof It results from Theorem 3 COROLLARY 4 If n N, n and z,z,,z n C, then a i z j a j z i, 8 z z z n n z j z i 9
4 40 OVIDIU T POP Proof The inequality 9 results from Theorem 4 if we take a a a n where THEOREM 5 If n N, n, x,x,,x n R and a,a,,a n 0,, then x x x n x x x n 0 a a a n a a a n a i x j a j x i A k,l a a a n, A k,l max Proof We have that T n m m m a i x j a j x i a i a j a kx l a l x k, k < l n a k a l a k a l am x l a l x m x k a k x m a l a k a k x l a la k x m a l a k x m a l x k al a k and applying the inequality for n, we obtain that T a k a l n a k x l a l x k n a k x l a l x k a k a l a k a l m m a k a l a k a l Taking the inequality above into account, we have that a i x j a j x i a a a n a k x l a l x k n am x l a l x m a a a n a k a l x k a k x m m a l x k a a a n a a a n a i x j a j x i a k x l a l x k a k a l n m a i x j a j x i a a a n, a k x l a l x k a k a l a k a l from where and taking identity 5 into account, the inequality 0 results
5 ABOUT BERGSTRÖM S INEQUALITY 4 REMARK From Theorem 5 the inequalities from and results THEOREM 6 If n N, n, x i,y i R, i {,,,3},then n x i n y i n y i if y i 0 for any i {,,,n}, n x i n y i n x i n x i y i x k y l x l y k y k y l x i y j x j y i n x i y i x p y q x q y p x p x q x i y j x j y i i, j {p,q} if x i 0 for any i {,,,}, wherek,l, p,q {,,,n}, k l, p q such that x max i y j x j y i x i y j x j y i is obtained for i k and j l, max y i y j x i is obtained x j for i p and j q Proof In Theorem 5 we change a i by y i and x i with x i y i, i {,,,n} and we obtain the inequality, respectively x i by y i, i {,,,n} in inequality and then we obtain inequality COROLLARY 5 If n N, n, x i,y i R\{0}, i {,,,n}, then the inequalities n x i n y i n x i y i n y i x i y j x j y i y i y j 3 and n x i n y i hold for any i, j {,,,n} n x i y i n xi y j x j y i x i x i y j 4 Proof It results from Theorem 6 REMARK 3 Using the inequalities from Corollary 5, we obtain some inequalities from paper [5]
6 4 OVIDIU T POP REFERENCES [] G HARDY, J E LITTLEWOOD AND G PÓLYA, Inequalities, Cambridge, 934 [] E F BECHENCBACH AND R BELLMAN, Inequalities, Springer, Berlin, Göttingen and Heidelberg, 96 [3] R BELLMAN, Notes on Matrix Theory - IV An Inequality Due to Bergström, Amer Math Montly, Vol 6 955, 7 73 [4] H BERGSTRÖM, A triangle inequality for matrices, Den Elfte Skandinaviske Matematikerkongress, 949, Trodheim, Johan Grundt Tanums Forlag, Oslo, 95, [5] D MĂRGHIDANU, J L DÍAZ-BARRERO AND S RĂDULESCU, New refinements of some classical inequalities, to appear in Math Ineq& Appl [6] D S MITRINOVIĆ, Analytic Inequalities, Springer-Verlag, Berlin, 970 Received October, 008 Ovidiu T Pop National College Mihai Eminescu 5 Mihai Eminescu Street Satu Mare Romania ovidiutiberiu@yahoocom Journal of Mathematical Inequalities wwwele-mathcom jmi@ele-mathcom
A new refinement of the Radon inequality
MATHEMATICAL COMMUNICATIONS 319 Math. Commun. 16(2011), 319 324. A new refinement of the Radon inequality Cristinel Mortici 1, 1 Valahia University of Târgovişte, Department of Mathematics, Bd. Unirii
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics NOTES ON AN INTEGRAL INEQUALITY QUÔ C ANH NGÔ, DU DUC THANG, TRAN TAT DAT, AND DANG ANH TUAN Department of Mathematics, Mechanics and Informatics,
More informationIdentities and inequalities in a quadrilateral
OCTOGON MATHEMATICAL MAGAZINE Vol. 17, No., October 009, pp 754-763 ISSN 1-5657, ISBN 978-973-8855-5-0, www.hetfalu.ro/octogon 754 Identities inequalities in a quadrilateral Ovidiu T. Pop 3 ABSTRACT. In
More informationOn mixed discriminants of positively definite matrix
Also available at http://amc-journal.eu ISSN 1855-3966 printed edn., ISSN 1855-3974 electronic edn. ARS MATHEMATICA CONTEMPORANEA 9 2015 261 266 On mixed discriminants of positively definite matrix Chang-Jian
More informationNOTE ON HADWIGER FINSLER S INEQUALITIES. 1. Introduction
Journal of Mathematical Inequalities Volume 6, Number 1 (01), 57 64 NOTE ON HADWIGER FINSLER S INEQUALITIES D.Ş. MARINESCU, M.MONEA, M.OPINCARIU AND M. STROE (Communicated by S. Segura Gomis) Abstract.
