New integral inequalities involving beta function via $P$-convexity
Copyright policy )New integral inequalities involving beta function via $P$-convexity
Summary: In this note we establish some estimates, involving the Euler-beta function, of the integral \(\int^b_a (x-a)^p(b-x)^qf(x)dx\) for functions when a power of the absolute value is \(P\)-convex. An extension to functions of several variables is also obtained.
QA Mathematics / matematika, integral inequality, Inequalities for sums, series and integrals, Euler-beta function, Hölder's inequality, \(P\)-convexity, Gamma, beta and polygamma functions, Convexity of real functions of several variables, generalizations
QA Mathematics / matematika, integral inequality, Inequalities for sums, series and integrals, Euler-beta function, Hölder's inequality, \(P\)-convexity, Gamma, beta and polygamma functions, Convexity of real functions of several variables, generalizations
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