On Some New Simpson’s Formula Type Inequalities for Convex Functions in Post-Quantum Calculus
Miguel J. Vivas-Cortez,
Muhammad Aamir Ali,
Shahid Qaisar,
Ifra Bashir Sial,
Sinchai Jansem,
Abdul Mateen
Affiliations
Miguel J. Vivas-Cortez
Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Católica del Ecuador, Escuela de Ciencias Matemáticas y Físicas, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador
Muhammad Aamir Ali
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
Shahid Qaisar
Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan
Ifra Bashir Sial
School of Control Science and Engineering, Jiangsu University, Zhenjiang 212000, China
Sinchai Jansem
Faculty of Education, Suan Dusit University, Bangkok 10300, Thailand
Abdul Mateen
Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan
In this work, we prove a new (p,q)-integral identity involving a (p,q)-derivative and (p,q)-integral. The newly established identity is then used to show some new Simpson’s formula type inequalities for (p,q)-differentiable convex functions. Finally, the newly discovered results are shown to be refinements of comparable results in the literature. Analytic inequalities of this type, as well as the techniques used to solve them, have applications in a variety of fields where symmetry is important.
