GENERALISATION OF HERMITE-HADAMARD LIKE INEQUALITIES FOR (α, β, γ, μ)-CONVEX FUNCTIONS IN MIXED KIND WITH APPLICATIONS
Faraz Mehmood*, Sumaira Yousuf Khan, Faisal Nawaz, Muhammad Awais Shaikh, Mateen Ahmed Ghaznavi, Akhmadjon Soleev
Abstract.
In the current paper, few generalised inequalities of Hermite-Hadamard like for functions whose modulus of the derivatives are (α,β,γ,µ)−convex in mixed kind and applications for theory of Probability & Numerical integration are deduced. Several established consequences of several published will capture as especial cases. Moreover, we deduce more especial cases of the class of (α,β,γ,µ)−convex function on various choices of α,β,γ,µ.
Keywords. Convex function, Hermite-Hadamard inequality, Power-mean inequality, H
lder inequality, Beta, Gamma function, Numerical integration, Probability density function.