Stability of Quadratic and Cubic Functional Equations in Paranormed Spaces
|
|
- Magnus Evans
- 6 years ago
- Views:
Transcription
1 IOSR Joua o Matheatics IOSR-JM e-issn 8-578, p-issn Voue, Issue Ve. IV Ju - Aug. 05, - Stabiit o uadatic ad ubic Fuctioa Equatios i aaoed Spaces Muiappa, Raa S Depatet o Matheatics, Adhiaaa oege o Egieeig, ai Nadu, Idia Depatet o Matheatics, Eode Ats ad Sciece oege, ai Nadu, Idia Abstact I this pape, we pove Hes-Ua Stabiit o a cass o uadatic ad ubic uctioa equatios i aaoed spaces. Kewods Hes-Ua Stabiit, uadatic Fuctioa Equatios, ubic Fuctioa Equatios, aaoed Spaces I. Itoductio he cocept o stabiit o uctioa equatios aises whe we epace the uctioa equatio b a iequait which acts as a petubatio o the equatio. I 90, S. M. Ua [] asked the questio coceig the stabiit o goup hooophiss. Net ea Hes [] gave the ist positive aswe to the questio o Ua o Baach spaces. I 978 h.m. Rassias [] povided a geeaizatio o the Hes theoe which aows the auch dieece to be ubouded. Ate this esut a o atheaticias wee attacted ad otivated to ivestigate the stabiit pobes o uctioa equatios. I paticua, the Stabiit pobees o dieet uctioa equatios have bee ivestigated i vaious spaces. Recet.ak ad D..Shi[] peseted Hes-Ua Stabiit o a cass o uadatic, ubic ad uatic uctioa equatios i paaoed spaces. he uctioa equatio. is a quadatic uctioa equatio ad eve soutio o the quadatic uctioa equatio is said to be a quadatic uctio. he Fuctioa equatio 5 5. is a cubic uctioa equatio ad eve soutio o the cubic uctioa equatio is said to be a cubic uctio. I this pape, we ivestigate the Hes-Ua Stabiit o the uadatic Equatio. ad ubic equatio. i aaoed spaces. his pape is ogaized as oows I Sectio, we pove the Hes-Ua stabiit o quadatic uctioa equatio. i paaoed space. I Sectio, we pove the Hes-Ua stabiit o cubic uctioa equatio. i paaoed space. II. eiiaies houghout this pape, we assue that, is a Fechet space ad that, is a Baach Space. Deiitio. A Noed Space ove K is a pai V,, whee V is a vecto space ove K ad V R, such that i 0 i 0 ii iii o a K ad v V o a, V Deiitio.[] Let be a vecto space. A paao [0, is a uctio o such that i 0 0 ii iii iage Iequait I t is a sequece o scaa with t t ad with 0, iv the t t 0, is caed a paaoed space. hods. he the pai DOI / age
2 Stabiit o uadatic ad ubic Fuctioa Equatio i aaoed Spaces DOI / age Deiitio. he aao is caed tota i i additio we have = 0 ipies = 0 Deiitio. he Fechet space is tota ad copete paaoed space. III. Hes - ua stabiit o quadatic uctioa equatios I this sectio, we dea with the stabiit pobe o the oowig quadatic uctioa equatio i paaoed spaces. heoe. Let, be positive ea ubes with, ad et be a appig satisig 0 = 0 ad. o a., he thee eists a uique quadatic appig such that. o a. oo uttig = i., we get o a. So o a., Hece. o a oegative iteges ad with > ad o a. It oows o. that the sequece is a auch sequece o a. Sice is copete, the sequece coveges. So oe ca deie the appig b i. o a. Moeove, ettig = 0 ad passig the iit i., we get..
3 Stabiit o uadatic ad ubic Fuctioa Equatio i aaoed Spaces DOI / age It oows o. that 0 i i i o a., Hece o a., ad so the appig is quadatic. Now et be aothe quadatic appig satisig.. he we have..8 which teds to zeo as o a. So we ca cocude that o a. his poves the uiqueess o. hus the appig is a uique quadatic appig satisig.. heoe. Let be a ea positive ube with, ad et be a appig satisig 0 = 0 ad.5 o a,. he thee eists a uique quadatic appig such that.6 o a oo Lettig = i.5, we get ad so
4 o a. Siia o a. Hece Stabiit o uadatic ad ubic Fuctioa Equatio i aaoed Spaces o a oegative iteges ad with > ad o a. It oows o.6 that the sequece is a auch sequece o a. Sice is copete, the sequece coveges. So oe ca deie the appig b i.8 o a. Moeove, ettig = 0 ad passig the iit i.7, we get.6. It oows o.5 that i DOI / age i i 0 o a,. hus o a, ad so the appig is quadatic. Now et be aothe quadatic appig satisig.6. he we have.. 8..
5 Stabiit o uadatic ad ubic Fuctioa Equatio i aaoed Spaces DOI / age which teds to zeo as o a. So we ca cocude that o a. his poves the uiqueess o. hus the appig is a uique quadatic appig satisig.5. IV. Hes ua stabiit o cubic uctioa equatio I this sectio we pove the Hes Ua stabiit o the oowig cubic uctioa equatio i paaoed spaces. 5 5 heoe. Let, be positive ea ubes with, ad et be a appig such that 5 5. o a., he thee eists a uique cubic appig such that. o a. ROOF uttig = 0 i., we get o a. So o a. Now o a. Hece.. o a oegative iteges ad with > ad o a. It oows o. that the sequece is a auch sequece o a. Sice is copete, the sequece coveges. So oe ca deie the appig b i o a.