More informationLOWELL. MICHIGAN. WEDNESDAY, FEBRUARY NUMllEE 33, Chicago. >::»«ad 0:30am, " 16.n«l w 00 ptn Jaekten,.'''4snd4:4(>a tii, ijilwopa
4/X6 X 896 & # 98 # 4 $2 q $ 8 8 $ 8 6 8 2 8 8 2 2 4 2 4 X q q!< Q 48 8 8 X 4 # 8 & q 4 ) / X & & & Q!! & & )! 2 ) & / / ;) Q & & 8 )
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics MATRIX AND OPERATOR INEQUALITIES FOZI M DANNAN Department of Mathematics Faculty of Science Qatar University Doha - Qatar EMail: fmdannan@queduqa
More informationGENERALIZATION ON KANTOROVICH INEQUALITY
Journal of Mathematical Inequalities Volume 7, Number 3 (203), 57 522 doi:0.753/jmi-07-6 GENERALIZATION ON KANTOROVICH INEQUALITY MASATOSHI FUJII, HONGLIANG ZUO AND NAN CHENG (Communicated by J. I. Fujii)
More informationd A L. T O S O U LOWELL, MICHIGAN. THURSDAY, DECEMBER 5, 1929 Cadillac, Nov. 20. Indignation
) - 5 929 XXX - $ 83 25 5 25 $ ( 2 2 z 52 $9285)9 7 - - 2 72 - - 2 3 zz - 9 86 - - - - 88 - q 2 882 q 88 - - - - - - ( 89 < - Q - 857-888 - - - & - - q - { q 7 - - - - q - - - - - - q - - - - 929 93 q
More informationGROWTH OF THE MAXIMUM MODULUS OF POLYNOMIALS WITH PRESCRIBED ZEROS M. S. PUKHTA. 1. Introduction and Statement of Result
Journal of Classical Analysis Volume 5, Number 2 (204, 07 3 doi:0.753/jca-05-09 GROWTH OF THE MAXIMUM MODULUS OF POLYNOMIALS WITH PRESCRIBED ZEROS M. S. PUKHTA Abstract. If p(z n a j j is a polynomial
More informationON THE QUASI MONOTONE AND ALMOST INCREASING SEQUENCES. 1. Introduction
Journal of Mathematical Inequalities Volume 1, Number 4 (2007), 529 534 ON THE QUASI MONOTONE AND ALMOST INCREASING SEQUENCES H. BOR AND H. S. ÖZARSLAN (communicated by G. Toader) Abstract. In this paper,
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics POLYNOMIALS AND CONVEX SEQUENCE INEQUALITIES A.McD. MERCER Department of Mathematics and Statistics University of Guelph Ontario, N1G 2W1, Canada.
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics A SURVEY ON CAUCHY-BUNYAKOVSKY-SCHWARZ TYPE DISCRETE INEQUALITIES S.S. DRAGOMIR School of Computer Science and Mathematics Victoria University of
More informationUNIQUENESS THEOREMS ON FUNCTIONAL INEQUALITIES CONCERNING CUBIC QUADRATIC ADDITIVE EQUATION
Journal of Mathematical Inequalities Volume, Number 08, 43 6 doi:0.753/jmi-08--04 UNIQUENESS THEOREMS ON FUNCTIONAL INEQUALITIES CONCERNING CUBIC QUADRATIC ADDITIVE EQUATION YANG-HI LEE, SOON-MO JUNG AND
More informationON THE HILBERT INEQUALITY. 1. Introduction. π 2 a m + n. is called the Hilbert inequality for double series, where n=1.
Acta Math. Univ. Comenianae Vol. LXXVII, 8, pp. 35 3 35 ON THE HILBERT INEQUALITY ZHOU YU and GAO MINGZHE Abstract. In this paper it is shown that the Hilbert inequality for double series can be improved
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics THE EXTENSION OF MAJORIZATION INEQUALITIES WITHIN THE FRAMEWORK OF RELATIVE CONVEXITY CONSTANTIN P. NICULESCU AND FLORIN POPOVICI University of Craiova
More informationOn the Iyengar Madhava Rao Nanjundiah inequality and its hyperbolic version
Notes on Number Theory and Discrete Mathematics Print ISSN 110 51, Online ISSN 67 875 Vol. 4, 018, No., 14 19 DOI: 10.7546/nntdm.018.4..14-19 On the Iyengar Madhava Rao Nanjundiah inequality and its hyperbolic
More informationA CLASS OF SCHUR MULTIPLIERS ON SOME QUASI-BANACH SPACES OF INFINITE MATRICES
A CLASS OF SCHUR MULTIPLIERS ON SOME QUASI-BANACH SPACES OF INFINITE MATRICES NICOLAE POPA Abstract In this paper we characterize the Schur multipliers of scalar type (see definition below) acting on scattered
More informationA RECIPROCAL SUM RELATED TO THE RIEMANN ζ FUNCTION. 1. Introduction. 1 n s, k 2 = n 1. k 3 = 2n(n 1),
Journal of Mathematical Inequalities Volume, Number 07, 09 5 doi:0.753/jmi--0 A RECIPROCAL SUM RELATED TO THE RIEMANN ζ FUNCTION LIN XIN AND LI XIAOXUE Communicated by J. Pečarić Abstract. This paper,
More informationLOWELL WEEKI.Y JOURINAL
