Simpson’s Type Inequalities for Co-Ordinated Convex Functions on Quantum Calculus

Abstract

In the present paper, we aim to prove a new lemma and quantum Simpson’s type inequalities for functions of two variables having convexity on co-ordinates over [ α , β ] × [ ψ , ϕ ] . Moreover, our deduction introduce new direction as well as validate the previous results.

T-Spherical Fuzzy Einstein Hybrid Aggregation Operators and Their Applications in Multi-Attribute Decision Making Problems

“…The continuous growth of interest has occurred in order to meet the requirements in needs of fertile applications of these inequalities. Such inequalities had been studied by many researchers who in turn used various techniques for the sake of exploring and offering these inequalities [31][32][33][34][35][36][37][38][39][40][41][42] and the references cited therein.…”

Some (p, q)-Estimates of Hermite-Hadamard-Type Inequalities for Coordinated Convex and Quasi- Convex Functions

“…The concept of q-derivatives over the definite interval [a, b] ⊂ R was attended by Tariboon et al [8,9] and addressed numerous problems on quantum analogues such as the q-Hölder inequality, the q-Ostrowski inequality, the q-Cauchy-Schwarz inequality, the q-Grüss-Čebyšev integral inequality, the q-Grüss inequality, and other integral inequalities by classical convexity. Most recently, Alp et al [10] proved the q-Hermite-Hadamard inequality and then acquired the generalized q-Hermite-Hadamard inequality; also, they studied some integral inequalities, which provide quantum estimates for the left part of the quantum analogue of the q-Hermite-Hadamard inequality through q-differentiable convex and quasi-convex functions, for more details and interesting applications see References [11][12][13][14][15][16]. A recent development in the context of the above concept was presented by Tunç and Göv [17][18][19], named as(p, q)-derivatives and (p, q)-integrals over [a, b] ⊂ R. Some well-known results that depend on (p, q)-calculus are the (p, q)-Minkowski inequality, the (p, q)-Hölder inequality, the (p, q)-Ostrowski inequality, the (p, q)-Cauchy-Schwarz inequality, the (p, q)-Grüss-Čebyšev integral inequality, the (p, q)-Grüss inequality, and other integral inequalities by classical convexity.…”

Some New Quantum Hermite–Hadamard-Type Estimates Within a Class of Generalized (s,m)-Preinvex Functions

“…Having numerous applications in mathematics as well as in physics, q-calculus has emerged as an interesting and most fascinating field of research in recent years. Many researchers have written a number of papers on quantum integrals, for more details, see [2][3][4][5][6][7][8][9].…”