Abstract
In accordance with the quantum calculus, we introduced the two variable forms of Hermite-Hadamard- (HH-) type inequality over finite rectangles for generalizedΨ-convex functions. This novel framework is the convolution of quantum calculus, convexity, and special functions. Taking into account theq^1q^2-integral identity, we demonstrate the novel generalizations of theHH-type inequality forq^1q^2-differentiable function by acquainting Raina’s functions. Additionally, we present a different approach that can be used to characterizeHH-type variants with respect to Raina’s function of coordinated generalizedΨ-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.
Highlights
A nonrestricted analysis is recognized as quantum calculus and has initiated numerous q -mathematical formulation as q ↦ 1−: In 1707–1783, Euler proposed q-calculus theory
The concept of q-calculus has been potentially utilized in quantum mechanics, special relativity theory, anomalous diffusion equations, orthogonal polynomials, fractional calculus, and
In [2, 3], authors contemplated the q-derivatives on finite intervals of real line and amplified several new generalizations of classical convexity, q-version of Grüss, q-Cebyšev’s, and q-Pólya-Szegö type inequalities
Summary
A nonrestricted analysis is recognized as quantum calculus (in short, q-calculus) and has initiated numerous q -mathematical formulation as q ↦ 1−: In 1707–1783, Euler proposed q-calculus theory. We intend to find the novel version of H H -type inequality in the frame of q1q2-integral on coordinated generalized Ψ-convex functions that correlates with Raina’s function. Owing to the above-mentioned work, this research is aimed at exploring the novel generalizations of H H-type inequalities on the coordinates by the use of generalized Ψ -convex functions which are elaborated. An auxiliary identity is derived with respect to the q1q2-derivative by the correlation of Raina’s function Considering this new approach, we derive certain novel quantum bounds of H H-type variants for coordinated generalized Ψ-convex mappings. For the change of parameter in Raina’s function, we generate numerous new outcomes depending on hypergeometric and MittagLeffler functions. This new study may stimulate further investigation in this dynamic field of inequality theory
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