Integral Inequalities and Generalized Convexity

By: Shashi Kant Mishra and Nidhi Sharma and Jaya Bisht

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Synopsis: The book covers several new research findings in the area of generalized convexity and integral inequalities. Integral inequalities using various type of generalized convex functions are applicable in many branches of mathematics such as mathematical analysis, fractional calculus, and discrete fractional calculus. The book contains integral inequalities of Hermite-Hadamard type, Hermite- Hadamard-Fejer type and majorization type for the generalized strongly convex functions. It presents Hermite-Hadamard type inequalities for functions defined on Time scales. Further, it provides the generalization and extensions of the concept of preinvexity for interval-valued functions and stochastic processes, and give Hermite-Hadamard type and Ostrowski type inequalities for these functions. These integral inequalities are utilized in numerous areas for the boundedness of generalized convex functions. Features: Covers Interval-valued calculus, Time scale calculus, Stochastic processes – all in one single book. Numerous examples to validate results Provides an overview of the current state of integral inequalities and convexity for a much wider audience, including practitioners. Applications of some special means of real numbers are also discussed. The book is ideal for anyone teaching or attending courses in integral inequalities along with researchers in this area.