A parameter-dependent refinement of the discrete Jensen’s inequality for convex and mid-convex functions. (English) Zbl 1268.26031
Summary: 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.
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26D10 | Inequalities involving derivatives and differential and integral operators |
Keywords:
Jensen’s inequality; convex and mid-convex functions; quasi-arithmetic and mixed symmetric meansReferences:
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