/ $ 8) 2 {!»!» X ( (!!!?! () ~ x 8» x /»!! $?» 8! ) ( ) 8 X x /! / x 9 ( 2 2! z»!!»! ) / x»! ( (»»!» [ ~!! 8 X / Q X x» ( (!»! Q ) X x X!! (? ( ()» 9 X»/ Q ( (X )!» / )! X» x / 6!»! }? ( q ( ) / X! 8 x»
More informationSome Equivalent Characterizations of Inner Product Spaces and Their Consequences
Filomat 9:7 (05), 587 599 DOI 0.98/FIL507587M Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Some Equivalent Characterizations
More informationMULTIVARIATE BIRKHOFF-LAGRANGE INTERPOLATION SCHEMES AND CARTESIAN SETS OF NODES. 1. Introduction
Acta Math. Univ. Comenianae Vol. LXXIII, 2(2004), pp. 217 221 217 MULTIVARIATE BIRKHOFF-LAGRANGE INTERPOLATION SCHEMES AND CARTESIAN SETS OF NODES N. CRAINIC Abstract. In this paper we study the relevance
More informationOptimisation Problems for the Determinant of a Sum of 3 3 Matrices
Irish Math. Soc. Bulletin 62 (2008), 31 36 31 Optimisation Problems for the Determinant of a Sum of 3 3 Matrices FINBARR HOLLAND Abstract. Given a pair of positive definite 3 3 matrices A, B, the maximum
More informationMore on Reverse Triangle Inequality in Inner Product. Spaces
More on Reverse Triangle Inequality in Inner Product arxiv:math/0506198v1 [math.fa] 10 Jun 005 Spaces A. H. Ansari M. S. Moslehian Abstract Refining some results of S. S. Dragomir, several new reverses
More informationAN EXTENDED MATRIX EXPONENTIAL FORMULA. 1. Introduction
Journal of Mathematical Inequalities Volume 1, Number 3 2007), 443 447 AN EXTENDED MATRIX EXPONENTIAL FORMULA HEESEOP KIM AND YONGDO LIM communicated by J-C Bourin) Abstract In this paper we present matrix
More informationINEQUALITIES FOR THE NORM AND THE NUMERICAL RADIUS OF LINEAR OPERATORS IN HILBERT SPACES
INEQUALITIES FOR THE NORM AND THE NUMERICAL RADIUS OF LINEAR OPERATORS IN HILBERT SPACES S.S. DRAGOMIR Abstract. In this paper various inequalities between the operator norm its numerical radius are provided.
More informationOPERATOR INEQUALITIES RELATED TO WEAK 2 POSITIVITY
Journal of Mathematical Inequalities Volume 7, Number 2 2013, 175 182 doi:10.7153/jmi-07-17 OPERATOR INEQUALITIES RELATED TO WEAK 2 POSITIVITY MOHAMMAD SAL MOSLEHIAN AND JUN ICHI FUJII Communicated by
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics INEQUALITIES FOR GENERAL INTEGRAL MEANS GHEORGHE TOADER AND JOZSEF SÁNDOR Department of Mathematics Technical University Cluj-Napoca, Romania. EMail:
More informationarxiv: v1 [math.fa] 1 Sep 2014
SOME GENERALIZED NUMERICAL RADIUS INEQUALITIES FOR HILBERT SPACE OPERATORS MOSTAFA SATTARI 1, MOHAMMAD SAL MOSLEHIAN 1 AND TAKEAKI YAMAZAKI arxiv:1409.031v1 [math.fa] 1 Sep 014 Abstract. We generalize
More informationSOME NEW INEQUALITIES SIMILAR TO HILBERT TYPE INTEGRAL INEQUALITY WITH A HOMOGENEOUS KERNEL. 1. Introduction. sin(
Journal of Mathematical Ineualities Volume 6 Number 2 22 83 93 doi:.753/jmi-6-9 SOME NEW INEQUALITIES SIMILAR TO HILBERT TYPE INTEGRAL INEQUALITY WITH A HOMOGENEOUS KERNEL VANDANJAV ADIYASUREN AND TSERENDORJ
More informationE. F. Beckenbach R. Bellman. Inequalities. Third Printing. '**" '»»..,,. t. Springer-Verlag Berlin Heidelberg New York 1971
) E. F. Beckenbach R. Bellman Inequalities Third Printing '**" '»»..,,. t Springer-Verlag Berlin Heidelberg New York 1971 I.! Chapter 1. The Fundamental Inequalities and Related Matters 1 1. Introduction
More informationON THE CONVERGENCE OF SERIES WITH RECURSIVELY DEFINED TERMS N. S. HOANG. 1. Introduction
Journal of Classical Analysis Volume 13, Number 2 (2018), 141 149 doi:10.7153/jca-2018-13-10 ON THE CONVERGENCE OF SERIES WITH RECURSIVELY DEFINED TERMS N. S. HOANG Abstract. We investigate the asymptotic
More informationA CLASS OF NEW TRIGONOMETRIC INEQUALITIES AND THEIR SHARPENINGS
Journal of Mathematical Inequalities Volume, Number 3 (008), 49 436 A CLASS OF NEW TRIGONOMETRIC INEQUALITIES AND THEIR SHARPENINGS KUN ZHU, HONG ZHANG AND KAIQING WENG (communicated by V. Volenec) Abstract.
