Related Experiment Video
Updated: Feb 20, 2026

Interfacial Molecular-level Structures of Polymers and Biomacromolecules Revealed via Sum Frequency Generation Vibrational Spectroscopy
Published on: August 13, 2019
On generalization of refinement of Jensen's inequality using Fink's identity and Abel-Gontscharoff Green function
Tasadduq Niaz1, Khuram Ali Khan1, Josip Pečarić2
1Department of Mathematics, University of Sargodha, Sargodha, 40100 Pakistan.
Abstract:
In this paper, we formulate new Abel-Gontscharoff type identities involving new Green functions for the 'two-point right focal' problem. We use Fink's identity and a new Abel-Gontscharoff-type Green's function for a 'two-point right focal' to generalize the refinement of Jensen's inequality given in (Horváth and Pečarić in Math. Inequal. Appl. 14: 777-791, 2011) from convex function to higher order convex function. Also we formulate the monotonicity of the linear functional obtained from these identities using the recent theory of inequalities for n-convex function at a point. Further we give the bounds for the identities related to the generalization of the refinement of Jensen's inequality using inequalities for the Cebyšev functional. Some results relating to the Grüss and Ostrowski-type inequalities are constructed.
More Related Videos
Related Concept Videos
Divergence and Stokes' Theorems
Fundamental Theorem of Calculus II
Improper Integrals: Infinite Intervals
Fundamental Theorem of Calculus I
Region of Convergence of Laplace Tarnsform
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This...
Reynolds Transport Theorem

