A two points Taylor's formula for the generalised Riemann integral and various bounds for the remainder are established. Moreover, particular instances of interest are given.
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In this paper we establish explicit estimates on some mixed Volterra-Fredholm type integral inequalities which can be used as tools in certain applications. Some applications are also given to illustrate the usefulness of the results.
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The aim of this note is to establish two new Gruss type integral inequalities involving functions and their derivatives by using a fairly elementary analysis.
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Let alphis an element of [0,1]. A function f :I -> R (0 is an element of I) is said to be alpha-star-convex on [...]. In this note we will present new geometric interpretation of alpha-star-convex functions and some Hadamards' like integral inequalities for such functions.
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The aim of the present paper os to establish some new integra1 inequalities associated to the zeros of the solutions of certain higher order differential equations by using elementary analysis. The inequalities obtained here can be effectively used in the study of qualitative behavior of solutions of the corresponding equations.
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