Asif R. Khan, Josip E. Pečarić, Positivity of general linear inequalities for n-convex functions via the Taylor formula using new Green functions, Vol. 2019 (2019), Article ID 5, pp. 1-20

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DOI: 10.23952/cot.2019.5

Received December 27, 2018; Accepted February 28, 2019; April 4, 2019

 

Abstract. New general linear identities and inequalities are given for n-convex functions via extensions of the Taylor’s formula using new Green functions. We state the conditions under which these inequalities are positive. We also study $n$-convexity at a point for our proposed inequalities. Bounds for the reminders in new generalizations of general linear inequalities are given by using the \v{C}eby\v{s}ev functional, the Ostrowski- and Gr\”uss- types inequalities. Mean value theorems and n-exponential convexity are also discussed for functionals related to new general lineal inequalities.

 

How to Cite this Article:
Asif R. Khan, Josip E. Pečarić, Positivity of general linear inequalities for n-convex functions via the Taylor formula using new Green functions, Journal of Nonlinear Functional Analysis, Vol. 2019 (2019), Article ID 5, pp. 1-20.