Abstract
In this paper, we present some inequalities involving k-gamma and k-beta functions via some classical inequalities like the Chebychev inequality for synchronous (asynchronous) mappings, and the Gruss and the Ostrowski inequality. Also, we give a new proof of the log-convexity of the k-gamma and k-beta functions by using the Holder inequality.
Highlights
1 Introduction we present some fundamental relations for k-gamma and k-beta functions introduced by the researchers [ – ]
We prove the log-convexity of the k-gamma and k-beta functions
2 Main results: inequalities via the Chebychev integral inequality we prove some inequalities which involve k-gamma and k-beta functions by using some natural inequalities [ ]
Summary
We present some fundamental relations for k-gamma and k-beta functions introduced by the researchers [ – ]. We prove the log-convexity of the k-gamma and k-beta functions. 2 Main results: inequalities via the Chebychev integral inequality we prove some inequalities which involve k-gamma and k-beta functions by using some natural inequalities [ ]. The following result is known in the literature as the Chebychev integral inequality for synchronous (asynchronous) functions.
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