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Full-Text Articles in Physical Sciences and Mathematics
The Most Important Inequalities Of $M$-Convex Functions, Zlatko Pavic, Merve Avci Ardiç
The Most Important Inequalities Of $M$-Convex Functions, Zlatko Pavic, Merve Avci Ardiç
Turkish Journal of Mathematics
The intention of this article is to investigate the most important inequalities of $m$-convex functions without using their derivatives. The article also provides a brief survey of general properties of $m$-convex functions.
More Accurate Jensen-Type Inequalities For Signed Measures Characterized Via Green Function And Applications, Mario Krnic, Josip Pecaric, Mirna Rodic
More Accurate Jensen-Type Inequalities For Signed Measures Characterized Via Green Function And Applications, Mario Krnic, Josip Pecaric, Mirna Rodic
Turkish Journal of Mathematics
In this paper we derive several improved forms of the Jensen inequality, giving the necessary and sufficient conditions for them to hold in the case of the real Stieltjes measure not necessarily positive.The obtained relations are characterized via the Green function. As an application, our main results are employed for constructing some classes of exponentially convex functions and some Cauchy-type means.