Loading...

Messages

Proposals

Stuck in your homework and missing deadline? Get urgent help in $10/Page with 24 hours deadline

Get Urgent Writing Help In Your Essays, Assignments, Homeworks, Dissertation, Thesis Or Coursework & Achieve A+ Grades.

Privacy Guaranteed - 100% Plagiarism Free Writing - Free Turnitin Report - Professional And Experienced Writers - 24/7 Online Support

470 resistor color code

28/12/2021 Client: muhammad11 Deadline: 2 Day

MORE ON REVERSE TRIANGLE INEQUALITY ININNER PRODUCT SPACESA. H. ANSARI AND M. S. MOSLEHIANReceived 8 February 2005 and in revised form 17 May 2005Refining some results of Dragomir, several new reverses of the generalized triangle in-equality in inner product spaces are given. Among several results, we establish some re-verses for the Schwarz inequality. In particular, it is proved that ifais a unit vector ina real or complex inner product space (H;·,·),r,s>0,p∈(0,s],D={x∈H,rx−sa≤p},x1,x2∈D−{0},andαr,s=min{(r2xk2−p2+s2)/2rsxk:1≤k≤2},then(x1x2−Rex1,x2)/(x1+x2)2≤αr,s.1. IntroductionIt is interesting to know under which conditions the triangle inequality went the otherway in a normed spaceX; in other words, we would like to know if there is a positiveconstantcwith the property thatcnk=1xk≤nk=1xkfor any finite setx1,...,xn∈X.Nakai and Tada [7] proved that the normed spaces with this property are precisely thoseof finite dimensional.The first authors investigating reverse of the triangle inequality in inner product spaceswere Diaz and Metcalf [2] by establishing the following result as an extension of an in-equality given by Petrovich [8] for complex numbers.Theorem1.1 (Diaz-Metcalf theorem).Letabe a unit vector in an inner product space(H;·,·).Supposethevectorsxk∈H,k∈{1,...,n}satisfy0≤r≤Rexk,axk,k∈{1,...,n}.(1.1)Thenrnk=1xk≤nk=1xk,(1.2)Copyright©2005 Hindawi Publishing CorporationInternational Journal of Mathematics and Mathematical Sciences 2005:18 (2005) 2883–2893DOI:10.1155/IJMMS.2005.2883
2884 Reverse triangle inequalitywhere equality holds if and only ifnk=1xk=rnk=1xka.(1.3)Inequalities related to the triangle inequality are of special interest (cf. [6,ChapterXVII]). They may be applied to get interesting inequalities in complex numbers or tostudy vector-valued integral inequalities [4,5].Using several ideas and following the terminology of [4,5], we modify or refine someresults of Dragomir and ours [1] and get some new reverses of triangle inequality. Amongseveral results, we show that ifais a unit vector in a real or complex inner productspace (H;·,·),xk∈H−{0},1≤k≤n,α=min{xk:1≤k≤n},p∈(0,√α2+1),max{xk−a:1≤k≤n}≤p,andβ=min{(xk2−p2+1)/2xk:1≤k≤n},thennk=1xk−nk=1xk≤1−ββRenk=1xk,a.(1.4)We also examine some reverses for the celebrated Schwarz inequality. In particular, it isproved that ifais a unit vector in a real or complex inner product space (H;·,·),r,s>0,p∈(0,s],D={x∈H,rx−sa≤p},x1,x2∈D−{0},andαr,s=min{(r2xk2−p2+s2)/2rsxk:1≤k≤2},thenx1x2−Rex1,x2x1+x22≤αr,s.(1.5)Throughout the paper, (H;·,·) denotes a real or complex inner product space. Weuse repeatedly the Cauchy-Schwarz inequality without mentioning it. The reader is re-ferred to [3,9] for the terminology on inner product spaces.2. Reverse of triangle inequalityWe start this section by pointing out the following theorem of [1] which is a modificationof [5,Theorem3].Theorem2.1.Leta1,...,ambe orthonormal vectors in the complex inner product space(H;·,·).Supposethatfor1≤t≤m,rt,ρt∈R, and that the vectorsxk∈H,k∈{1,...,n}satisfy0≤r2txk≤Rexk,rtat,0≤ρ2txk≤Imxk,ρtat,1≤t≤m.(2.1)Thenmt=1r2t+ρ2t1/2nk=1xk≤nk=1xk(2.2)

Homework is Completed By:

Writer Writer Name Amount Client Comments & Rating
Instant Homework Helper

ONLINE

Instant Homework Helper

$36

She helped me in last minute in a very reasonable price. She is a lifesaver, I got A+ grade in my homework, I will surely hire her again for my next assignments, Thumbs Up!

