ON A NEW α-CONVEXITY WITH RESPECT TO A PARAMETER: APPLICATIONS ON THE MEANS AND FRACTIONAL INEQUALITIES

Muhammad Samraiz (), Tahira Atta (), Hossam A. Nabwey, Saima Naheed () and Sina Etemad
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Muhammad Samraiz: Department of Mathematics, University of Sargodha, Sargodha, Punjab 40100, Pakistan
Tahira Atta: Department of Mathematics, University of Sargodha, Sargodha, Punjab 40100, Pakistan
Hossam A. Nabwey: ��Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
Saima Naheed: Department of Mathematics, University of Sargodha, Sargodha, Punjab 40100, Pakistan
Sina Etemad: ��Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran§Mathematics in Applied Sciences and Engineering Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah 64001, Iraq

FRACTALS (fractals), 2024, vol. 32, issue 07n08, 1-22

Abstract: In this research, we introduce a new and generalized family of convex functions, entitled the α-convex functions in the second sense with respect to a parameter and examine their important algebraic properties. Based on this novel convexity concept, we explore a new class of fractional integral inequalities for functions that are twice differentiable. These results are derived from fundamental identities obtained using classical Riemann–Liouville fractional integrals. To validate our findings, we provide 2D and 3D graphs of the main results. Furthermore, as an additional aspect of our study, we explore error estimates for differences of generalized means.

Keywords: α-Convexity; Generalized Convexity; Hermite–Hadamard Inequality; Generalized Means (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24400358

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