Simpson and Newton type inequalities for convex functions via newly defined quantum integrals

H Budak, S Erden, MA Ali - Mathematical Methods in the …, 2021 - Wiley Online Library
We first establish two new identities, based on the kernel functions with either two section or
three sections, involving quantum integrals by using new definition of quantum derivative …

Some new quantum Hermite–Hadamard-like inequalities for coordinated convex functions

H Budak, MA Ali, M Tarhanaci - Journal of Optimization Theory and …, 2020 - Springer
Some New Quantum Hermite–Hadamard-Like Inequalities for Coordinated Convex Functions |
Journal of Optimization Theory and Applications Skip to main content SpringerLink Account Menu …

New quantum boundaries for quantum Simpson's and quantum Newton's type inequalities for preinvex functions

MA Ali, M Abbas, H Budak, P Agarwal… - Advances in Difference …, 2021 - Springer
In this research, we derive two generalized integral identities involving the q ϰ 2
q^\varkappa_2-quantum integrals and quantum numbers, the results are then used to …

Some new Simpson's type inequalities for coordinated convex functions in quantum calculus

MA Ali, H Budak, Z Zhang… - Mathematical Methods in …, 2021 - Wiley Online Library
In this article, by using the notion of newly defined q 1 q 2 derivatives and integrals, some
new Simpson's type inequalities for coordinated convex functions are proved. The outcomes …

Quantum Hermite–Hadamard-type inequalities for functions with convex absolute values of second -derivatives

MA Ali, H Budak, M Abbas, YM Chu - Advances in Difference Equations, 2021 - Springer
In this paper, we obtain Hermite–Hadamard-type inequalities of convex functions by
applying the notion of qb q^b-integral. We prove some new inequalities related with right …

Quantum Ostrowski-type inequalities for twice quantum differentiable functions in quantum calculus

MA Ali, H Budak, A Akkurt, YM Chu - Open Mathematics, 2021 - degruyter.com
In this paper, we first prove an identity for twice quantum differentiable functions. Then, by
utilizing the convexity of∣ D q 2 bf∣ and∣ D q 2 af∣, we establish some quantum …

Some trapezoid and midpoint type inequalities for newly defined quantum integrals

H Budak - Proyecciones (Antofagasta), 2021 - SciELO Chile
In this paper, we first obtain prove two new identities for the quantum integrals. Then we
establish Trapezoid and Midpoint type inequalities for quantum integrals defined by …

Quantum variant of Montgomery identity and Ostrowski-type inequalities for the mappings of two variables

MA Ali, YM Chu, H Budak, A Akkurt, H Yıldırım… - Advances in Difference …, 2021 - Springer
In this investigation, we demonstrate the quantum version of Montgomery identity for the
functions of two variables. Then we use the result to derive some new Ostrowski-type …

Some new Newton's type integral inequalities for co-ordinated convex functions in quantum calculus

M Vivas-Cortez, M Aamir Ali, A Kashuri, I Bashir Sial… - Symmetry, 2020 - mdpi.com
Some recent results have been found treating the famous Simpson's rule in connection with
the convexity property of functions and those called generalized convex. The purpose of this …

Some New Hermite–Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral

M Vivas-Cortez, MA Ali, H Budak, H Kalsoom… - Entropy, 2021 - mdpi.com
In this investigation, for convex functions, some new (p, q)–Hermite–Hadamard-type
inequalities using the notions of (p, q) π 2 derivative and (p, q) π 2 integral are obtained …