Hermite-Hadamard type and Fejér type inequalities for general weights (I)

In this paper, we establish some weighted versions of the Hermite-Hadamard type and Fejer type inequalities and from which generalize Hermite-Hadamard inequality, Fejer inequality and several results in (Dragomir in J. Math. Anal. Appl. 167:49-56, 1992; Yang and Hong in Tamkang. J. Math. 28(1):33-37, 1997; Yang and Tseng in J. Math. Anal. Appl. 239:180-187, 1999; Yang and Tseng in Taiwan. J. Math. 7(3):433-440, 2003).