Convex function : Advances in quantum integral inequalities
*Sopan Raosaheb ShindeCorresponding authorscholarswapnil@gmail.comDepartment of Computer EngineeringDr. D. Y. Patil College of Engineering and InnovationPune, Maharashtra, 410507, IndiaView full profile → , Kalyani Vishal Dokejivansagharsh@gmail.comDepartment of Engineering Science and HumanitiesSandip Institute of Technology and Research Centre (SITRC)Mahiravani Trimbak Road, Nashik, Maharashtra, 422213, IndiaView full profile → , Santosh Dnyandev Jadhavsdjmaths23@gmail.comDepartment of General EngineeringN. K. Orchid College of Engineering and TechnologySolapur, Maharashtra, 413002, IndiaView full profile →
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- Received:
- 01 Feb 2026
- Published Online:
- 25 Aug 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2630
- Pages:
- 2453–2461
Abstract
In this research work, we study 𝔮-calculus focusing on the development of quantum estimates involving 𝔮-differentials and 𝔮-integrals. By constructing identities based on these quantum tools, we analyze the structure and behavior of convex functions within 𝔮-calculus.
We present generalized formulations of various q-inequalities, offering a foundation for further investigation of different types of integral inequalities in the quantum setting.
Our approach highlights the utility of convex function properties in 𝔮-analysis and contributes to the advancement of inequality theory in quantum integral.
In our research work, based on quantum analog of Hermite-Hadamard inequality, the quantum analog of some trapezoid, midpoint, Bullen and Simpson type inequalities are established. Moreover, by taking the special selection of κ and s and taking limit 𝔮→1– some new results are obtained, and some old results are verified.
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References
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