In this study, new and general variants have been obtained on Chebyshev’s inequality, which is quite old in inequality theory but also a useful and effective type of inequality. The main findings obtained by using integrable functions and generalized fractional integral operators have generalized many existing results as well as iterating the Chebyshev inequality in special cases.

In this work, we discuss and introduce the novel literature about Raina-convex function and its algebraic properties. In addition, We elaborate and investigate Hermite-Hadamard and Fejer-type inequalities for newly discussed definition. Finally, using newly introduced definition, we find and prove amazing new integral type inequalities and applications for mean to positive real numbers. The amazing techniques and wonderful ideas of this paper may inspire and motivate for further activities and research in this direction furthermore.