Functions with Nondecreasing Increments

Nazia Irshad, Asif R. Khan, Faraz Mehmood and Josip Pečarić
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Nazia Irshad: Dawood University of Engineering and Technology, Department of Mathematics
Asif R. Khan: University of Karachi, Department of Mathematics
Faraz Mehmood: Dawood University of Engineering and Technology, Department of Mathematics
Josip Pečarić: Croatian Academy of Sciences and Arts

Chapter Chapter 3 in New Perspectives on the Theory of Inequalities for Integral and Sum, 2021, pp 193-212 from Springer

Abstract: Abstract The main purpose of the present chapter is to establish the relationship of functions with nondecreasing increments (FWNDI) with other functions of high importance. Our special emphasis will be on the role of representation and connection among functions with nondecreasing increments and arithmetic integral mean, Wright convex functions, convex functions, ∇-convex functions, Jensen m-convex functions, m-convex functions, m-∇-convex functions, k-monotonic functions, absolutely monotonic functions, completely monotonic functions, Laplace transform and exponentially convex functions, by using the finite difference operator as different cases of Δ h m f $$\Delta _{h}^{m}f$$ . We will also consider function with nondecreasing increments of order three and get a generalization of the Levinson’s type inequality and Jensen-Mercer’s type inequality by using Jensen-Boas inequality and also deduce some results.

Date: 2021
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DOI: 10.1007/978-3-030-90563-7_3

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