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APPROXIMATE CONVEXITY WITH RESPECT TO INTEGRAL ARITHMETIC MEAN
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 Title & Authors
APPROXIMATE CONVEXITY WITH RESPECT TO INTEGRAL ARITHMETIC MEAN
Zoldak, Marek;
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 Abstract
Let (, , ) be a probabilistic measure space, , , p > 0 be given numbers and let be an open interval. We consider a class of functions , satisfying the inequality for each -measurable simple function . We show that if additionally the set of values of is equal to [0, 1] then satisfies the above condition if and only if for , . We also prove some basic properties of such functions, e.g. the existence of subdifferentials, Hermite-Hadamard inequality.
 Keywords
approximate convexity;Jensen integral inequality;Hermite-Hadamard inequality;
 Language
English
 Cited by
 References
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