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Full Description
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.
Contents
1. Introduction. 2. Integral Inequalities for Strongly Generalized Convex Functions. 3. Integral Inequalities for Strongly Generalized Convex Functions of Higher Order. 4. Integral Inequalities for Generalized Preinvex Functions. 5. Some Majorization Integral Inequalities for Functions Defined on Rectangles via Strong Convexity. 6. Hermite-Hadamard type Inclusions for Interval-Valued Generalized Preinvex Functions. 7. Some Inequalities for Multidimensional General h-Harmonic Preinvex and Strongly Generalized Convex Stochastic Processes. 8. Applications.
