NEW NEWTON’S TYPE ESTIMATES PERTAINING TO LOCAL FRACTIONAL INTEGRAL VIA GENERALIZED p-CONVEXITY WITH APPLICATIONS

Yong-Min Li (), Saima Rashid (), Zakia Hammouch, Dumitru Baleanu () and Yu-Ming Chu
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Yong-Min Li: Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China
Saima Rashid: Department of Mathematics, Government College University, Faisalabad 38000, Pakistan
Zakia Hammouch: Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam4Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan5Ecole Normale Supérieure, Moulay Ismail University of Meknes, 5000, Morocco
Dumitru Baleanu: Department of Mathematics, Cankaya University, Ankara, Turkey
Yu-Ming Chu: College of Science, Hunan City University, Yiyang 413000, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 05, 1-20

Abstract: This paper aims to investigate the notion of p-convex functions on fractal sets ℠α̂(0 < α̂ ≤ 1). Based on these novel ideas, we derived an auxiliary result depend on a three-step quadratic kernel by employing generalized p-convexity. Take into account the local fractal identity, we established novel Newton’s type variants for the local differentiable functions. Several special cases are apprehended in the light of generalized convex functions and generalized harmonically convex functions. This novel strategy captures several existing results in the relative literature. Application is obtained in cumulative distribution function and generalized special weighted means to confirm the relevance and computational effectiveness of the considered method. Finally, we supposed that the consequences of this paper can stimulate those who are interested in fractal analysis.

Keywords: Generalized Convex Function; Generalized Harmonically Convex Function; Generalized p-Convex Functions; Newton’s Type Inequality; Fractal Sets (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21400181

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