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Estimates of (1+x)1/x involved in Carleman’s inequality and Keller’s limit

Estimates of (1+x)1/x involved in Carleman’s inequality and Keller’s limit

The aim of this work is to extend the results obtained by Yang Bicheng and L. Debnath in [Some inequalities involving the constant e and an application to Carleman?s inequality, J. Math. Anal. Appl., 223 (1998), 347-353]. We present a simple proof of our new result which can be also …