More informationInequalities For Singular Values And Traces Of Quaternion Hermitian Matrices
Inequalities For Singular Values And Traces Of Quaternion Hermitian Matrices K. Gunasekaran M. Rahamathunisha Ramanujan Research Centre, PG and Research Department of Mathematics, Government Arts College
More informationarxiv: v4 [math.mg] 1 Dec 2015
arxiv:1404.0525v4 [math.mg] 1 Dec 2015 The Euler and Grace-Danielsson inequalities for nested triangles and tetrahedra: a derivation and generalisation using quantum information theory Antony Milne Controlled
More informationCORACH PORTA RECHT INEQUALITY FOR CLOSED RANGE OPERATORS
M athematical I nequalities & A pplications Volume 16, Number 2 (2013), 477 481 doi:10.7153/mia-16-34 CORACH PORTA RECHT INEQUALITY FOR CLOSED RANGE OPERATORS MARYAM KHOSRAVI Abstract. By B(H ) we denote
More informationVarious proofs of the Cauchy-Schwarz inequality
OCTOGON MATHEMATICAL MAGAZINE Vol 17, No1, April 009, pp 1-9 ISSN 1-5657, ISBN 978-973-8855-5-0, wwwhetfaluro/octogon 1 Various proofs of the Cauchy-Schwarz inequality Hui-Hua Wu and Shanhe Wu 0 ABSTRACT
More informationPOLYNOMIALS WITH A SHARP CAUCHY BOUND AND THEIR ZEROS OF MAXIMAL MODULUS
M athematical Inequalities & Applications Volume 18, Number 4 (2015), 1387 1392 doi:10.7153/mia-18-108 POLYNOMIALS WITH A SHARP CAUCHY BOUND AND THEIR ZEROS OF MAXIMAL MODULUS HARALD K. WIMMER (Communicated
More informationON A ERDOS INSCRIBED TRIANGLE INEQUALITY REVISITED
ON A ERDOS INSCRIBED TRIANGLE INEQUALITY REVISITED CEZAR LUPU, ŞTEFAN SPĂTARU Abstract In this note we give a refinement of an inequality obtained by Torrejon [10] between the area of a triangle and that
More informationSOME INEQUALITIES FOR THE EUCLIDEAN OPERATOR RADIUS OF TWO OPERATORS IN HILBERT SPACES
SOME INEQUALITIES FOR THE EUCLIDEAN OPERATOR RADIUS OF TWO OPERATORS IN HILBERT SPACES SEVER S DRAGOMIR Abstract Some sharp bounds for the Euclidean operator radius of two bounded linear operators in Hilbert
More informationTWO WEIGHT INEQUALITIES FOR HARDY OPERATOR AND COMMUTATORS
Journal of Mathematical Inequalities Volume 9, Number 3 (215), 653 664 doi:1.7153/jmi-9-55 TWO WEIGHT INEQUALITIES FOR HARDY OPERATOR AND COMMUTATORS WENMING LI, TINGTING ZHANG AND LIMEI XUE (Communicated
More informationON SOME INEQUALITIES FOR THE INCOMPLETE GAMMA FUNCTION
MATHEMATICS OF COMPUTATION Volume 66, Number 28, April 997, Pages 77 778 S 25-578(97)84-4 ON SOME INEQUALITIES FOR THE INCOMPLETE GAMMA FUNCTION HORST ALZER Abstract. Let p be a positive real number. We
More informationThe Euler and Grace-Danielsson inequalities for nested triangles and tetrahedra: a derivation and generalisation using quantum information theory
J. Geom. 106 (2015), 455 463 c 2014 The Author(s). This article is published with open access at Springerlink.com 0047-2468/15/030455-9 published online December 18, 2014 DOI 10.1007/s00022-014-0257-8
More informationSCHUR-CONVEX FUNCTIONS AND ISOPERIMETRIC INEQUALITIES
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 16, Number, February 1998, Pages 461 470 S 000-9939(98)04151-3 SCHUR-CONVEX FUNCTIONS AND ISOPERIMETRIC INEQUALITIES XIN-MIN ZHANG (Communicated
More informationPOLYA CONDITIONS FOR MULTIVARIATE BIRKHOFF INTERPOLATION: FROM GENERAL TO RECTANGULAR SETS OF NODES. 1. Introduction
Acta Math. Univ. Comenianae Vol. LXXIX, 1(20), pp. 9 18 9 POLYA CONDITIONS FOR MULTIVARIATE BIRKHOFF INTERPOLATION: FROM GENERAL TO RECTANGULAR SETS OF NODES M. CRAINIC and N. CRAINIC Abstract. Polya conditions
More informationarxiv: v1 [math.fa] 19 Aug 2017
EXTENSIONS OF INTERPOLATION BETWEEN THE ARITHMETIC-GEOMETRIC MEAN INEQUALITY FOR MATRICES M. BAKHERAD 1, R. LASHKARIPOUR AND M. HAJMOHAMADI 3 arxiv:1708.0586v1 [math.fa] 19 Aug 017 Abstract. In this paper,
More informationMOMENTS OF A q BASKAKOV BETA OPERATORS IN CASE 0 < q < Introduction
Journal of Classical Analysis Volume 2, Number 1 213, 9 22 doi:1.7153/jca-2-2 MOMENTS OF A BASKAKOV BETA OPERATORS IN CASE < < 1 A. R. GAIROLA, P.N.AGRAWAL, G.DOBHAL AND K. K. SINGH Abstract. In this paper
More informationarxiv: v1 [math.ca] 28 Apr 2013
