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Some new general integral inequalities for h-convex and h-concave functions
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İmdat İşcan
Published/Copyright:
January 15, 2014
Abstract.
In this paper, we derive new integral inequalities for functions with h -convex and h-concave first derivatives. As a consequence, we give new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are h-convex and h -concave and we point out the results for some special classes of functions.
Keywords: Hermite–Hadamard-type inequalities; Simpson-type inequality; h-convex function; s-convex function; P-function
Received: 2013-09-03
Revised: 2014-01-10
Accepted: 2014-01-12
Published Online: 2014-01-15
Published in Print: 2014-03-01
© 2014 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Frontmatter
- A note on generalized absolute Cesàro summability
- Sinc-type functions on a class of nilpotent Lie groups
- Some new general integral inequalities for h-convex and h-concave functions
- The construction of periodic unfolding operators on some compact Riemannian manifolds
- Integration operators from the space of Cauchy integral transforms to the Dirichlet space
Keywords for this article
Hermite–Hadamard-type inequalities;
Simpson-type inequality;
h-convex function;
s-convex function;
P-function
Articles in the same Issue
- Frontmatter
- A note on generalized absolute Cesàro summability
- Sinc-type functions on a class of nilpotent Lie groups
- Some new general integral inequalities for h-convex and h-concave functions
- The construction of periodic unfolding operators on some compact Riemannian manifolds
- Integration operators from the space of Cauchy integral transforms to the Dirichlet space
