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THE MULTI-PARAMETER FRACTAL–FRACTIONAL INEQUALITIES FOR FRACTAL $(P, m)$ -CONVEX FUNCTIONS

XIAOMAN YUAN

https://orcid.org/0009-0003-1285-9971

Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China

Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China

E-mail Address: xiaomanyuan1999@163.com

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HÜSEYIN BUDAK

https://orcid.org/0000-0001-8843-955X

Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey

E-mail Address: hsyn.budak@gmail.com

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, and

TINGSONG DU

https://orcid.org/0000-0002-6072-1788

Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China

Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China

E-mail Address: tingsongdu@ctgu.edu.cn

Corresponding author.

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https://doi.org/10.1142/S0218348X24500257Cited by:7 (Source: Crossref)

Abstract

Local fractional calculus theory and parameterized method have greatly assisted in the advancement of the field of inequalities. To continue its enrichment, this study investigates the multi-parameter fractal–fractional integral inequalities containing the fractal $(P, m)$ -convex functions. Initially, we formulate the new conception of the fractal $(P, m)$ -convex functions and work on a variety of properties. Through the assistance of the fractal–fractional integrals, the $2 ℓ$ -fractal identity with multiple parameters is established, and from that, integral inequalities are inferred regarding twice fractal differentiable functions which are fractal $(P, m)$ -convex. Furthermore, a few typical and novel outcomes are discussed and visualized for specific parameter values, separately. It concludes with some applications in respect of the special means, the quadrature formulas and random variable moments, respectively.

Keywords:

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