ON SOME TYPE OF HARDY S INEQUALITY INVOLVING GENERALIZED POWER MEANS PAWE L PASTECZKA arxiv:1304.7448v1 [math.ca] 28 Apr 2013 Abstract. We discuss properties of certain generalization of Power Meansproposedin1971byCarlson,MeanyandNelson.Foranyfixedparameter
More informationON THE ZEROS OF POLYNOMIALS WITH RESTRICTED COEFFICIENTS. Peter Borwein and Tamás Erdélyi. Abstract. It is proved that a polynomial p of the form
ON THE ZEROS OF POLYNOMIALS WITH RESTRICTED COEFFICIENTS Peter Borwein and Tamás Erdélyi Abstract. It is proved that a polynomial p of the form a j x j, a 0 = 1, a j 1, a j C, has at most c n zeros inside
More informationGeneralized Numerical Radius Inequalities for Operator Matrices
International Mathematical Forum, Vol. 6, 011, no. 48, 379-385 Generalized Numerical Radius Inequalities for Operator Matrices Wathiq Bani-Domi Department of Mathematics Yarmouk University, Irbed, Jordan
More informationLet D be the open unit disk of the complex plane. Its boundary, the unit circle of the complex plane, is denoted by D. Let
HOW FAR IS AN ULTRAFLAT SEQUENCE OF UNIMODULAR POLYNOMIALS FROM BEING CONJUGATE-RECIPROCAL? Tamás Erdélyi Abstract. In this paper we study ultraflat sequences (P n) of unimodular polynomials P n K n in
More informationMANY BILLS OF CONCERN TO PUBLIC
- 6 8 9-6 8 9 6 9 XXX 4 > -? - 8 9 x 4 z ) - -! x - x - - X - - - - - x 00 - - - - - x z - - - x x - x - - - - - ) x - - - - - - 0 > - 000-90 - - 4 0 x 00 - -? z 8 & x - - 8? > 9 - - - - 64 49 9 x - -
More informationL p -Width-Integrals and Affine Surface Areas
LIBERTAS MATHEMATICA, vol XXX (2010) L p -Width-Integrals and Affine Surface Areas Chang-jian ZHAO and Mihály BENCZE Abstract. The main purposes of this paper are to establish some new Brunn- Minkowski
More informationHERMITE-HADAMARD TYPE INEQUALITIES FOR OPERATOR GEOMETRICALLY CONVEX FUNCTIONS
HERMITE-HADAMARD TYPE INEQUALITIES FOR OPERATOR GEOMETRICALLY CONVEX FUNCTIONS A TAGHAVI, V DARVISH, H M NAZARI, S S DRAGOMIR Abstract In this paper, we introduce the concept of operator geometrically
More informationA Hilbert-type Integral Inequality with Parameters
Global Journal of Science Frontier Research Vol. Issue 6(Ver.) October P a g e 87 A Hilbert-type Integral Inequality with Parameters Peng Xiuying, Gao Mingzhe GJSFR- F Clasification FOR 8,6,33B,6D5 6D5
More informationThe Approximation of Some Invertible Operators Using Newton s Method in Banach Spaces
Int. Journal of Math. Analysis, Vol. 2, 28, no. 15, 713-72 The Approximation of Some Invertible Operators Using Newton s Method in Banach Spaces Alexandru V. Blaga National College Mihai Eminescu 5 Mihai
More informationGiaccardi s Inequality for Convex-Concave Antisymmetric Functions and Applications
Southeast Asian Bulletin of Mathematics 01) 36: 863 874 Southeast Asian Bulletin of Mathematics c SEAMS 01 Giaccardi s Inequality for Convex-Concave Antisymmetric Functions and Applications J Pečarić Abdus
More informationNEW CLASSES OF SET-THEORETIC COMPLETE INTERSECTION MONOMIAL IDEALS
NEW CLASSES OF SET-THEORETIC COMPLETE INTERSECTION MONOMIAL IDEALS M. R. POURNAKI, S. A. SEYED FAKHARI, AND S. YASSEMI Abstract. Let be a simplicial complex and χ be an s-coloring of. Biermann and Van
More informationBanach Journal of Mathematical Analysis ISSN: (electronic)
Banach J. Math. Anal. 6 (2012), no. 1, 139 146 Banach Journal of Mathematical Analysis ISSN: 1735-8787 (electronic) www.emis.de/journals/bjma/ AN EXTENSION OF KY FAN S DOMINANCE THEOREM RAHIM ALIZADEH
More informationPanHomc'r I'rui;* :".>r '.a'' W"»' I'fltolt. 'j'l :. r... Jnfii<on. Kslaiaaac. <.T i.. %.. 1 >
5 28 (x / &» )»(»»» Q ( 3 Q» (» ( (3 5» ( q 2 5 q 2 5 5 8) 5 2 2 ) ~ ( / x {» /»»»»» (»»» ( 3 ) / & Q ) X ] Q & X X X x» 8 ( &» 2 & % X ) 8 x & X ( #»»q 3 ( ) & X 3 / Q X»»» %» ( z 22 (»» 2» }» / & 2 X
More informationGENERALIZED NORMS INEQUALITIES FOR ABSOLUTE VALUE OPERATORS
International Journal of Analysis Alications ISSN 9-8639 Volume 5, Number (04), -9 htt://www.etamaths.com GENERALIZED NORMS INEQUALITIES FOR ABSOLUTE VALUE OPERATORS ILYAS ALI, HU YANG, ABDUL SHAKOOR Abstract.
