On Levinson's inequality involving averages of 3-convex functions
Copyright policy )On Levinson's inequality involving averages of 3-convex functions
By using the Levinson inequality we give the extension for 3-convex functions of Wulbert's result from Favard's Inequality on Average Values of Convex Functions, Math. Comput. Model. 37 (2003), 1383-1391. Also, we obtain inequalities with divided differences, and as a consequence, the convexity of higher order for function defined by divided difference is proved. Further, we construct a new family of exponentially convex functions and Cauchy-type means by looking at linear functionals associated with these new inequalities.
- University of Zagreb Croatia
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n-convex function, m)-convex function, Levinson's inequality, divided differences, $n$-convex function, $(n, m)$-convex function, means, exponential convexity, Levinson’s inequality, $(n, Levinson’s inequality ; divided difference ; n-convex function ; (n, m)-convex function ; mean, divided difference, (n, m)$-convex function, mean, Convexity of real functions in one variable, generalizations, Levinson inequality, $n$-convex function, \(n\)-convex function, divided differences, means, Inequalities for sums, series and integrals, Levinson's inequality, exponential convexity, Inequalities involving other types of functions, \((n, m)\)-convex function
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