On New Estimates of <i>q</i>-Hermite–Hadamard Inequalities with Applications in Quantum Calculus
Saowaluck Chasreechai,
Muhammad Aamir Ali,
Muhammad Amir Ashraf,
Thanin Sitthiwirattham,
Sina Etemad,
Manuel De la Sen,
Shahram Rezapour
Affiliations
Saowaluck Chasreechai
Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Muhammad Aamir Ali
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
Muhammad Amir Ashraf
Department of Mathematics and Statistics, University of Agriculture Faisalabad, Faisalabad 38000, Pakistan
Thanin Sitthiwirattham
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
Sina Etemad
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran
Manuel De la Sen
Institute of Research and Development of Processes, Department of Electricity and Electronics, Faculty of Science and Technology, University of the Basque Country (UPV/EHU), 48940 Leioa, Bizkaia, Spain
Shahram Rezapour
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran
In this paper, we first establish two quantum integral (q-integral) identities with the help of derivatives and integrals of the quantum types. Then, we prove some new q-midpoint and q-trapezoidal estimates for the newly established q-Hermite-Hadamard inequality (involving left and right integrals proved by Bermudo et al.) under q-differentiable convex functions. Finally, we provide some examples to illustrate the validity of newly obtained quantum inequalities.
