Abstract
In this paper we prove a new variant of q-Hermite–Hadamard–Mercer-type inequality for the functions that satisfy the Jensen–Mercer inequality (JMI). Moreover, we establish some new midpoint- and trapezoidal-type inequalities for differentiable functions using the JMI. The newly developed inequalities are also shown to be extensions of preexisting inequalities in the literature.
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11971241
Funding statement: This work was partially supported by National Natural Science Foundation of China (No. 11971241).
Acknowledgements
Both authors also gratefully acknowledge the helpful comments of the anonymous referee.
References
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© 2023 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- A family of Apostol–Euler polynomials associated with Bell polynomials
- Some finite integrals involving Mittag-Leffler confluent hypergeometric function
- Results concerning multi-index Wright generalized Bessel function
- On some new inequalities of Hermite–Hadamard–Mercer midpoint and trapezoidal type in q-calculus
- The (p,q)-sine and (p,q)-cosine polynomials and their associated (p,q)-polynomials
Articles in the same Issue
- Frontmatter
- A family of Apostol–Euler polynomials associated with Bell polynomials
- Some finite integrals involving Mittag-Leffler confluent hypergeometric function
- Results concerning multi-index Wright generalized Bessel function
- On some new inequalities of Hermite–Hadamard–Mercer midpoint and trapezoidal type in q-calculus
- The (p,q)-sine and (p,q)-cosine polynomials and their associated (p,q)-polynomials