Order & Get This Solution Within 3 Hours in $25/Page

Custom Original Solution And Get A+ Grades

  • 100% Plagiarism Free
  • Proper APA/MLA/Harvard Referencing
  • Delivery in 3 Hours After Placing Order
  • Free Turnitin Report
  • Unlimited Revisions
  • Privacy Guaranteed

Order & Get This Solution Within 6 Hours in $20/Page

Custom Original Solution And Get A+ Grades

  • 100% Plagiarism Free
  • Proper APA/MLA/Harvard Referencing
  • Delivery in 6 Hours After Placing Order
  • Free Turnitin Report
  • Unlimited Revisions
  • Privacy Guaranteed

Order & Get This Solution Within 12 Hours in $15/Page

Custom Original Solution And Get A+ Grades

  • 100% Plagiarism Free
  • Proper APA/MLA/Harvard Referencing
  • Delivery in 12 Hours After Placing Order
  • Free Turnitin Report
  • Unlimited Revisions
  • Privacy Guaranteed

6 writers have sent their proposals to do this homework:

Writer Writer Name Offer Chat

Writers are writing their proposals. Just wait here to get the offers for your project...

Let our expert academic writers to help you in achieving a+ grades in your homework, assignment, quiz or exam.

Similar Homework Questions

Wharton executive mba application - Juvenile court proceedings were originally conceptualized as civil proceedings - Angular distance and displacement - Owls ii sample report - Nbaa tanzania examination form final stage - Promotions Management - Gantt chart for wedding project - Erikson's stages of development chart - As firms downsize, a control system based on rewards and culture becomes dysfunctional. - Lynch company manufactures and sells a single product - Chint power systems america - 4-1 multiplexer truth table - Acap master of social work qualifying - CATHERINE OWENS ONLY - Social cultural environment marketing - Pardoner's tale cliff notes - Write a 2 page paper for answers for both questions in Logistics Management - How to find cbus member number - Maternity leave plan template free - Cosine compound angle formula - Research Paper - America the story of us - Stability strategies in business pros and cons - Lección 4 grammar quiz completar - Establishing an employee leave donation program? - Weeek-3 - Components of emergency management multi agency interoperability - Answering selection criteria nsw health - Cisco commands cheat sheet - Wegmans case study - Describe a Significant Clinical Issue - Ielts first language code list - Read the slide and answer the following questions in 400 words. ---Due in 4hours - Flakt woods me1 6 - Choosing a performance measurement approach at paychex inc - Use the given minimum and maximum data entries - Pp - Discussion POST 375 WORDS DUE IN 12 HOURS - Discussion: Involuntary Group Members - Ps music balance sheet - Cambs fire service jobs - Federal circuit court dandenong - Add and subtract in scientific notation - 7 dimensions of ABA - Paper 08/07 - Paraxial mesoderm gives rise to - Incremental analysis is most useful - Prada group annual report - Wk 3, HCS 430: Types of Consent and Payers - Zinn chapter 1 questions and answers - Hindu symbols and meanings - Lines that don t intersect - Breaking down a topic brainstorming - Economy Quiz - Is 0 odd or even - Future of life institute open letter - Microprocessor programming - Middle school density problems - America on film benshoff pdf - Unisa acknowledgement of country - What is minimum impact camping - Collaboration Process to Improve Team Communication - Hannah hoch the beautiful girl analysis - Enzyme amylase action on starch answers - Types of religious organization - The mean incubation time of fertilized eggs is - Mk echo k5418r switch receiver - 5.5 a cad model features conclusion answers - Oahu kiki tracks the number of units purchased and sold - Penetration testing rules of engagement example - Coca cola company mission vision and objectives - 1965 freedom ride map - Case study on swot analysis of walmart - Harvey norman highpoint contact - Impact wrench repair troubleshooting - The other wes moore essay outline - Morgan spurlock 30 days minimum wage summary - The irrational number between 2 and 3 is - Teresa's pet feed simi valley - Discussion - Spaceage furniture - Weiss symptom record scoring - How to make hydrometer with straw - Written techniques in advertising - Intellectual courage critical thinking examples - Confusion between theological beliefs and ethical principles - Don juan tirso de molina pdf - Ecce romani ii chapter 35 translation - Worksheet on separating mixtures - Brian ray creed original motion picture soundtrack songs - Nicolas bernardi em lyon - Used jack haggis saddle for sale - Rad hard op amp - American greetings case - Vce chem study design - What is gdp gnp nnp - Argos pet insurance reviews - Breast cancer case study nursing - 44 historic drive highbury - Aldi average store sales