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

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.

[1]  Jessada Tariboon,et al.  Quantum integral inequalities for convex functions , 2015 .

[2]  Muhammad Aslam Noor,et al.  Some quantum integral inequalities via preinvex functions , 2015, Appl. Math. Comput..

[3]  S. Bermudo,et al.  On q-Hermite–Hadamard inequalities for general convex functions , 2020 .

[4]  Jorge Esteban Hernández Hormazabal,et al.  Quantum Trapezium-Type Inequalities Using Generalized ϕ-Convex Functions , 2020, Axioms.

[5]  Jorge Esteban Hernández Hormazabal,et al.  Some New q - Integral Inequalities Using Generalized Quantum Montgomery Identity via Preinvex Functions , 2020, Symmetry.

[6]  Miguel Vivas-Cortez,et al.  Ostrowski Type Inequalities for Functions Whose Derivatives are (m,h1,h2)-Convex , 2017 .

[7]  Miguel J. Vivas-Cortez,et al.  New Quantum Estimates of Trapezium-Type Inequalities for Generalized ϕ-Convex Functions , 2019, Mathematics.

[8]  Poom Kumam,et al.  NEWTON’S-TYPE INTEGRAL INEQUALITIES VIA LOCAL FRACTIONAL INTEGRALS , 2020 .

[9]  Thabet Abdeljawad,et al.  Simpson’s Integral Inequalities for Twice Differentiable Convex Functions , 2020, Mathematical Problems in Engineering.

[10]  Mehmet Zeki Sarikaya,et al.  q-Hermite Hadamard inequalities and quantum estimates for midpoint type inequalities via convex and quasi-convex functions , 2016 .

[11]  Miguel Vivas Cortez,et al.  Ostrowski-Type Inequalities for Functions Whose Derivative Modulus is Relatively Convex. , 2019, Applied Mathematics & Information Sciences.

[12]  Sabir Hussain,et al.  Simpson's Type Inequalities for Co-Ordinated Convex Functions on Quantum Calculus , 2019, Symmetry.

[13]  Muhammad Amer Latif,et al.  Some q-analogues of Hermite–Hadamard inequality of functions of two variables on finite rectangles in the plane , 2017 .

[14]  H. Gauchman,et al.  Integral inequalities in q-calculus , 2004 .

[15]  Muhammad Aslam Noor,et al.  Some quantum estimates for Hermite-Hadamard inequalities , 2015, Appl. Math. Comput..

[16]  Ravi P. Agarwal,et al.  On Simpson's inequality and applications. , 2000 .

[17]  Wenjun Liu,et al.  Some Quantum Estimates of Hermite-Hadamard Inequalities for Quasi-Convex Functions , 2019, Mathematics.

[18]  Miguel Vivas Cortez,et al.  Jensen’s Inequality for Convex Functions on N-Coordinates , 2018, Applied Mathematics & Information Sciences.

[19]  Miguel Vivas Cortez.  Fejer Type Inequalities for (s,m)-Convex Functions in Second Sense , 2016 .

[20]  Jessada Tariboon,et al.  Quantum calculus on finite intervals and applications to impulsive difference equations , 2013 .

[21]  Jorge Esteban Hernández Hormazabal,et al.  Quantum Estimates of Ostrowski Inequalities for Generalized ϕ-Convex Functions , 2019, Symmetry.

[22]  Jessada Tariboon,et al.  Quantum integral inequalities on finite intervals , 2014 .

[23]  Hüseyin Budak,et al.  Some New Quantum Hermite–Hadamard-Like Inequalities for Coordinated Convex Functions , 2020, Journal of Optimization Theory and Applications.