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On A New α-Convexity With Respect To A Parameter: Applications On The Means And Fractional Inequalities

Author

Listed:
  • 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)

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.

Suggested Citation

  • Muhammad Samraiz & Tahira Atta & Hossam A. Nabwey & Saima Naheed & Sina Etemad, 2024. "On A New α-Convexity With Respect To A Parameter: Applications On The Means And Fractional Inequalities," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 32(07n08), pages 1-22.
    • Handle: RePEc:wsi:fracta:v:32:y:2024:i:07n08:n:s0218348x24400358
    DOI: 10.1142/S0218348X24400358
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