More informationGENERALIZED POPOVICIU FUNCTIONAL EQUATIONS IN BANACH MODULES OVER A C ALGEBRA AND APPROXIMATE ALGEBRA HOMOMORPHISMS. Chun Gil Park
NEW ZEALAND JOURNAL OF MATHEMATICS Volume 3 (003), 183 193 GENERALIZED POPOVICIU FUNCTIONAL EQUATIONS IN BANACH MODULES OVER A C ALGEBRA AND APPROXIMATE ALGEBRA HOMOMORPHISMS Chun Gil Park (Received March
More informationVector spaces. DS-GA 1013 / MATH-GA 2824 Optimization-based Data Analysis.
Vector spaces DS-GA 1013 / MATH-GA 2824 Optimization-based Data Analysis http://www.cims.nyu.edu/~cfgranda/pages/obda_fall17/index.html Carlos Fernandez-Granda Vector space Consists of: A set V A scalar
More informationDedicated to Professor Milosav Marjanović on the occasion of his 80th birthday
THE TEACHING OF MATHEMATICS 2, Vol. XIV, 2, pp. 97 6 SOME CLASSICAL INEQUALITIES AND THEIR APPLICATION TO OLYMPIAD PROBLEMS Zoran Kadelburg Dedicated to Professor Milosav Marjanović on the occasion of
More informationarxiv: v1 [math.ca] 4 Aug 2012
SHARP POWER MEANS BOUNDS FOR NEUMAN-SÁNDOR MEAN arxiv:08.0895v [math.ca] 4 Aug 0 ZHEN-HANG YANG Abstract. For a,b > 0 with a b, let N a,b) denote the Neuman-Sándor mean defined by N a,b) = arcsinh a+b
More informationEVANESCENT SOLUTIONS FOR LINEAR ORDINARY DIFFERENTIAL EQUATIONS
EVANESCENT SOLUTIONS FOR LINEAR ORDINARY DIFFERENTIAL EQUATIONS Cezar Avramescu Abstract The problem of existence of the solutions for ordinary differential equations vanishing at ± is considered. AMS
More informationEXTENSIONS OF THE BLOCH PÓLYA THEOREM ON THE NUMBER OF REAL ZEROS OF POLYNOMIALS
EXTENSIONS OF THE BLOCH PÓLYA THEOREM ON THE NUMBER OF REAL ZEROS OF POLYNOMIALS Tamás Erdélyi Abstract. We prove that there are absolute constants c 1 > 0 and c 2 > 0 for every {a 0, a 1,..., a n } [1,
More informationRESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES RIMS A Note on an Anabelian Open Basis for a Smooth Variety. Yuichiro HOSHI.
