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We establish a generalization of the inequality introduced by Mitrinovi and Peari in 1988. We prove mean value theorems of Cauchy type for that new inequality by taking its difference. Furthermore, we prove the positive semidefiniteness of the matrices generated by the difference of the inequality which implies the exponential convexity and logarithmic convexity. Finally, we define new means of Cauchy type and prove the monotonicity of these means. Copyright © 2010 Sajid Iqbal et al.

Generalization of an Inequality for Integral Transforms with Kernel and Related Results