A parameter-dependent refinement of the discrete Jensen's inequality for convex and mid-convex functions
<p>Abstract</p> <p>In this paper, a new parameter-dependent refinement of the discrete Jensen's inequality is given for convex and mid-convex functions. The convergence of the introduced sequences is also studied. One of the proofs requires an interesting convergence theorem w...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2011-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2011/1/26 |
| Summary: | <p>Abstract</p> <p>In this paper, a new parameter-dependent refinement of the discrete Jensen's inequality is given for convex and mid-convex functions. The convergence of the introduced sequences is also studied. One of the proofs requires an interesting convergence theorem with probability theoretical background. We apply the results to define some new quasi-arithmetic and mixed symmetric means and study their monotonicity and convergence.</p> |
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| ISSN: | 1025-5834 1029-242X |