Refined estimates and generalization of some recent results with applications

Abstract

In this paper, we firstly give improvement of Hermite-Hadamard type and Fej$ \acute{e} $r type inequalities. Next, we extend Hermite-Hadamard type and Fej$ \acute{e} $r types inequalities to a new class of functions. Further, we give bounds for newly defined class of functions and finally presents refined estimates of some already proved results. Furthermore, we obtain some new discrete inequalities for univariate harmonic convex functions on linear spaces related to a variant most recently presented by Baloch et al. of Jensen-type result that was established by S. S. Dragomir.

Keywords

• convex functions
• harmonic convex functions
• hermite-hadamard inequality
• fejér type inequality
• hermite-hadamard type inequality
• jensen-type inequality
• a variant of jensen type inequality
• hölder's inequality
• weighted hga inequality