RIMS-1898 A Note on an Anabelian Open Basis for a Smooth Variety By Yuichiro HOSHI January 2019 RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES KYOTO UNIVERSITY, Kyoto, Japan A Note on an Anabelian Open Basis
More informationSINGULAR VALUE INEQUALITIES FOR COMPACT OPERATORS
SINGULAR VALUE INEQUALITIES FOR OMPAT OPERATORS WASIM AUDEH AND FUAD KITTANEH Abstract. A singular value inequality due to hatia and Kittaneh says that if A and are compact operators on a complex separable
More informationON AN INEQUALITY OF V. CSISZÁR AND T.F. MÓRI FOR CONCAVE FUNCTIONS OF TWO VARIABLES
ON AN INEQUALITY OF V. CSISZÁR AND T.F. MÓRI FOR CONCAVE FUNCTIONS OF TWO VARIABLES BOŽIDAR IVANKOVIĆ Faculty of Transport and Traffic Engineering University of Zagreb, Vukelićeva 4 0000 Zagreb, Croatia
More informationON AN ERDOS INSCRIBED TRIANGLE INEQUALITY REVISITED
ON AN ERDOS INSCRIBED TRIANGLE INEQUALITY REVISITED CEZAR LUPU, ŞTEFAN SPĂTARU Abstract. In this note we give a refinement of an inequality obtained by Torrejon [10] between the area of a triangle and
More informationAPPROXIMATE FUNCTIONAL INEQUALITIES BY ADDITIVE MAPPINGS
Joural of Mathematical Iequalities Volume 6, Number 3 0, 46 47 doi:0.753/jmi-06-43 APPROXIMATE FUNCTIONAL INEQUALITIES BY ADDITIVE MAPPINGS HARK-MAHN KIM, JURI LEE AND EUNYOUNG SON Commuicated by J. Pečarić
More informationSome Inequalities for Commutators of Bounded Linear Operators in Hilbert Spaces
Some Inequalities for Commutators of Bounded Linear Operators in Hilbert Spaces S.S. Dragomir Abstract. Some new inequalities for commutators that complement and in some instances improve recent results
More informationCLASSIFICATION OF TREES EACH OF WHOSE ASSOCIATED ACYCLIC MATRICES WITH DISTINCT DIAGONAL ENTRIES HAS DISTINCT EIGENVALUES
Bull Korean Math Soc 45 (2008), No 1, pp 95 99 CLASSIFICATION OF TREES EACH OF WHOSE ASSOCIATED ACYCLIC MATRICES WITH DISTINCT DIAGONAL ENTRIES HAS DISTINCT EIGENVALUES In-Jae Kim and Bryan L Shader Reprinted
More informationGROWTH OF MAXIMUM MODULUS OF POLYNOMIALS WITH PRESCRIBED ZEROS. Abdul Aziz and B. A. Zargar University of Kashmir, Srinagar, India
GLASNIK MATEMATIČKI Vol. 37(57)(2002), 73 81 GOWTH OF MAXIMUM MODULUS OF POLYNOMIALS WITH PESCIBED ZEOS Abdul Aziz and B. A. Zargar University of Kashmir, Srinagar, India Abstract. Let P (z) be a polynomial
More informationSOME PÓLYA-TYPE IRREDUCIBILITY CRITERIA FOR MULTIVARIATE POLYNOMIALS NICOLAE CIPRIAN BONCIOCAT, YANN BUGEAUD, MIHAI CIPU, AND MAURICE MIGNOTTE
SOME PÓLYA-TYPE IRREDUCIBILITY CRITERIA FOR MULTIVARIATE POLYNOMIALS NICOLAE CIPRIAN BONCIOCAT, YANN BUGEAUD, MIHAI CIPU, AND MAURICE MIGNOTTE Abstract. We provide irreducibility criteria for multivariate
More informationInstitut für Mathematik
U n i v e r s i t ä t A u g s b u r g Institut für Mathematik Martin Rasmussen, Peter Giesl A Note on Almost Periodic Variational Equations Preprint Nr. 13/28 14. März 28 Institut für Mathematik, Universitätsstraße,
More informationPOLYNOMIALS WITH COEFFICIENTS FROM A FINITE SET
ao DOI: 1.478/s1175-14-8-y Math. Slovaca 64 (14), No. 6, 1397 148 POLYNOMIALS WITH COEFFICIENTS FROM A FINITE SET Javad Baradaran* Mohsen Taghavi** (Communicated by Stanis lawa Kanas ) ABSTRACT. This paper
More informationSome New Facts in Discrete Asymptotic Analysis
Mathematica Balkanica New Series Vol 2, 2007, Fasc 3-4 Some New Facts in Discrete Asymptotic Analysis Cristinel Mortici, Andrei Vernescu Presented by P Boyvalenkov This paper is closely related to [7]
More informationBanach Journal of Mathematical Analysis ISSN: (electronic)
Banach J. Math. Anal. 2 (2008), no., 70 77 Banach Journal of Mathematical Analysis ISSN: 735-8787 (electronic) http://www.math-analysis.org WIDTH-INTEGRALS AND AFFINE SURFACE AREA OF CONVEX BODIES WING-SUM
More informationNumerical Range in C*-Algebras
Journal of Mathematical Extension Vol. 6, No. 2, (2012), 91-98 Numerical Range in C*-Algebras M. T. Heydari Yasouj University Abstract. Let A be a C*-algebra with unit 1 and let S be the state space of
More informationSOME NEW INEQUALITIES FOR AN INTERIOR POINT OF A TRIANGLE JIAN LIU. 1. Introduction
Journal of Mathematical Inequalities Volume 6, Number 2 (2012), 195 204 doi:10.7153/jmi-06-20 OME NEW INEQUALITIE FOR AN INTERIOR POINT OF A TRIANGLE JIAN LIU (Communicated by. egura Gomis) Abstract. In
More informationON A SUBCLASS OF ANALYTIC CLOSE TO CONVEX FUNCTIONS IN q ANALOGUE ASSOCIATED WITH JANOWSKI FUNCTIONS. 1. Introduction and definitions
Journal of Classical Analysis Volume 13, Number 1 2018, 83 93 doi:10.7153/jca-2018-13-05 ON A SUBCLASS OF ANALYTIC CLOSE TO CONVEX FUNCTIONS IN q ANALOGUE ASSOCIATED WITH JANOWSKI FUNCTIONS BAKHTIAR AHMAD,
More information2x (x 2 + y 2 + 1) 2 2y. (x 2 + y 2 + 1) 4. 4xy. (1, 1)(x 1) + (1, 1)(y + 1) (1, 1)(x 1)(y + 1) 81 x y y + 7.
