Analytic Inequalities

Abstract

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On integral inequalities similar to Opial's inequality

“…note that the inequality (3) is analogous to Godunova and Levin's inequality (see [3]» Theorem 13» p.159) and we believe that the inequality (3) is new to the literature.…”

“…(ii) Putting f(r) -r and hence f'(r) = 1 in (3) and applying the Schwarz inequality to the resulting integral on the right-hand side of (3), we get the Opial inequality given in ( [3], theorem 2% p.154).…”

Some inequalities that arise in measure theory

“…Proceeding as on earlier occasions we differentiate (1 + x + x 2 + x 3 )(l + x + x 2 )-x (l + x* + x 2 ')-1 /' of use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1446788700032298 [10] to see that we should consider zeros of G(x) defined by G(x) = (1 + 2x + 3x 2 )(l + x + x 2 )(l + x* + x 2t )…”

An Integral Inequality

“…In spite of its simplicity and its resemblance to the Tchebycheff inequality [4,Theorem 10,p. 40], this inequality does not appear to have been discussed in the standard treatises on inequalities [2][3][4].…”

“…40], this inequality does not appear to have been discussed in the standard treatises on inequalities [2][3][4]. Our interest in (1) was triggered by the special case [6] in which E = (0, 1), pit) = t, git) = J0(vt), f(t) = t2j[¡(vt), v is a fixed constant, and 70 is the Bessel function of the first kind and order zero.…”