On Fejér’s inequality: generalizations and applications

This paper deals with generalizations and refinements of Fejér’s inequality with some new applications. We introduce a real mapping ℳ_f^ω(t) and obtain some its functional properties. We present several inequalities in connection with fractional integrals and their refinements by monotone functions. We also give some inequalities related to Euler’s gamma and beta functions. Furthermore, we obtain some upper and lower bounds for generalized logarithmic mean and the expected value of random variables by using the arithmetic mean.