Hermite-Hadamard and Ostrowski type inequalities via $ \alpha $-exponential type convex functions with applications

Attazar Bakht; Matloob Anwar; Attazar Bakht; Matloob Anwar

doi:10.3934/math.2024465

AIMS Mathematics

2024, Volume 9, Issue 4: 9519-9535. doi: 10.3934/math.2024465

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Hermite-Hadamard and Ostrowski type inequalities via $ \alpha $-exponential type convex functions with applications

Attazar Bakht ^,,
Matloob Anwar

Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad, Pakistan

Received: 23 August 2023 Revised: 13 November 2023 Accepted: 21 November 2023 Published: 07 March 2024
MSC : 26A33, 26A51, 26D07, 26D10, 26D15

This paper introduced and investigated a new form of convex mapping known as $ \alpha $-exponential type convexity. We presented several algebraic properties associated with this newly introduced convexity. Additionally, we established novel adaptations of well-known inequalities, including the Hermite-Hadamard and Ostrowski-type inequalities, specifically for this convex function. We also derived special cases of these newly established results. Furthermore, we provided new estimations for the trapezoidal formula, demonstrating practical applications of this research.
- Hermite Hadamard inequality,
- exponential type convexity,
- Ostrowski inequality,
- convex function,
- Holder's inequality
Citation: Attazar Bakht, Matloob Anwar. Hermite-Hadamard and Ostrowski type inequalities via $ \alpha $-exponential type convex functions with applications[J]. AIMS Mathematics, 2024, 9(4): 9519-9535. doi: 10.3934/math.2024465

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Abstract

This paper introduced and investigated a new form of convex mapping known as $ \alpha $-exponential type convexity. We presented several algebraic properties associated with this newly introduced convexity. Additionally, we established novel adaptations of well-known inequalities, including the Hermite-Hadamard and Ostrowski-type inequalities, specifically for this convex function. We also derived special cases of these newly established results. Furthermore, we provided new estimations for the trapezoidal formula, demonstrating practical applications of this research.

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