On an operator preserving inequalities between polynomials View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2021-09-20

AUTHORS

Imtiaz Hussain, A. Liman

ABSTRACT

Let P(z) be a polynomial of degree at most n. We consider an operator N, which carries a polynomial P(z) into N[P](z):=∑j=0mλj(nz2)jP(j)(z)j!,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} N[P](z):=\sum \limits _{j=0}^{m}\lambda _j\bigg (\frac{nz}{2}\bigg )^j\frac{P^{(j)}(z)}{j!}, \end{aligned}$$\end{document}where λ0,λ1,…,λm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _0,\lambda _1,\ldots ,\lambda _m$$\end{document} are such that all the zeros of u(z)=∑j=0mnjλjzj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} u(z)=\sum \limits _{j=0}^{m}\left( {\begin{array}{c}n\\ j\end{array}}\right) \lambda _jz^j \end{aligned}$$\end{document}lie in the half plane |z|≤|z-n2|.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} |z|\le \bigg |z-\frac{n}{2}\bigg |. \end{aligned}$$\end{document}In this paper, we estimate the minimum and maximum modulii of N[P(z)] on |z|=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|z|=1$$\end{document} with restrictions on the zeros of P(z) and thereby obtain compact generalizations of some well known polynomial inequalities. More... »

PAGES

285-292

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11565-021-00375-5

DOI

http://dx.doi.org/10.1007/s11565-021-00375-5

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1141239888


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Department of Mathematics, National Institute of Technology, 190006, Srinagar, J&K, India", 
          "id": "http://www.grid.ac/institutes/grid.419487.7", 
          "name": [
            "Department of Mathematics, National Institute of Technology, 190006, Srinagar, J&K, India"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Hussain", 
        "givenName": "Imtiaz", 
        "id": "sg:person.010104715710.91", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010104715710.91"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Department of Mathematics, National Institute of Technology, 190006, Srinagar, J&K, India", 
          "id": "http://www.grid.ac/institutes/grid.419487.7", 
          "name": [
            "Department of Mathematics, National Institute of Technology, 190006, Srinagar, J&K, India"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Liman", 
        "givenName": "A.", 
        "id": "sg:person.013241354317.42", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013241354317.42"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/s11139-020-00261-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1129503502", 
          "https://doi.org/10.1007/s11139-020-00261-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf02418550", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1012406114", 
          "https://doi.org/10.1007/bf02418550"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2021-09-20", 
    "datePublishedReg": "2021-09-20", 
    "description": "Let P(z) be a polynomial of degree at most n. We consider an operator N, which carries a polynomial P(z) into N[P](z):=\u2211j=0m\u03bbj(nz2)jP(j)(z)j!,\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} N[P](z):=\\sum \\limits _{j=0}^{m}\\lambda _j\\bigg (\\frac{nz}{2}\\bigg )^j\\frac{P^{(j)}(z)}{j!}, \\end{aligned}$$\\end{document}where \u03bb0,\u03bb1,\u2026,\u03bbm\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\lambda _0,\\lambda _1,\\ldots ,\\lambda _m$$\\end{document} are such that all the zeros of u(z)=\u2211j=0mnj\u03bbjzj\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} u(z)=\\sum \\limits _{j=0}^{m}\\left( {\\begin{array}{c}n\\\\ j\\end{array}}\\right) \\lambda _jz^j \\end{aligned}$$\\end{document}lie in the half plane |z|\u2264|z-n2|.\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\begin{aligned} |z|\\le \\bigg |z-\\frac{n}{2}\\bigg |. \\end{aligned}$$\\end{document}In this paper, we estimate the minimum and maximum modulii of N[P(z)] on |z|=1\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$|z|=1$$\\end{document} with restrictions on the zeros of P(z) and thereby obtain compact generalizations of some well known polynomial inequalities.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s11565-021-00375-5", 
    "inLanguage": "en", 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136062", 
        "issn": [
          "0430-3202", 
          "1827-1510"
        ], 
        "name": "Annali dell' Universit\u00e0 di Ferrara", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "67"
      }
    ], 
    "keywords": [
      "polynomials of degree", 
      "polynomials", 
      "operator N", 
      "zeros", 
      "half plane", 
      "compact generalization", 
      "polynomial inequalities", 
      "plane", 
      "modulii", 
      "restriction", 
      "generalization", 
      "inequality", 
      "operators", 
      "degree", 
      "paper", 
      "maximum modulii"
    ], 
    "name": "On an operator preserving inequalities between polynomials", 
    "pagination": "285-292", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1141239888"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s11565-021-00375-5"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s11565-021-00375-5", 
      "https://app.dimensions.ai/details/publication/pub.1141239888"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-01-01T18:57", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20220101/entities/gbq_results/article/article_894.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s11565-021-00375-5"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s11565-021-00375-5'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s11565-021-00375-5'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11565-021-00375-5'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11565-021-00375-5'


 

This table displays all metadata directly associated to this object as RDF triples.

