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

Attazar Bakht; Matloob Anwar; Attazar Bakht; Matloob Anwar

doi:10.3934/math.20241364

AIMS Mathematics

2024, Volume 9, Issue 10: 28130-28149. doi: 10.3934/math.20241364

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Research article

Ostrowski and Hermite-Hadamard type inequalities via $ (\alpha-s) $ 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: 26 July 2024 Revised: 12 September 2024 Accepted: 14 September 2024 Published: 27 September 2024
MSC : 26A33, 26A51, 26D07, 26D10, 26D15

Integral inequalities involving exponential convexity are significant in both theoretical and applied mathematics. In this paper, we establish a new Hermite-Hadamard type inequality for the class of exponentially convex functions by using the concept of $ (\alpha-s) $ exponentially convex function. Additionally, using the well-known Hermite-Hadamard and Ostrowski inequalities, we establish several new integral inequalities. These newly obtained results contain several well-known results as special cases. Finally, new estimations for the trapezoidal formula have been provided, illustrating the practical applications of the research.
- convex function,
- exponential type s-convexity,
- Hermite Hadamard inequality,
- Ostrowski inequality,
- Holder's inequality
Citation: Attazar Bakht, Matloob Anwar. Ostrowski and Hermite-Hadamard type inequalities via $ (\alpha-s) $ exponential type convex functions with applications[J]. AIMS Mathematics, 2024, 9(10): 28130-28149. doi: 10.3934/math.20241364

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Abstract

Integral inequalities involving exponential convexity are significant in both theoretical and applied mathematics. In this paper, we establish a new Hermite-Hadamard type inequality for the class of exponentially convex functions by using the concept of $ (\alpha-s) $ exponentially convex function. Additionally, using the well-known Hermite-Hadamard and Ostrowski inequalities, we establish several new integral inequalities. These newly obtained results contain several well-known results as special cases. Finally, new estimations for the trapezoidal formula have been provided, illustrating the practical applications of the research.

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