Bounds for the Combinations of Neuman-Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean
We give the greatest values r1, r2 and the least values s1, s2 in (1/2, 1) such that the double inequalities C(r1a+(1-r1)b,r1b+(1-r1)a)<αA(a,b)+(1-α)T(a,b)<C(s1a+(1-s1)b,s1b+(1-s1)a) and C(r2a+(1-r2)b,r2b+(1-r2)a)<αA(a,b)+(1-α)M(a,b)<C(s2a+(1-s2)b,s2b+(1-s2)a) hold for any α∈(0,1) and al...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/903982 |
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| author | Zai-Yin He Wei-Mao Qian Yun-Liang Jiang Ying-Qing Song Yu-Ming Chu |
| author_facet | Zai-Yin He Wei-Mao Qian Yun-Liang Jiang Ying-Qing Song Yu-Ming Chu |
| author_sort | Zai-Yin He |
| collection | DOAJ |
| description | We give the greatest values r1, r2 and the least values s1, s2 in (1/2, 1) such that the double inequalities C(r1a+(1-r1)b,r1b+(1-r1)a)<αA(a,b)+(1-α)T(a,b)<C(s1a+(1-s1)b,s1b+(1-s1)a) and C(r2a+(1-r2)b,r2b+(1-r2)a)<αA(a,b)+(1-α)M(a,b)<C(s2a+(1-s2)b,s2b+(1-s2)a) hold for any α∈(0,1) and all a,b>0 with a≠b, where A(a,b), M(a,b), C(a,b), and T(a,b) are the arithmetic, Neuman-Sándor, contraharmonic, and second Seiffert means of a and b, respectively. |
| format | Article |
| id | doaj-art-b42383bec2404b17ac04b4a9ecfe0f16 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b42383bec2404b17ac04b4a9ecfe0f162025-02-03T07:26:09ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/903982903982Bounds for the Combinations of Neuman-Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic MeanZai-Yin He0Wei-Mao Qian1Yun-Liang Jiang2Ying-Qing Song3Yu-Ming Chu4Department of Mathematics, Huzhou Teachers College, Huzhou 313000, ChinaSchool of Distance Education, Huzhou Broadcast and TV University, Huzhou 313000, ChinaSchool of Information and Engineering, Huzhou Teachers College, Huzhou 313000, ChinaSchool of Mathematics and Computation Science, Hunan City University, Yiyang 413000, ChinaSchool of Mathematics and Computation Science, Hunan City University, Yiyang 413000, ChinaWe give the greatest values r1, r2 and the least values s1, s2 in (1/2, 1) such that the double inequalities C(r1a+(1-r1)b,r1b+(1-r1)a)<αA(a,b)+(1-α)T(a,b)<C(s1a+(1-s1)b,s1b+(1-s1)a) and C(r2a+(1-r2)b,r2b+(1-r2)a)<αA(a,b)+(1-α)M(a,b)<C(s2a+(1-s2)b,s2b+(1-s2)a) hold for any α∈(0,1) and all a,b>0 with a≠b, where A(a,b), M(a,b), C(a,b), and T(a,b) are the arithmetic, Neuman-Sándor, contraharmonic, and second Seiffert means of a and b, respectively.http://dx.doi.org/10.1155/2013/903982 |
| spellingShingle | Zai-Yin He Wei-Mao Qian Yun-Liang Jiang Ying-Qing Song Yu-Ming Chu Bounds for the Combinations of Neuman-Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean Abstract and Applied Analysis |
| title | Bounds for the Combinations of Neuman-Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean |
| title_full | Bounds for the Combinations of Neuman-Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean |
| title_fullStr | Bounds for the Combinations of Neuman-Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean |
| title_full_unstemmed | Bounds for the Combinations of Neuman-Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean |
| title_short | Bounds for the Combinations of Neuman-Sándor, Arithmetic, and Second Seiffert Means in terms of Contraharmonic Mean |
| title_sort | bounds for the combinations of neuman sandor arithmetic and second seiffert means in terms of contraharmonic mean |
| url | http://dx.doi.org/10.1155/2013/903982 |
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