Recently Nikodem, Rajba and W\k{a}sowicz compared the classes ofn-Wright-convex functions and n-Jensen-convex functions by showing that thefirst one is a proper subclass of the latter one, whenever n is an odd naturalnumber. Till now the case of even n was an open problem. In this paper thecomplete solution is given: it is shown that the inclusion is proper for anynatural n. The classes of strongly n-Wright-convex and strongly n-Jensen-convexfunctions are also compared (with the same assertion).
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机译:最近,Nikodem,Rajba和W \ k {a} sowicz比较了n-怀特-凸函数和n-Jensen-凸函数的类,表明只要n是奇数自然数,第一个是后者的一个适当子类。直到现在,偶数n的情况仍然是一个未解决的问题。本文给出了完整的解:表明包含对于任何自然n是适当的。还比较了强n-怀特-凸函数和强n-Jensen-凸函数的类(具有相同的断言)。
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