6 Stabiit o uadatic ad ubic Fuctioa Equatio i aaoed Spaces DOI / age Moeove, ettig = 0 ad passig the iit i., we get.. It oows o. that i 0 i 5 5 i o a., Hece 5 5 o a, ad so the appig is cubic. Now et be aothe quadatic appig satisig.. he we have.. which teds to zeo as o a. So we ca cocude that o a. his poves the uiqueess o. hus the appig is a uique cubic appig satisig.. heoe. Let be a ea positive ube with, ad et be a appig such that 5 5. o a., he thee eists a uique quadatic appig such that.5 o a. oo Lettig = 0 i., we get o a ad so o a. Hece
7 Stabiit o uadatic ad ubic Fuctioa Equatio i aaoed Spaces.6 o a oegative iteges ad with > ad o a. It oows o.6 that the sequece is a auch sequece o a. Sice is copete, the sequece coveges. So oe ca deie the appig b i o a. Moeove, ettig = 0 ad passig the iit i.6, we get.5. It oows o. that 5 5 i DOI / age i i 0 o a,. hus 5 5 o a, ad so the appig is cubic. Now et be aothe quadatic appig satisig.5. he we have.. which teds to zeo as o a. So we ca cocude that o a. his poves the uiqueess o. hus the appig is a uique cubic appig satisig.5. Reeeces []..ak ad D..Shi, Fuctioa Equatios i aaoed Spaces, advaces i dieece equatios 0. []. hoewa, W Reaks o the stabiit o uctioa equatios, Aequatioes Math., []. zewik, S O the stabiit o the quadatic appig i oed spaces, Abh. Math. Se. Uiv. Habug 6, []. Jug, S Hes-Ua-Rassias stabiit o uctioa equatios i atheatica aasis, Hadoic ess Ic., a Habo, Foida 00. [5]. Rassias, M Fuctioa Equatios ad Iequaities, Kuwe Acadeic, Dodecht 000. [6]. D.H. Hes, O the stabiit o the iea uctioa equatio, oc. Nat. Acad.Sci [7]. Rassias, M, O the stabiit o uctioa equatios i baach spaces, J. Math.Aa.App.5, [8]. Rassias, M, O the stabiit o uctioa equatio ad a pobe o Ua. Acta Math.App, 6, [9]. Ju, K, Ki, H he geaized Hes-Ua-Rassias stabiit o a cubic uctioa equatio J.Math.Aa.App,
8 Stabiit o uadatic ad ubic Fuctioa Equatio i aaoed Spaces [0]. h.m. Rassias, O the stabiit o the iea appig i Baach spaces,oc.ae.math. Soc., 7 978, []. S.M. Ua, obes i Mode Matheatics, Red. hap.vi,wie, New ok, 90. []. D.H.Hes, o the stabiit o the iea uctioa equatios, oc.nat.acad.sci., 9, -. []. h.m.rassias, o the stabiit o iea appig i Baach spaces, oc.ae.soc., 7978, [].. Aoki, O the stabiit o the iea tasoatio i Baach spaces, J.Math.Soc.Japa.950. DOI / age
FIXED POINT AND HYERS-ULAM-RASSIAS STABILITY OF A QUADRATIC FUNCTIONAL EQUATION IN BANACH SPACES
IJRRAS 6 () July 0 www.apapess.com/volumes/vol6issue/ijrras_6.pdf FIXED POINT AND HYERS-UAM-RASSIAS STABIITY OF A QUADRATIC FUNCTIONA EQUATION IN BANACH SPACES E. Movahedia Behbaha Khatam Al-Abia Uivesity
More informationInternational Journal of Mathematics Trends and Technology (IJMTT) Volume 47 Number 1 July 2017
Iteatioal Joual of Matheatics Teds ad Techology (IJMTT) Volue 47 Nube July 07 Coe Metic Saces, Coe Rectagula Metic Saces ad Coo Fixed Poit Theoes M. Sivastava; S.C. Ghosh Deatet of Matheatics, D.A.V. College
More informationModular Spaces Topology
Applied Matheatics 23 4 296-3 http://ddoiog/4236/a234975 Published Olie Septebe 23 (http://wwwscipog/joual/a) Modula Spaces Topology Ahed Hajji Laboatoy of Matheatics Coputig ad Applicatio Depatet of Matheatics
More informationStrong Result for Level Crossings of Random Polynomials
IOSR Joual of haacy ad Biological Scieces (IOSR-JBS) e-issn:78-8, p-issn:19-7676 Volue 11, Issue Ve III (ay - Ju16), 1-18 wwwiosjoualsog Stog Result fo Level Cossigs of Rado olyoials 1 DKisha, AK asigh
More informationStrong Result for Level Crossings of Random Polynomials. Dipty Rani Dhal, Dr. P. K. Mishra. Department of Mathematics, CET, BPUT, BBSR, ODISHA, INDIA
Iteatioal Joual of Reseach i Egieeig ad aageet Techology (IJRET) olue Issue July 5 Available at http://wwwijetco/ Stog Result fo Level Cossigs of Rado olyoials Dipty Rai Dhal D K isha Depatet of atheatics
More informationBy the end of this section you will be able to prove the Chinese Remainder Theorem apply this theorem to solve simultaneous linear congruences
Chapte : Theoy of Modula Aithmetic 8 Sectio D Chiese Remaide Theoem By the ed of this sectio you will be able to pove the Chiese Remaide Theoem apply this theoem to solve simultaeous liea cogueces The
More informationGeneralization of Horadam s Sequence
Tuish Joual of Aalysis ad Nube Theoy 6 Vol No 3-7 Available olie at http://pubssciepubco/tjat///5 Sciece ad Educatio Publishig DOI:69/tjat---5 Geealizatio of Hoada s Sequece CN Phadte * YS Valaulia Depatet
More informationA New Result On A,p n,δ k -Summabilty
OSR Joual of Matheatics (OSR-JM) e-ssn: 2278-5728, p-ssn:239-765x. Volue 0, ssue Ve. V. (Feb. 204), PP 56-62 www.iosjouals.og A New Result O A,p,δ -Suabilty Ripeda Kua &Aditya Kua Raghuashi Depatet of