Homework 8 Solutions, November 007. (1 We calculate some derivatives: f x = f y = x (x + y + 1 y (x + y + 1 x = (x + y + 1 4x (x + y + 1 4 y = (x + y + 1 4y (x + y + 1 4 x y = 4xy (x + y + 1 4 Substituting
More informationSOME EQUATIONS WITH FEATURES OF DIGIT REVERSAL AND POWERS
SOME EQUATIONS WITH FEATURES OF DIGIT REVERSAL AND POWERS GEOFFREY B CAMPBELL AND ALEKSANDER ZUJEV Abstract. In this paper we consider integers in base 10 like abc, where a, b, c are digits of the integer,
More informationON LANDAU S THEOREMS. 1. Introduction E. Landau has proved the following theorems [11]:
GLASNIK MATEMATIČKI Vol. 39(59)(004), 57 64 ON LANDAU S THEOREMS Dragoslav S. Mitrinović, Josip E. Pečarić and Hrvoje Kraljević University of Belgrade, Yugoslavia and University of Zagreb, Croatia Abstract.
More informationSimultaneous Estimation in a Restricted Linear Model*
journal of multivariate analysis 61, 6166 (1997) article no. MV971657 Simultaneous Estimation in a Restricted Linear Model* C. Rueda, B. Salvador, and M. A. Ferna ndez Universidad de Valladolid, Spain
More informationA general coefficient inequality 1
General Mathematics Vol. 17, No. 3 (2009), 99 104 A general coefficient inequality 1 Sukhwinder Singh, Sushma Gupta and Sukhjit Singh Abstract In the present note, we obtain a general coefficient inequality
More informationInequalities related to the Cauchy-Schwarz inequality
Sankhyā : he Indian Journal of Statistics 01, Volume 74-A, Part 1, pp. 101-111 c 01, Indian Statistical Institute Inequalities related to the Cauchy-Schwarz inequality R. Sharma, R. Bhandari and M. Gupta
More informationON SOME GENERALIZED NORM TRIANGLE INEQUALITIES. 1. Introduction In [3] Dragomir gave the following bounds for the norm of n. x j.
Rad HAZU Volume 515 (2013), 43-52 ON SOME GENERALIZED NORM TRIANGLE INEQUALITIES JOSIP PEČARIĆ AND RAJNA RAJIĆ Abstract. In this paper we characterize equality attainedness in some recently obtained generalized
More informationA trigonometric orthogonality with respect to a nonnegative Borel measure
Filomat 6:4 01), 689 696 DOI 10.98/FIL104689M Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat A trigonometric orthogonality with
More informationA plane extension of the symmetry relation
A plane extension of the symmetry relation Alexandru Blaga National College Mihai Eminescu Satu Mare, Romania alblga005@yahoo.com The idea of this article comes as a response to a problem of symmetry.
More informationr/lt.i Ml s." ifcr ' W ATI II. The fnncrnl.icniccs of Mr*. John We mil uppn our tcpiiblicnn rcprc Died.
$ / / - (\ \ - ) # -/ ( - ( [ & - - - - \ - - ( - - - - & - ( ( / - ( \) Q & - - { Q ( - & - ( & q \ ( - ) Q - - # & - - - & - - - $ - 6 - & # - - - & -- - - - & 9 & q - / \ / - - - -)- - ( - - 9 - - -
More informationW i n t e r r e m e m b e r t h e W O O L L E N S. W rite to the M anageress RIDGE LAUNDRY, ST. H E LE N S. A uction Sale.
> 7? 8 «> ««0? [ -! ««! > - ««>« ------------ - 7 7 7 = - Q9 8 7 ) [ } Q ««
More informationSecond Hankel Determinant Problem for a Certain Subclass of Univalent Functions
International Journal of Mathematical Analysis Vol. 9, 05, no. 0, 493-498 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/ijma.05.55 Second Hankel Determinant Problem for a Certain Subclass of Univalent
More informationAN INEQUALITY AND SOME EQUALITIES FOR THE MIDRADIUS OF A TETRAHEDRON
Annales Univ. Sci. Budapest., Sect. Comp. 46 (2017) 165 176 AN INEQUALITY AND SOME EQUALITIES FOR THE MIDRADIUS OF A TETRAHEDRON Lajos László (Budapest, Hungary) Dedicated to the memory of Professor Antal
More informationSufficiency Conditions for Finite Escape Times in Systems of Quadratic Differential Equations
/. Inst. Maths Applies (1977) 19, 377-383 Sufficiency Conditions for Finite Escape Times in Systems of Quadratic Differential Equations W. M. GETZ AND D. H. JACOBSON National Research Institute for Mathematical
More informationThe principal inverse of the gamma function
The principal inverse of the gamma function Mitsuru Uchiyama Shimane University 2013/7 Mitsuru Uchiyama (Shimane University) The principal inverse of the gamma function 2013/7 1 / 25 Introduction The gamma
More information