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

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-con...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 4; pp. 3525 - 3545
Main Authors Yu, Yuping, Lei, Hui, Hu, Gou, Du, Tingsong
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
hadamard fractional integrals
p-convex mappings
riemann–liouville fractional integrals
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021210