More informationStructure and Some Geometric Properties of Nakano Difference Sequence Space
Stuctue ad Soe Geoetic Poeties of Naao Diffeece Sequece Sace N Faied ad AA Baey Deatet of Matheatics, Faculty of Sciece, Ai Shas Uivesity, Caio, Egyt awad_baey@yahooco Abstact: I this ae, we exted the
More informationGlobal asymptotic stability in a rational dynamic equation on discrete time scales
Iteatioal Joual of Egieeig Reseach & Sciece (IJOER) ISSN: [395-699] [Vol-, Issue-, Decebe- 6] Global asyptotic stability i a atioal dyaic euatio o discete tie scales a( t) b( ( t)) ( ( t)), t T c ( ( (
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 informationOn ARMA(1,q) models with bounded and periodically correlated solutions
Reseach Repot HSC/03/3 O ARMA(,q) models with bouded ad peiodically coelated solutios Aleksade Weo,2 ad Agieszka Wy oma ska,2 Hugo Steihaus Cete, Woc aw Uivesity of Techology 2 Istitute of Mathematics,
More information2012 GCE A Level H2 Maths Solution Paper Let x,
GCE A Level H Maths Solutio Pape. Let, y ad z be the cost of a ticet fo ude yeas, betwee ad 5 yeas, ad ove 5 yeas categoies espectively. 9 + y + 4z =. 7 + 5y + z = 8. + 4y + 5z = 58.5 Fo ude, ticet costs
More informationCommon Coupled Fixed Point of Mappings Satisfying Rational Inequalities in Ordered Complex Valued Generalized Metric Spaces
IOSR Joural of Mathematics (IOSR-JM) e-issn: 78-578, p-issn:319-765x Volume 10, Issue 3 Ver II (May-Ju 014), PP 69-77 Commo Coupled Fixed Poit of Mappigs Satisfyig Ratioal Iequalities i Ordered Complex
More informationRange Symmetric Matrices in Minkowski Space
BULLETIN of the Bull. alaysia ath. Sc. Soc. (Secod Seies) 3 (000) 45-5 LYSIN THETICL SCIENCES SOCIETY Rae Symmetic atices i ikowski Space.R. EENKSHI Depatmet of athematics, amalai Uivesity, amalaiaa 608
More informationComplementary Dual Subfield Linear Codes Over Finite Fields
1 Complemetay Dual Subfield Liea Codes Ove Fiite Fields Kiagai Booiyoma ad Somphog Jitma,1 Depatmet of Mathematics, Faculty of Sciece, Silpao Uivesity, Naho Pathom 73000, hailad e-mail : ai_b_555@hotmail.com
More informationOn a Problem of Littlewood
Ž. JOURAL OF MATHEMATICAL AALYSIS AD APPLICATIOS 199, 403 408 1996 ARTICLE O. 0149 O a Poblem of Littlewood Host Alze Mosbache Stasse 10, 51545 Waldbol, Gemay Submitted by J. L. Bee Received May 19, 1995
More informationMath 7409 Homework 2 Fall from which we can calculate the cycle index of the action of S 5 on pairs of vertices as
Math 7409 Hoewok 2 Fall 2010 1. Eueate the equivalece classes of siple gaphs o 5 vetices by usig the patte ivetoy as a guide. The cycle idex of S 5 actig o 5 vetices is 1 x 5 120 1 10 x 3 1 x 2 15 x 1
More informationStability of a Monomial Functional Equation on a Restricted Domain
mathematics Article Stability of a Moomial Fuctioal Equatio o a Restricted Domai Yag-Hi Lee Departmet of Mathematics Educatio, Gogju Natioal Uiversity of Educatio, Gogju 32553, Korea; yaghi2@hamail.et
More informationQuantum Mechanics Lecture Notes 10 April 2007 Meg Noah
The -Patice syste: ˆ H V This is difficut to sove. y V 1 ˆ H V 1 1 1 1 ˆ = ad with 1 1 Hˆ Cete of Mass ˆ fo Patice i fee space He Reative Haitoia eative coodiate of the tota oetu Pˆ the tota oetu tota
More informationOn the Basis Property of Eigenfunction. of the Frankl Problem with Nonlocal Parity Conditions. of the Third Kind
It.. Cotemp. Math. Scieces Vol. 9 o. 3 33-38 HIKARI Lt www.m-hikai.com http://x.oi.og/.988/ijcms..33 O the Basis Popety o Eigeuctio o the Fakl Poblem with Nolocal Paity Coitios o the Thi Ki A. Sameipou
More informationULAM STABILITY OF THE RECIPROCAL FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN FIELDS. 1. Introduction
Acta Math. Uiv. Comeiaae Vol. LXXXV, (06, pp. 3 4 3 ULAM STABILITY OF THE RECIPROCAL FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN FIELDS A. BODAGHI, P. NARASIMMAN, J. M. RASSIAS ad K. RAVI Abstract. I this paper,
More informationTaylor Transformations into G 2
Iteatioal Mathematical Foum, 5,, o. 43, - 3 Taylo Tasfomatios ito Mulatu Lemma Savaah State Uivesity Savaah, a 344, USA Lemmam@savstate.edu Abstact. Though out this pape, we assume that
More informationConditional Convergence of Infinite Products
Coditioal Covegece of Ifiite Poducts William F. Tech Ameica Mathematical Mothly 106 1999), 646-651 I this aticle we evisit the classical subject of ifiite poducts. Fo stadad defiitios ad theoems o this
More informationRelation (12.1) states that if two points belong to the convex subset Ω then all the points on the connecting line also belong to Ω.
