Quantum Integral Inequalities with Respect to Raina's Function via Coordinated Generalized Ψ-Convex Functions with Applications. (27th January 2021)

• Record Type: Journal Article
• Authors: Rashid, Saima; Butt, Saad Ihsan; Kanwal, Shazia; Ahmad, Hijaz; Wang, Miao-Kun
• Other Names: Acar Tuncer Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-01-27
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/6631474
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : In accordance with the quantum calculus, we introduced the two variable forms of Hermite-Hadamard- (H H -) type inequality over finite rectangles for generalized Ψ -convex functions. This novel framework is the convolution of quantum calculus, convexity, and special functions. Taking into account the q ^ 1 q ^ 2 -integral identity, we demonstrate the novel generalizations of the H H -type inequality for q ^ 1 q ^ 2 -differentiable function by acquainting Raina's functions. Additionally, we present a different approach that can be used to characterize H H -type variants with respect to Raina's function of coordinated generalized Ψ -convex functions within the quantum techniques. This new study has the ability to generate certain novel bounds and some well-known consequences in the relative literature. As application viewpoint, the proposed study for changing parametric values associated with Raina's functions exhibits interesting results in order to show the applicability and supremacy of the obtained results. It is expected that this method which is very useful, accurate, and versatile will open a new venue for the real-world phenomena of special relativity and quantum theory.