Improved Hermite-Hadamard type inequalities by using the p-convexity of differentiable mappings

Abstract

In this paper, a new identity is established for differentiable mappings. By using the mathematical analysis techniques, some new integral inequalities of Hermite-Hadamard type for differentiable p-convex functions are proved. A comparison of the established results with previously obtained results is demonstrated to show that the results presented in this paper are better than those already exist in literature.

Mathematics Subject Classification (2010):

• 26D15
• 26A51

Key words:

• Convex functions
• p-convex functions
• harmonically convex function
• Hermite-Hadamard inequalities