Lectue 6. Poectio Opeato Deiitio A.: Subset Ω R is cove i [ y Ω R ] λ + λ [ y = z Ω], λ,. Relatio. states that i two poits belog to the cove subset Ω the all the poits o the coectig lie also belog to Ω.
More informationOn the Stability of the Quadratic Functional Equation of Pexider Type in Non- Archimedean Spaces
I J C T A, 8(), 015, pp. 749-754 Iteratioal Sciece Press O the Stability of the Quadratic Fuctioal Equatio of Pexider Type i No- Archimedea Spaces M. Aohammady 1, Z. Bagheri ad C. Tuc 3 Abstract: I this
More informationGeneralized k-normal Matrices
Iteatioal Joual of Computatioal Sciece ad Mathematics ISSN 0974-389 Volume 3, Numbe 4 (0), pp 4-40 Iteatioal Reseach Publicatio House http://wwwiphousecom Geealized k-omal Matices S Kishamoothy ad R Subash
More informationSOME ARITHMETIC PROPERTIES OF OVERPARTITION K -TUPLES
#A17 INTEGERS 9 2009), 181-190 SOME ARITHMETIC PROPERTIES OF OVERPARTITION K -TUPLES Deick M. Keiste Depatmet of Mathematics, Pe State Uivesity, Uivesity Pak, PA 16802 dmk5075@psu.edu James A. Selles Depatmet
More informationI PUC MATHEMATICS CHAPTER - 08 Binomial Theorem. x 1. Expand x + using binomial theorem and hence find the coefficient of
Two Maks Questios I PU MATHEMATIS HAPTER - 08 Biomial Theoem. Epad + usig biomial theoem ad hece fid the coefficiet of y y. Epad usig biomial theoem. Hece fid the costat tem of the epasio.. Simplify +
More informationFuzzy n-normed Space and Fuzzy n-inner Product Space
Global Joural o Pure ad Applied Matheatics. ISSN 0973-768 Volue 3, Nuber 9 (07), pp. 4795-48 Research Idia Publicatios http://www.ripublicatio.co Fuzzy -Nored Space ad Fuzzy -Ier Product Space Mashadi
More informationPAijpam.eu IRREGULAR SET COLORINGS OF GRAPHS
Iteratioal Joural of Pure ad Applied Mathematics Volume 109 No. 7 016, 143-150 ISSN: 1311-8080 (prited versio); ISSN: 1314-3395 (o-lie versio) url: http://www.ijpam.eu doi: 10.173/ijpam.v109i7.18 PAijpam.eu
More informationLacunary Weak I-Statistical Convergence
Ge. Mat. Notes, Vol. 8, No., May 05, pp. 50-58 ISSN 9-784; Copyigt ICSRS Publicatio, 05 www.i-css.og vailable ee olie at ttp//www.gema.i Lacuay Wea I-Statistical Covegece Haize Gümüş Faculty o Eegli Educatio,
More informationCongruences for sequences similar to Euler numbers
Coguece fo equece iila to Eule ube Zhi-Hog Su School of Matheatical Sciece, Huaiyi Noal Uiveity, Huaia, Jiagu 00, Peole Reublic of Chia Received July 00 Revied 5 Augut 0 Couicated by David Go Abtact a
More informationGeneralized Fixed Point Theorem. in Three Metric Spaces
It. Joural of Math. Aalysis, Vol. 4, 00, o. 40, 995-004 Geeralized Fixed Poit Thee i Three Metric Spaces Kristaq Kikia ad Luljeta Kikia Departet of Matheatics ad Coputer Scieces Faculty of Natural Scieces,
More informationGeneralized Fibonacci-Lucas Sequence
Tuish Joual of Aalysis ad Numbe Theoy, 4, Vol, No 6, -7 Available olie at http://pubssciepubcom/tjat//6/ Sciece ad Educatio Publishig DOI:6/tjat--6- Geealized Fiboacci-Lucas Sequece Bijeda Sigh, Ompaash
More informationHyers-Ulam-Rassias Stability of n-apollonius Type
It. Joural of Math. Aalysis, Vol. 6, 2012, o. 3, 111-128 Hyers-Ulam-Rassias Stability of -Apolloius Type Additive Mappig ad Isomorphisms i C -Algebras Fridou Moradlou Departmet of Mathematics Sahad Uiversity
More informationSome Properties of the K-Jacobsthal Lucas Sequence
Deepia Jhala et. al. /Iteatioal Joual of Mode Scieces ad Egieeig Techology (IJMSET) ISSN 349-3755; Available at https://www.imset.com Volume Issue 3 04 pp.87-9; Some Popeties of the K-Jacobsthal Lucas
More informationA NOTE ON DOMINATION PARAMETERS IN RANDOM GRAPHS
Discussioes Mathematicae Gaph Theoy 28 (2008 335 343 A NOTE ON DOMINATION PARAMETERS IN RANDOM GRAPHS Athoy Boato Depatmet of Mathematics Wilfid Lauie Uivesity Wateloo, ON, Caada, N2L 3C5 e-mail: aboato@oges.com
More informationSolution and stability of a reciprocal type functional equation in several variables
Available online at www.tjnsa.co J. Nonlinear Sci. Appl. 7 04, 8 7 Research Article Solution and stability of a reciprocal type functional equation in several variables K. Ravi a,, E. Thandapani b, B.V.
