Inequalities on the Generalized <i>ABC</i> Index
In this work, we obtained new results relating the generalized atom-bond connectivity index with the general Randić index. Some of these inequalities for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><...
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MDPI AG
2021-05-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/10/1151 |
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| author | Paul Bosch Edil D. Molina José M. Rodríguez José M. Sigarreta |
| author_facet | Paul Bosch Edil D. Molina José M. Rodríguez José M. Sigarreta |
| author_sort | Paul Bosch |
| collection | DOAJ |
| description | In this work, we obtained new results relating the generalized atom-bond connectivity index with the general Randić index. Some of these inequalities for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>B</mi><msub><mi>C</mi><mi>α</mi></msub></mrow></semantics></math></inline-formula> improved, when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula>, known results on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>B</mi><mi>C</mi></mrow></semantics></math></inline-formula> index. Moreover, in order to obtain our results, we proved a kind of converse Hölder inequality, which is interesting on its own. |
| first_indexed | 2024-03-10T11:14:35Z |
| format | Article |
| id | doaj.art-cd7a4dc75c664876baec3e27e5f25562 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T11:14:35Z |
| publishDate | 2021-05-01 |
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| series | Mathematics |
| spelling | doaj.art-cd7a4dc75c664876baec3e27e5f255622023-11-21T20:32:02ZengMDPI AGMathematics2227-73902021-05-01910115110.3390/math9101151Inequalities on the Generalized <i>ABC</i> IndexPaul Bosch0Edil D. Molina1José M. Rodríguez2José M. Sigarreta3Facultad de Ingeniería, Universidad del Desarrollo, Ave. La Plaza 680, San Carlos de Apoquindo, Las Condes, Santiago 7610658, ChileFacultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No.54 Col. Garita, 39650 Acalpulco Gro., MexicoDepartamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, SpainFacultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No.54 Col. Garita, 39650 Acalpulco Gro., MexicoIn this work, we obtained new results relating the generalized atom-bond connectivity index with the general Randić index. Some of these inequalities for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>B</mi><msub><mi>C</mi><mi>α</mi></msub></mrow></semantics></math></inline-formula> improved, when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>α</mi><mo>=</mo><mn>1</mn><mo>/</mo><mn>2</mn></mrow></semantics></math></inline-formula>, known results on the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>A</mi><mi>B</mi><mi>C</mi></mrow></semantics></math></inline-formula> index. Moreover, in order to obtain our results, we proved a kind of converse Hölder inequality, which is interesting on its own.https://www.mdpi.com/2227-7390/9/10/1151<i>ABC</i> index<i>generalizedABC</i> indexgeneral Randić indextopological indicesconverse Hölder inequality |
| spellingShingle | Paul Bosch Edil D. Molina José M. Rodríguez José M. Sigarreta Inequalities on the Generalized <i>ABC</i> Index Mathematics <i>ABC</i> index <i>generalizedABC</i> index general Randić index topological indices converse Hölder inequality |
| title | Inequalities on the Generalized <i>ABC</i> Index |
| title_full | Inequalities on the Generalized <i>ABC</i> Index |
| title_fullStr | Inequalities on the Generalized <i>ABC</i> Index |
| title_full_unstemmed | Inequalities on the Generalized <i>ABC</i> Index |
| title_short | Inequalities on the Generalized <i>ABC</i> Index |
| title_sort | inequalities on the generalized i abc i index |
| topic | <i>ABC</i> index <i>generalizedABC</i> index general Randić index topological indices converse Hölder inequality |
| url | https://www.mdpi.com/2227-7390/9/10/1151 |
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