Estimates of upper bound for differentiable mappings related to Katugampola fractional integrals and $ p $-convex mappings

Yuping Yu; Hui Lei; Gou Hu; Tingsong Du; Yuping Yu; Hui Lei; Gou Hu; Tingsong Du

doi:10.3934/math.2021210

AIMS Mathematics

2021, Volume 6, Issue 4: 3525-3545. doi: 10.3934/math.2021210

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Research article

Estimates of upper bound for differentiable mappings related to Katugampola fractional integrals and $ p $-convex mappings

1.
Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China
2.
School of Mathematics, Hunan University, Changsha 410082, P. R. China

Received: 08 September 2020 Accepted: 13 January 2021 Published: 21 January 2021
MSC : 26A33, 26A51, 26D10, 26D15

We use the definition of a fractional integral operators, recently introduced by Katugampola, to establish a parameterized identity associated with differentiable mappings. The identity is then used to derive the estimates of upper bound for mappings whose first derivatives absolute values are $ p $-convex mappings. Four examples are also provided to illustrate the obtained results.
- Riemann–Liouville fractional integrals,
- Hadamard fractional integrals,
- $ p $-convex mappings
Citation: Yuping Yu, Hui Lei, Gou Hu, Tingsong Du. Estimates of upper bound for differentiable mappings related to Katugampola fractional integrals and $ p $-convex mappings[J]. AIMS Mathematics, 2021, 6(4): 3525-3545. doi: 10.3934/math.2021210

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Abstract

We use the definition of a fractional integral operators, recently introduced by Katugampola, to establish a parameterized identity associated with differentiable mappings. The identity is then used to derive the estimates of upper bound for mappings whose first derivatives absolute values are $ p $-convex mappings. Four examples are also provided to illustrate the obtained results.

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