More informationResearch Article Approximate Riesz Algebra-Valued Derivations
Abstract ad Applied Aalysis Volume 2012, Article ID 240258, 5 pages doi:10.1155/2012/240258 Research Article Approximate Riesz Algebra-Valued Derivatios Faruk Polat Departmet of Mathematics, Faculty of
More informationSOME NEW SEQUENCE SPACES AND ALMOST CONVERGENCE
Faulty of Siees ad Matheatis, Uivesity of Niš, Sebia Available at: http://www.pf.i.a.yu/filoat Filoat 22:2 (28), 59 64 SOME NEW SEQUENCE SPACES AND ALMOST CONVERGENCE Saee Ahad Gupai Abstat. The sequee
More informationOn the Variations of Some Well Known Fixed Point Theorem in Metric Spaces
Turkish Joural of Aalysis ad Number Theory, 205, Vol 3, No 2, 70-74 Available olie at http://pubssciepubcom/tjat/3/2/7 Sciece ad Educatio Publishig DOI:0269/tjat-3-2-7 O the Variatios of Some Well Kow
More informationAvailable online at J. Math. Comput. Sci. 4 (2014), No. 3, ISSN:
Available olie at http://scik.org J. Math. Coput. Sci. (1, No. 3, 9-5 ISSN: 197-537 ON SYMMETRICAL FUNCTIONS WITH BOUNDED BOUNDARY ROTATION FUAD. S. M. AL SARARI 1,, S. LATHA 1 Departet of Studies i Matheatics,
More informationIJITE Vol.2 Issue-11, (November 2014) ISSN: Impact Factor
IJITE Vol Issue-, (November 4) ISSN: 3-776 ATTRACTIVITY OF A HIGHER ORDER NONLINEAR DIFFERENCE EQUATION Guagfeg Liu School of Zhagjiagag Jiagsu Uiversit of Sciece ad Techolog, Zhagjiagag, Jiagsu 56,PR
More informationABSOLUTE INDEXED SUMMABILITY FACTOR OF AN INFINITE SERIES USING QUASI-F-POWER INCREASING SEQUENCES
Available olie a h://sciog Egieeig Maheaics Lees 2 (23) No 56-66 ISSN 249-9337 ABSLUE INDEED SUMMABILIY FACR F AN INFINIE SERIES USING QUASI-F-WER INCREASING SEQUENCES SKAIKRAY * RKJAI 2 UKMISRA 3 NCSAH
More informationOn the Circulant Matrices with. Arithmetic Sequence
It J Cotep Math Scieces Vol 5 o 5 3 - O the Ciculat Matices with Aithetic Sequece Mustafa Bahsi ad Süleya Solak * Depatet of Matheatics Educatio Selçuk Uivesity Mea Yeiyol 499 Koya-Tukey Ftly we have defied
More informationSome Results on Certain Symmetric Circulant Matrices
Joural of Iformatics ad Mathematical Scieces Vol 7, No, pp 81 86, 015 ISSN 0975-5748 olie; 0974-875X prit Pulished y RGN Pulicatios http://wwwrgpulicatioscom Some Results o Certai Symmetric Circulat Matrices
More informationarxiv: v1 [math.nt] 26 Feb 2014
FROBENIUS NUMBERS OF PYTHAGOREAN TRIPLES BYUNG KEON GIL, JI-WOO HAN, TAE HYUN KIM, RYUN HAN KOO, BON WOO LEE, JAEHOON LEE, KYEONG SIK NAM, HYEON WOO PARK, AND POO-SUNG PARK arxiv:1402.6440v1 [ath.nt] 26
More informationExistence of Nonoscillatory Solution of High Order Linear Neutral Delay Difference Equation
oder Appied Sciece ovember, 008 Existece of oosciatory Soutio of High Order Liear eutra Deay Differece Equatio Shasha Zhag, Xiaozhu Zhog, Pig Yu, Wexia Zhag & ig Li Departmet of athematics Yasha Uiversity
More informationGeneralized Wavelet Transform Associated with Legendre Polynomials
Geeralized Waelet Trasor Associated with Legedre oloials C ade Aja Kuar Garg Egieerig College Ghaziabad Idia MM Dixit North Easter Regioal Istitute o Sciece ad Techolog Nirjuli-799 Idia Rajesh Kuar Noida
More informationON WEAK -STATISTICAL CONVERGENCE OF ORDER
UPB Sci Bu, Series A, Vo 8, Iss, 8 ISSN 3-77 ON WEAK -STATISTICAL CONVERGENCE OF ORDER Sia ERCAN, Yavuz ALTIN ad Çiğdem A BEKTAŞ 3 I the preset paper, we give the cocept of wea -statistica covergece of
More informationDepartment of Applied Mathematics, National Chiao Tung University, Hsinchu 30050, Taiwan.
