Author:
Akbar Saira Bano,Abbas Mujahid,Budak Hüseyin
Abstract
AbstractThe aim of this paper is first to introduce generalizations of quantum integrals and derivatives which are called $$(\phi \,-\,h)$$
(
ϕ
-
h
)
integrals and $$(\phi \,-\,h)$$
(
ϕ
-
h
)
derivatives, respectively. Then we investigate some implicit integral inequalities for $$(\phi \,-\,h)$$
(
ϕ
-
h
)
integrals. Different classes of convex functions are used to prove these inequalities for symmetric functions. Under certain assumptions, Hermite–Hadamard-type inequalities for q-integrals are deduced. The results presented herein are applicable to convex, m-convex, and $$\hbar $$
ħ
-convex functions defined on the non-negative part of the real line.
Publisher
Springer Science and Business Media LLC
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