Some New Newton’s Type Integral Inequalities for Co-Ordinated Convex Functions in Quantum Calculus

Abstract

Some recent results have been found treating the famous Simpson’s rule in connection with the convexity property of functions and those called generalized convex. The purpose of this article is to address Newton-type integral inequalities by associating with them certain criteria of quantum calculus and the convexity of the functions of various variables. In this article, by using the concept of recently defined q1q2 -derivatives and integrals, some of Newton’s type inequalities for co-ordinated convex functions are revealed. We also employ the limits of q1,q2→1− in new results, and attain some new inequalities of Newton’s type for co-ordinated convex functions through ordinary integral. Finally, we provide a thorough application of the newly obtained key outcomes, these new consequences can be useful in the integral approximation study for symmetrical functions, or with some kind of symmetry.

New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions

“…In 2013, Tariboon introduced using classical convexity. Many mathematicians have done studies in q-calculus analysis; the interested reader can check [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Quantum Hermite–Hadamard-type inequalities for functions with convex absolute values of second $q^{b}$-derivatives

“…Many well-known integral inequalities such as the Hölder, Hermite-Hadamard, Ostrowski, Cauchy-Bunyakovsky-Schwarz, Gruss, Gruss-Chebyshev, and other integral inequalities have been studied in the setup of q-calculus using the concept of classical convexity. For more results in this direction, we refer to [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18].…”

Some New Hermite–Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral

“…Khan et al proved quantum Hermite–Hadamard inequality using the green function in [ 28 ]. Budak et al [ 29 ], Ali et al [ 30 , 31 ], and Vivas-Cortez et al [ 32 ] developed new quantum Simpson’s and quantum Newton’s type inequalities for convex and coordinated convex functions. For quantum Ostrowski’s inequalities for convex and co-ordinated convex functions, one can consult [ 33 , 34 , 35 ].…”