85 TRIPLES      22 PREDICATES      42 URIs      33 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s11565-021-00375-5 schema:about anzsrc-for:01
2 schema:author Ne645bec21a044a7c803c339032d05b16
3 schema:citation sg:pub.10.1007/bf02418550
4 sg:pub.10.1007/s11139-020-00261-2
5 schema:datePublished 2021-09-20
6 schema:datePublishedReg 2021-09-20
7 schema:description Let P(z) be a polynomial of degree at most n. We consider an operator N, which carries a polynomial P(z) into N[P](z):=∑j=0mλj(nz2)jP(j)(z)j!,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} N[P](z):=\sum \limits _{j=0}^{m}\lambda _j\bigg (\frac{nz}{2}\bigg )^j\frac{P^{(j)}(z)}{j!}, \end{aligned}$$\end{document}where λ0,λ1,…,λm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda _0,\lambda _1,\ldots ,\lambda _m$$\end{document} are such that all the zeros of u(z)=∑j=0mnjλjzj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} u(z)=\sum \limits _{j=0}^{m}\left( {\begin{array}{c}n\\ j\end{array}}\right) \lambda _jz^j \end{aligned}$$\end{document}lie in the half plane |z|≤|z-n2|.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} |z|\le \bigg |z-\frac{n}{2}\bigg |. \end{aligned}$$\end{document}In this paper, we estimate the minimum and maximum modulii of N[P(z)] on |z|=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|z|=1$$\end{document} with restrictions on the zeros of P(z) and thereby obtain compact generalizations of some well known polynomial inequalities.
8 schema:genre article
9 schema:inLanguage en
10 schema:isAccessibleForFree false
11 schema:isPartOf N81bbf97f7d11431bac2e5e799aebc179
12 Ned253d46ffce4edfb1d56bbfda49cdaf
13 sg:journal.1136062
14 schema:keywords compact generalization
15 degree
16 generalization
17 half plane
18 inequality
19 maximum modulii
20 modulii
21 operator N
22 operators
23 paper
24 plane
25 polynomial inequalities
26 polynomials
27 polynomials of degree
28 restriction
29 zeros
30 schema:name On an operator preserving inequalities between polynomials
31 schema:pagination 285-292
32 schema:productId N26cd9a2268ea4ee6bd0a22cde43b2250
33 Nb91d288e0b3b4971b7017429b9d4d93c
34 schema:sameAs https://app.dimensions.ai/details/publication/pub.1141239888
35 https://doi.org/10.1007/s11565-021-00375-5
36 schema:sdDatePublished 2022-01-01T18:57
37 schema:sdLicense https://scigraph.springernature.com/explorer/license/
38 schema:sdPublisher Na13947ed3d4a4e4ba90099725dad4421
39 schema:url https://doi.org/10.1007/s11565-021-00375-5
40 sgo:license sg:explorer/license/
41 sgo:sdDataset articles
42 rdf:type schema:ScholarlyArticle
43 N26cd9a2268ea4ee6bd0a22cde43b2250 schema:name dimensions_id
44 schema:value pub.1141239888
45 rdf:type schema:PropertyValue
46 N81bbf97f7d11431bac2e5e799aebc179 schema:volumeNumber 67
47 rdf:type schema:PublicationVolume
48 N9dc9ad26b96b47a7bc92b15605f40622 rdf:first sg:person.013241354317.42
49 rdf:rest rdf:nil
50 Na13947ed3d4a4e4ba90099725dad4421 schema:name Springer Nature - SN SciGraph project
51 rdf:type schema:Organization
52 Nb91d288e0b3b4971b7017429b9d4d93c schema:name doi
53 schema:value 10.1007/s11565-021-00375-5
54 rdf:type schema:PropertyValue
55 Ne645bec21a044a7c803c339032d05b16 rdf:first sg:person.010104715710.91
56 rdf:rest N9dc9ad26b96b47a7bc92b15605f40622
57 Ned253d46ffce4edfb1d56bbfda49cdaf schema:issueNumber 2
58 rdf:type schema:PublicationIssue
59 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
60 schema:name Mathematical Sciences
61 rdf:type schema:DefinedTerm
62 sg:journal.1136062 schema:issn 0430-3202
63 1827-1510
64 schema:name Annali dell' Università di Ferrara
65 schema:publisher Springer Nature
66 rdf:type schema:Periodical
67 sg:person.010104715710.91 schema:affiliation grid-institutes:grid.419487.7
68 schema:familyName Hussain
69 schema:givenName Imtiaz
70 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010104715710.91
71 rdf:type schema:Person
72 sg:person.013241354317.42 schema:affiliation grid-institutes:grid.419487.7
73 schema:familyName Liman
74 schema:givenName A.
75 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013241354317.42
76 rdf:type schema:Person
77 sg:pub.10.1007/bf02418550 schema:sameAs https://app.dimensions.ai/details/publication/pub.1012406114
78 https://doi.org/10.1007/bf02418550
79 rdf:type schema:CreativeWork
80 sg:pub.10.1007/s11139-020-00261-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1129503502
81 https://doi.org/10.1007/s11139-020-00261-2
82 rdf:type schema:CreativeWork
83 grid-institutes:grid.419487.7 schema:alternateName Department of Mathematics, National Institute of Technology, 190006, Srinagar, J&K, India
84 schema:name Department of Mathematics, National Institute of Technology, 190006, Srinagar, J&K, India
85 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...