Generalized Inequalities of Hermite-Hadamard Like for (m_1,m_2)−Convex Function Via Ho ̈lder & Power-Mean Inequalities and Implementations
Keywords:
Convex func, H-H inequality (inequal.), Power-mean inequal, Holder inequal, Numerical integration, Prob. density func
Abstract
In the present article, we prove the generalized Hermite-Hadamard (H-H) like inequalities for −convex (conv.) via H lder & Power-mean inequalities and implementations for theory of probability (prob.) & numerical integration are deduced. Some consequences of several published articles would be captured as especial cases. Moreover, we deduce few especial cases of −conv. function (func.).
References
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Ali Hassan, Asif R. Khan, Faraz Mehmood and Maria Khan, Fuzzy Ostrowski Type Inequalities Via 𝝓−𝝀−Convex Functions, Journal of Mathematics and Computer Science, 28 (2023), 224-235.
Nazia Irshad, Asif R. Khan, Faraz Mehmood and Josip E. Pecaric, New Perspectives on the Theory of Inequalities for Integral and Sum, Birkhäuser (Springer Nature Switzerland), 2021.
Huriye Kadakal, (α,m_1,m_2)−Convexity and some Inequalities of Hermite-Hadamard Type, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2) (2019), 2128–2142.
Havva Kavurmaci, Merve Avci and M. E. O ̈zdemir, new inequalities of hermite-hadamard type for convex functions with applications, Journal of Inequalities and Applications, 2011(86) (2011), 11 pages.
Asif R. Khan and Faraz Mehmood, Some Remarks on Functions with Non-decreasing Increments, Journal of Mathematical Analysis, 11(1) (2020), 1-16.
Faraz Mehmood, Asif R. Khan and Muhammad Adnan, Positivity of Integrals for Higher Order ∇−Convex and Completely Monotonic Functions, Sahand Communications in Mathematical Analysis, 19(1) (2022), 119-137.
Faraz Mehmood, Faisal Nawaz, Sumaira Yousuf Khan and Akhmadjon Soleev, Hermite-Hadamard Like Inequalities for s−Convex Function in the 1st Kind & Applications, Journal of Liaoning Technical University (Natural Science Edition), 18(8) (2024), 134-142.
Faraz Mehmood, Muhammad Awais Shaikh, Syeda Ismat Zehra, Fouzia Abid and Mateen Ahmed Ghaznzvi, Inequalities of Hermite-Hadamard Like for s−Convex Function in the 2nd Kind and Implementations in Numerical Integration and Probability Theory, Dialogue Social Science Review (DSSR), 3(11) (2025), 37-48.
Ali Hassan, Asif R. Khan, Faraz Mehmood and Maria Khan, Fuzzy Ostrowski Type Inequalities Via 𝝓−𝝀−Convex Functions, Journal of Mathematics and Computer Science, 28 (2023), 224-235.
Nazia Irshad, Asif R. Khan, Faraz Mehmood and Josip E. Pecaric, New Perspectives on the Theory of Inequalities for Integral and Sum, Birkhäuser (Springer Nature Switzerland), 2021.
Huriye Kadakal, (α,m_1,m_2)−Convexity and some Inequalities of Hermite-Hadamard Type, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2) (2019), 2128–2142.
Havva Kavurmaci, Merve Avci and M. E. O ̈zdemir, new inequalities of hermite-hadamard type for convex functions with applications, Journal of Inequalities and Applications, 2011(86) (2011), 11 pages.
Asif R. Khan and Faraz Mehmood, Some Remarks on Functions with Non-decreasing Increments, Journal of Mathematical Analysis, 11(1) (2020), 1-16.
Faraz Mehmood, Asif R. Khan and Muhammad Adnan, Positivity of Integrals for Higher Order ∇−Convex and Completely Monotonic Functions, Sahand Communications in Mathematical Analysis, 19(1) (2022), 119-137.
Faraz Mehmood, Faisal Nawaz, Sumaira Yousuf Khan and Akhmadjon Soleev, Hermite-Hadamard Like Inequalities for s−Convex Function in the 1st Kind & Applications, Journal of Liaoning Technical University (Natural Science Edition), 18(8) (2024), 134-142.
Faraz Mehmood, Muhammad Awais Shaikh, Syeda Ismat Zehra, Fouzia Abid and Mateen Ahmed Ghaznzvi, Inequalities of Hermite-Hadamard Like for s−Convex Function in the 2nd Kind and Implementations in Numerical Integration and Probability Theory, Dialogue Social Science Review (DSSR), 3(11) (2025), 37-48.
Published
2026-08-02
How to Cite
Mehmood, F. (2026). Generalized Inequalities of Hermite-Hadamard Like for (m_1,m_2)−Convex Function Via Ho ̈lder & Power-Mean Inequalities and Implementations. International Journal of Artificial Intelligence & Mathematical Sciences, 5(1), 12-20. https://doi.org/10.58921/ijaims.v5i1.181
