Abstract
In this paper, Hölder, Minkowski, and power mean inequalities are used to establish Ostrowski type inequalities for s -convex functions via h -calculus. The new inequalities are generalized versions of Ostrowski type inequalities available in literature.
Highlights
The quantum calculus is equivalent to usual infinitesimal calculus without depending upon the concept of limit
It has two major branches, q-calculus and the h-calculus. It is really the calculus of finite differences, but a more systematic analogy with classical calculus makes it transparent. e definite h-integral is a Riemann sum so that the fundamental theorem of h-calculus allows one to evaluate finite sums and h-integration by parts which is the Abel transform. e theory of h-discrete calculus is the rapidly developing area of great interest both from theoretical and applied point of view. is calculus is the study of the definitions, properties, and applications of the related concepts, the fractional calculus and discrete fractional calculus
Our results extend and generalize the results of Alomari et al In this work, some important Ostrowski type inequalities are established in the context of h-calculus. e derived results constitute contributions to the theory of h-integral and can be specialized to yield numerous interesting integral inequalities including some known results
Summary
The quantum calculus is equivalent to usual infinitesimal calculus without depending upon the concept of limit. E h-integral is defined as follows: let φ: T] ⟶ R, T] {], ] + h, ] + 2h, . Let φ, g: [], μ] ⟶ R be the continuous functions and θ ∈ [], μ], the formula of h-integration by parts is stated as μ μ If |φ′(θ)| ≤ M for all θ ∈ [], μ], the following inequality holds:
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
