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In the current investigation, we offer the generalized version of q 1 ⁢ q 2 -Simpson's type inequalities via (α , m) -coordinated convex functions. To validate their generalized behavior, we demonstrate the link between our outcomes and the already derived ones. Moreover, we provide some application to special means of positive real numbers to support our findings. The principal outcomes raised in this investigation are extensions and generalizations of the comparable results in the history on Simpson's inequalities for coordinated convex functions. [ABSTRACT FROM AUTHOR]

In this study, we develop three new quantum Hermite-Hadamard inequalities for the class of p, (p-s) and modified type (p-s) -convex functions by utilizing left and right quantum integral. As special cases of these inequalities, we get known and new Hermite-Hadamard type inequality for modified type (p-s) -convex functions. The ideas and techniques of this article may be the starting point for further research in this field. [ABSTRACT FROM AUTHOR]

In this investigation, we established some new post quantum-Hermite-Hadamard inequalities for differentiable convex function with critical point by using the notion of -integeral. The perseverance of this article is to establish different results on the left hand side of - Hermite-Hadamard inequality for differentiable convex function along with critical a point. Some Special cases are obtain for different - Hermite Hadamard inequalies at critical point c for some specific values of q. [ABSTRACT FROM AUTHOR]

The main objective of this study is to establish two important right q-integral equalities involving a right-quantum derivative with parameter m ∈ [ 0 , 1 ] . Then, utilizing these equalities, we derive some new variants for midpoint- and trapezoid-type inequalities for the right-quantum integral via differentiable (α , m) -convex functions. The fundamental benefit of these inequalities is that they may be transformed into q-midpoint- and q-trapezoid-type inequalities for convex functions, classical midpoint inequalities for convex functions and classical trapezoid-type inequalities for convex functions are transformed without having to prove each one independently. In addition, we present some applications of our results to special means of positive real numbers. It is expected that the ideas and techniques may stimulate further research in this field. [ABSTRACT FROM AUTHOR]

Co-ordinated convex function of two variables and corresponding inequalities have been studied before by many researchers. This paper deals with Co-ordinated convex function of three variables. In the present paper the idea of co-ordinated convex function of two variables in a rectangle from the plane R² is extended to that of three variables in a rectangle from space R³. Moreover corresponding extended right handed Hermite-Hadamard type inequalities are also incorporated. At the end some applications of resulting inequalities to special means are also given. [ABSTRACT FROM AUTHOR]