Abstract
In this paper, the newly proposed concept of Raina’s function and quantum calculus are utilized to anticipate the quantum behavior of two variable Ostrowski-type inequalities. This new technique is the convolution of special functions with hypergeometric and Mittag–Leffler functions, respectively. This new concept will have the option to reduce self-similitudes in the quantum attractors under investigation. We discuss the implications and other consequences of the quantum Ostrowski-type inequalities by deriving an auxiliary result for a q 1 q 2 -differentiable function by inserting Raina’s functions. Meanwhile, we present a numerical scheme that can be used to derive variants for Ostrowski-type inequalities in the sense of coordinated generalized Φ -convex functions with the quantum approach. This new scheme of study for varying values of parameters with the involvement of Raina’s function yields extremely intriguing outcomes with an illustrative example. It is supposed that this investigation will provide new directions for the capricious nature of quantum theory.
Highlights
Quantum calculus is the non-limited analysis of calculus, and it is recognized as q-calculus.We get the initial mathematical formulas in q-calculus as q reaches 1−
The idea of q-calculus is used in numerous areas of mathematics and physics especially in orthogonal polynomials, number theory, hypergeometric functions, mechanics, and the theory of relativity
Noor et al [34] proposed the quantum estimates for Ostrowski-type inequalities based on the convexity function of one variable, which are associated with the equality below
Summary
Quantum calculus is the non-limited analysis of calculus, and it is recognized as q-calculus. In [33], the classical Ostrowski-type inequality for coordinated convex functions was established via the following equality: Theorem 2. Noor et al [34] proposed the quantum estimates for Ostrowski-type inequalities based on the convexity function of one variable, which are associated with the equality below. For several recent results on different types of inequalities for functions that satisfy different kinds of convexity on the coordinates on the rectangle from the plane R2 , we refer the reader to [36,37,38,39,40]. We derive an identity for q1 q2 differentiable by involving Raina’s functions Applying this new identity, we develop some new quantum analogs of Ostrowski inequalities for a coordinated generalized Φ-convex function. The ideas and techniques of the paper may open a new venue for further research in this field
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