Gaphs and Cobinatoics (1999) 15 : 95±301 Gaphs and Cobinatoics ( Spinge-Veag 1999 T-Cooings and T-Edge Spans of Gaphs* Shin-Jie Hu, Su-Tzu Juan, and Gead J Chang Depatent of Appied Matheatics, Nationa
More informationPoincaré Problem for Nonlinear Elliptic Equations of Second Order in Unbounded Domains
Advaces i Pure Mathematics 23 3 72-77 http://dxdoiorg/4236/apm233a24 Published Olie Jauary 23 (http://wwwscirporg/oural/apm) Poicaré Problem for Noliear Elliptic Equatios of Secod Order i Ubouded Domais
More information1.2 AXIOMATIC APPROACH TO PROBABILITY AND PROPERTIES OF PROBABILITY MEASURE 1.2 AXIOMATIC APPROACH TO PROBABILITY AND
NTEL- robability ad Distributios MODULE 1 ROBABILITY LECTURE 2 Topics 1.2 AXIOMATIC AROACH TO ROBABILITY AND ROERTIES OF ROBABILITY MEASURE 1.2.1 Iclusio-Exclusio Forula I the followig sectio we will discuss
More informationSome Topics on Weighted Generalized Inverse and Kronecker Product of Matrices
Malaysia Soe Joual Topics of Matheatical o Weighted Scieces Geealized (): Ivese 9-22 ad Koece (27) Poduct of Matices Soe Topics o Weighted Geealized Ivese ad Koece Poduct of Matices Zeyad Abdel Aziz Al
More informationA Fixed Point Result Using a Function of 5-Variables
Joural of Physical Scieces, Vol., 2007, 57-6 Fixed Poit Result Usig a Fuctio of 5-Variables P. N. Dutta ad Biayak S. Choudhury Departmet of Mathematics Begal Egieerig ad Sciece Uiversity, Shibpur P.O.:
More informationA 2nTH ORDER LINEAR DIFFERENCE EQUATION
A 2TH ORDER LINEAR DIFFERENCE EQUATION Doug Aderso Departmet of Mathematics ad Computer Sciece, Cocordia College Moorhead, MN 56562, USA ABSTRACT: We give a formulatio of geeralized zeros ad (, )-discojugacy
More informationInternational Journal of Mathematical Archive-3(5), 2012, Available online through ISSN
Iteatioal Joual of Matheatical Achive-3(5,, 8-8 Available olie though www.ija.ifo ISSN 9 546 CERTAIN NEW CONTINUED FRACTIONS FOR THE RATIO OF TWO 3 ψ 3 SERIES Maheshwa Pathak* & Pakaj Sivastava** *Depatet
More informationSome Common Fixed Point Theorems in Cone Rectangular Metric Space under T Kannan and T Reich Contractive Conditions
ISSN(Olie): 319-8753 ISSN (Prit): 347-671 Iteratioal Joural of Iovative Research i Sciece, Egieerig ad Techology (A ISO 397: 7 Certified Orgaizatio) Some Commo Fixed Poit Theorems i Coe Rectagular Metric
More informationCOMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES FOR SEMI-COMPATIBLE MAPPINGS
PK ISSN 0022-2941; CODEN JNSMAC Vol. 49, No.1 & 2 (April & October 2009) PP 33-47 COMMON FIXED POINT THEOREMS IN FUZZY METRIC SPACES FOR SEMI-COMPATIBLE MAPPINGS *M. A. KHAN, *SUMITRA AND ** R. CHUGH *Departmet
More informationA Common Fixed Point Theorem Using Compatible Mappings of Type (A-1)
Aals of Pure ad Applied Mathematics Vol. 4, No., 07, 55-6 ISSN: 79-087X (P), 79-0888(olie) Published o 7 September 07 www.researchmathsci.org DOI: http://dx.doi.org/0.457/apam.v4a8 Aals of A Commo Fixed
More informationCrosscorrelation of m-sequences, Exponential sums and Dickson
Cosscoelatio o m-equeces, Epoetial sums ad Dicso polyomials To Helleseth Uiesity o Bege NORWAY Joit wo with Aia Johase ad Aleade Kholosha Itoductio Outlie m-sequeces Coelatio o sequeces Popeties o m-sequeces
More informationarxiv:math/ v3 [math.oc] 5 Apr 2008
Least-Squaes Pices of Games Yukio Hiashita axiv:math/0703079v3 [math.oc] 5 Ap 2008 Abstact What ae the pices of adom vaiables? I this pape, we defie the least-squaes pices of coi-flippig games, which ae
More informationAsymptotic Expansions of Legendre Wavelet
Asptotic Expasios of Legede Wavelet C.P. Pade M.M. Dixit * Depatet of Matheatics NERIST Nijuli Itaaga Idia. Depatet of Matheatics NERIST Nijuli Itaaga Idia. Astact A e costuctio of avelet o the ouded iteval
More informationLecture 24: Observability and Constructibility
ectue 24: Obsevability ad Costuctibility 7 Obsevability ad Costuctibility Motivatio: State feedback laws deped o a kowledge of the cuet state. I some systems, xt () ca be measued diectly, e.g., positio
More informationA smoothing Newton method for the minimum norm solution of linear program
ISSN 746-7659, Eglad, UK Joual of Ifoatio ad Coputig Sciece Vol. 9, No. 4, 04, pp. 67-76 A soothig Newto ethod fo the iiu o solutio of liea poga Lia Zhag, Zhesheg Yu, Yaya Zhu Uivesity of Shaghai fo Sciece
More informationThe Pigeonhole Principle 3.4 Binomial Coefficients
Discete M athematic Chapte 3: Coutig 3. The Pigeohole Piciple 3.4 Biomial Coefficiets D Patic Cha School of Compute Sciece ad Egieeig South Chia Uivesity of Techology Ageda Ch 3. The Pigeohole Piciple
More informationAn Interpolation Process on Laguerre Polynomial
