Multidirectional mean value inequalities and weak

Yu. S. Ledyaev and Q. J. Zhu

Abstract: Multidirectional mean value inequalities provide estimates of the difference of the extremal value of a function on a given bounded set and its value at a given point in terms of its (sub)-gradient at some intermediate point. We demonstrate that such multidirectional mean value inequalities and their
generalizations can be obtained by using sufficient conditions for the approximate weak monotone
decrease of a function along approximate trajectories of differential inclusions which allows us to remove a traditional assumption of lower boundedness on the function. We also obtain criteria for the approximate weak monotonicity and r-growth of lower semicontinuous functions


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