Some New Quantum Hermite–Hadamard Inequalities for Co-Ordinated Convex Functions

• Published in: Mathematics
• Main Authors: Fongchan Wannalookkhee, Kamsing Nonlaopon, Sotiris K. Ntouyas, Mehmet Zeki Sarikaya, Hüseyin Budak, Muhammad Aamir Ali
• Format: Article
• Language: English
• Published: MDPI AG 2022-06-01
• Subjects: Hermite–Hadamard inequalities; convex functions; co-ordinated convex functions; quantum calculus
• Online Access: https://www.mdpi.com/2227-7390/10/12/1962
• ISSN: 2227-7390

In this paper, we establish some new versions of Hermite–Hadamard type inequalities for co-ordinated convex functions via <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>q</mi><mn>1</mn></msub><mo>,</mo><msub><mi>q</mi><mn>2</mn></msub></mrow></semantics></math></inline-formula>-integrals. Since the inequalities are newly proved, we therefore consider some examples of co-ordinated convex functions and show their validity for particular choices of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>q</mi><mn>1</mn></msub><mo>,</mo><msub><mi>q</mi><mn>2</mn></msub><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. We hope that the readers show their interest in these results.