Global Joural of Pure ad Applied Mathematics. ISSN 0973-1768 Volume 13, Number 10 (2017), pp. 7089-7099 Research Idia Publicatios http://www.ripublicatio.com A Iterpolatio Process o Laguerre Polyomial
More informationINTUITIONISTIC RANDOM STABILITY OF A QUADRATIC FUNCTIONAL EQUATION ORIGINATING FROM THE SUM OF THE MEDIANS OF A TRIANGLE
Iteratioal Joural of Differece Equatios ISSN 0973-6069 Volume 1 Number 1 (017) pp. 55-70 Research Idia Publicatios http://www.ripublicatio.com INTUITIONISTIC RANDOM STABIITY OF A QUADRATIC FUNCTIONA EQUATION
More informationA FIXED POINT THEOREM IN THE MENGER PROBABILISTIC METRIC SPACE. Abdolrahman Razani (Received September 2004)
NEW ZEALAND JOURNAL OF MATHEMATICS Volume 35 (2006), 109 114 A FIXED POINT THEOREM IN THE MENGER PROBABILISTIC METRIC SPACE Abdolrahma Razai (Received September 2004) Abstract. I this article, a fixed
More informationOn Generalized Fibonacci Numbers
Applied Mathematical Scieces, Vol. 9, 215, o. 73, 3611-3622 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/1.12988/ams.215.5299 O Geeralized Fiboacci Numbers Jerico B. Bacai ad Julius Fergy T. Rabago Departmet
More informationOn n-collinear elements and Riesz theorem
Available olie at www.tjsa.com J. Noliear Sci. Appl. 9 (206), 3066 3073 Research Article O -colliear elemets ad Riesz theorem Wasfi Shataawi a, Mihai Postolache b, a Departmet of Mathematics, Hashemite
More informationCOMMON FIXED POINT THEOREM FOR FINITE NUMBER OF WEAKLY COMPATIBLE MAPPINGS IN QUASI-GAUGE SPACE
IJRRAS 19 (3) Jue 2014 www.arpapress.com/volumes/vol19issue3/ijrras_19_3_05.pdf COMMON FIXED POINT THEOREM FOR FINITE NUMBER OF WEAKLY COMPATIBLE MAPPINGS IN QUASI-GAUGE SPACE Arihat Jai 1, V. K. Gupta
More informationMATH /19: problems for supervision in week 08 SOLUTIONS
MATH10101 2018/19: poblems fo supevisio i week 08 Q1. Let A be a set. SOLUTIONS (i Pove that the fuctio c: P(A P(A, defied by c(x A \ X, is bijective. (ii Let ow A be fiite, A. Use (i to show that fo each
More informationMA131 - Analysis 1. Workbook 7 Series I
MA3 - Aalysis Workbook 7 Series I Autum 008 Cotets 4 Series 4. Defiitios............................... 4. Geometric Series........................... 4 4.3 The Harmoic Series.........................
More informationOn Edge Regular Fuzzy Line Graphs
Iteratioal Joural of Computatioal ad Applied Mathematics ISSN 1819-4966 Volume 11, Number 2 (2016), pp 105-118 Research Idia Publicatios http://wwwripublicatiocom O Edge Regular Fuzz Lie Graphs K Radha
More informationOn common fixed point theorems for weakly compatible mappings in Menger space
Available olie at www.pelagiaresearchlibrary.com Advaces i Applied Sciece Research, 2016, 7(5): 46-53 ISSN: 0976-8610 CODEN (USA): AASRFC O commo fixed poit theorems for weakly compatible mappigs i Meger
More informationCHAPTER 5: FOURIER SERIES PROPERTIES OF EVEN & ODD FUNCTION PLOT PERIODIC GRAPH
CHAPTER : FOURIER SERIES PROPERTIES OF EVEN & ODD FUNCTION POT PERIODIC GRAPH PROPERTIES OF EVEN AND ODD FUNCTION Fuctio is said to be a eve uctio i: Fuctio is said to be a odd uctio i: Fuctio is said
More informationKANTOROVICH TYPE INEQUALITIES FOR THE DIFFERENCE WITH TWO NEGATIVE PARAMETERS. Received April 13, 2010; revised August 18, 2010
Scientiae Matheaticae Japonicae Online, e-200, 427 439 427 KANTOROVICH TYPE INEQUALITIES FOR THE DIFFERENCE WITH TWO NEGATIVE PARAMETERS Young Ok Ki, Jun Ichi Fujii, Masatoshi Fujii + and Yuki Seo ++ Received
More informationInternational Journal of Mathematical Archive-4(9), 2013, 1-5 Available online through ISSN
Iteratioal Joural o Matheatical Archive-4(9), 03, -5 Available olie through www.ija.io ISSN 9 5046 THE CUBIC RATE OF CONVERGENCE OF GENERALIZED EXTRAPOLATED NEWTON RAPHSON METHOD FOR SOLVING NONLINEAR
More informationThe Discrete-Time Fourier Transform (DTFT)
EEL: Discrete-Time Sigals ad Systems The Discrete-Time Fourier Trasorm (DTFT) The Discrete-Time Fourier Trasorm (DTFT). Itroductio I these otes, we itroduce the discrete-time Fourier trasorm (DTFT) ad
More informationOn the Diophantine equation x 2 2 ˆ y n
Arch. Math. 74 (000) 50±55 000-889/00/05050-06 $.70/0 Birkhäuser Verag, Base, 000 Archiv der Mathematik O the Diohatie equatio x ˆ y By B. SURY Abstract. We give a eemetary roof of the fact that the oy
More informationAuchmuty High School Mathematics Department Sequences & Series Notes Teacher Version
equeces ad eies Auchmuty High chool Mathematics Depatmet equeces & eies Notes Teache Vesio A sequece takes the fom,,7,0,, while 7 0 is a seies. Thee ae two types of sequece/seies aithmetic ad geometic.
