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

Abstract

In this article, by using the notion of newly defined q1q2 derivatives and integrals, some new Simpson's type inequalities for coordinated convex functions are proved. The outcomes raised in this paper are extensions and generalizations of the comparable results in the literature on Simpson's inequalities for coordinated convex functions.

Some Generalizations of Different Types of Quantum Integral Inequalities for Differentiable Convex Functions with Applications

“…Some authors generalized the quantum Hermite-Hadamard inequalities for coordinated convex functions in [18][19][20]. In [21][22][23], the authors used convexity and coordinated convexity to prove some Simpson's and Newton's type inequalities via q-calculus. For the study of Ostrowski's inequalities, one can consult [24,25].…”

Generalization of Quantum Ostrowski-Type Integral Inequalities

“…Because of its enormous importance in a wide range of applied and pure sciences, in recent decades, the definition of convex and bounded functions has received much attention. Since the theory of inequalities and the concept of convex and bounded functions are closely related, various inequalities for convex, differentiable convex and differentiable bounded functions can be found in the literatur; see [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Inspired by this study, we prove some new quantum Ostrowski's inequalities to expand the relationship between differentiable bounded functions and quantum integral inequalities.…”

On Some Generalized Simpson’s and Newton’s Inequalities for (α, m)-Convex Functions in q-Calculus

“…Khan et al proved quantum Hermite-Hadamard inequality using the green function in [31]. For convex and coordinated convex functions, Budak et al [32], Ali et al [33,34], and Vivas-Cortez et al [35] developed new quantum Simpson's and quantum Newton's type inequalities. For quantum Ostrowski's inequalities for convex and coordinated convex functions, one can consult [36][37][38].…”