More informationCommon Fixed Points for Multivalued Mappings
Advaces i Applied Mathematical Bioscieces. ISSN 48-9983 Volume 5, Number (04), pp. 9-5 Iteratioal Research Publicatio House http://www.irphouse.com Commo Fixed Poits for Multivalued Mappigs Lata Vyas*
More information3.3 Rules for Differentiation Calculus. Drum Roll please [In a Deep Announcer Voice] And now the moment YOU VE ALL been waiting for
. Rules or Dieretiatio Calculus. RULES FOR DIFFERENTIATION Drum Roll please [I a Deep Aoucer Voice] A ow the momet YOU VE ALL bee waitig or Rule #1 Derivative o a Costat Fuctio I c is a costat value, the
More informationAn almost sure invariance principle for trimmed sums of random vectors
Proc. Idia Acad. Sci. Math. Sci. Vol. 20, No. 5, November 200, pp. 6 68. Idia Academy of Scieces A almost sure ivariace priciple for trimmed sums of radom vectors KE-ANG FU School of Statistics ad Mathematics,
More informationThe Structure of Z p when p is Prime
LECTURE 13 The Structure of Z p whe p is Prime Theorem 131 If p > 1 is a iteger, the the followig properties are equivalet (1) p is prime (2) For ay [0] p i Z p, the equatio X = [1] p has a solutio i Z
More informationCh 3.4 Binomial Coefficients. Pascal's Identit y and Triangle. Chapter 3.2 & 3.4. South China University of Technology
Disc ete Mathem atic Chapte 3: Coutig 3. The Pigeohole Piciple 3.4 Biomial Coefficiets D Patic Cha School of Compute Sciece ad Egieeig South Chia Uivesity of Techology Pigeohole Piciple Suppose that a
More informationA Study on the Bases of Space of Vector Valued Entire Multiple Dirichlet Series
A Study o te Bses of Spce of Vecto Vued tie Mutipe Diicet Seies Mustq Si A Hussei d Nge R Nge * Deptet of Mtetics Coege of Sciece Uivesity of Mustsiy Bgdd Iq Abstct: Let f ( s s e ( s s ( s it beig icesig
More informationNATIONAL UNIVERSITY OF SINGAPORE FACULTY OF SCIENCE SEMESTER 1 EXAMINATION ADVANCED CALCULUS II. November 2003 Time allowed :
NATIONAL UNIVERSITY OF SINGAPORE FACULTY OF SCIENCE SEMESTER EXAMINATION 003-004 MA08 ADVANCED CALCULUS II November 003 Time allowed : hours INSTRUCTIONS TO CANDIDATES This examiatio paper cosists of TWO
More information62. Power series Definition 16. (Power series) Given a sequence {c n }, the series. c n x n = c 0 + c 1 x + c 2 x 2 + c 3 x 3 +
62. Power series Defiitio 16. (Power series) Give a sequece {c }, the series c x = c 0 + c 1 x + c 2 x 2 + c 3 x 3 + is called a power series i the variable x. The umbers c are called the coefficiets of
More informationCS537. Numerical Analysis and Computing
CS57 Numerical Aalysis ad Computig Lecture Locatig Roots o Equatios Proessor Ju Zhag Departmet o Computer Sciece Uiversity o Ketucky Leigto KY 456-6 Jauary 9 9 What is the Root May physical system ca be
More informationTechnical Report: Bessel Filter Analysis
Sasa Mahmoodi 1 Techical Repot: Bessel Filte Aalysis 1 School of Electoics ad Compute Sciece, Buildig 1, Southampto Uivesity, Southampto, S17 1BJ, UK, Email: sm3@ecs.soto.ac.uk I this techical epot, we
More informationBINOMIAL THEOREM An expression consisting of two terms, connected by + or sign is called a
BINOMIAL THEOREM hapte 8 8. Oveview: 8.. A epessio cosistig of two tems, coected by + o sig is called a biomial epessio. Fo eample, + a, y,,7 4 5y, etc., ae all biomial epessios. 8.. Biomial theoem If
More informationNon-Archimedean Analysis on the Extended Hyperreal Line d and the Solution of Some Very Old Transcendence Conjectures over the Field
Avaces i Pue atheatics 25 5 587-628 Pubishe Oie August 25 i SciRes htt://wwwsciog/joua/a htt://xoiog/4236/a25556 No-Achieea Aaysis o the Extee Hyeea Lie a the Soutio of Soe Vey O Tasceece Cojectues ove
More informationTaylor Polynomials and Approximations - Classwork
Taylor Polyomials ad Approimatios - Classwork Suppose you were asked to id si 37 o. You have o calculator other tha oe that ca do simple additio, subtractio, multiplicatio, or divisio. Fareched\ Not really.
More informationLecture 10: Bounded Linear Operators and Orthogonality in Hilbert Spaces
Lecture : Bouded Liear Operators ad Orthogoality i Hilbert Spaces 34 Bouded Liear Operator Let ( X, ), ( Y, ) i i be ored liear vector spaces ad { } X Y The, T is said to be bouded if a real uber c such
More informationON EUCLID S AND EULER S PROOF THAT THE NUMBER OF PRIMES IS INFINITE AND SOME APPLICATIONS
Joual of Pue ad Alied Mathematics: Advaces ad Alicatios Volume 0 Numbe 03 Pages 5-58 ON EUCLID S AND EULER S PROOF THAT THE NUMBER OF PRIMES IS INFINITE AND SOME APPLICATIONS ALI H HAKAMI Deatmet of Mathematics
More informationDominating Sets and Domination Polynomials of Square Of Cycles
IOSR Joural of Mathematics IOSR-JM) ISSN: 78-78. Volume 3, Issue 4 Sep-Oct. 01), PP 04-14 www.iosrjourals.org Domiatig Sets ad Domiatio Polyomials of Square Of Cycles A. Vijaya 1, K. Lal Gipso 1 Assistat
More informationUsing Difference Equations to Generalize Results for Periodic Nested Radicals
Usig Diffeece Equatios to Geealize Results fo Peiodic Nested Radicals Chis Lyd Uivesity of Rhode Islad, Depatmet of Mathematics South Kigsto, Rhode Islad 2 2 2 2 2 2 2 π = + + +... Vieta (593) 2 2 2 =
More information