Estimations of Upper Bounds for n-th Order Differentiable Functions Involving χ-Riemann–Liouville Integrals via γ-Preinvex Functions

A new fractional integral identity is obtained involving n-th order differentiable functions and χ-Riemann–Liouville fractional integrals. Then, some associated estimates of upper bounds involving γ-preinvex functions are obtained. In order to relate some unrelated results, several special cases are...

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Autores principales:	Sadia Talib, Muhammad Uzair Awan
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/13defcb21ac84ac6806a3728077aabac
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spelling	oai:doaj.org-article:13defcb21ac84ac6806a3728077aabac2021-11-22T01:11:32ZEstimations of Upper Bounds for n-th Order Differentiable Functions Involving χ-Riemann–Liouville Integrals via γ-Preinvex Functions1563-514710.1155/2021/6882882https://doaj.org/article/13defcb21ac84ac6806a3728077aabac2021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/6882882https://doaj.org/toc/1563-5147A new fractional integral identity is obtained involving n-th order differentiable functions and χ-Riemann–Liouville fractional integrals. Then, some associated estimates of upper bounds involving γ-preinvex functions are obtained. In order to relate some unrelated results, several special cases are discussed.Sadia TalibMuhammad Uzair AwanHindawi LimitedarticleEngineering (General). Civil engineering (General)TA1-2040MathematicsQA1-939ENMathematical Problems in Engineering, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939
spellingShingle	Engineering (General). Civil engineering (General) TA1-2040 Mathematics QA1-939 Sadia Talib Muhammad Uzair Awan Estimations of Upper Bounds for n-th Order Differentiable Functions Involving χ-Riemann–Liouville Integrals via γ-Preinvex Functions
description	A new fractional integral identity is obtained involving n-th order differentiable functions and χ-Riemann–Liouville fractional integrals. Then, some associated estimates of upper bounds involving γ-preinvex functions are obtained. In order to relate some unrelated results, several special cases are discussed.
format	article
author	Sadia Talib Muhammad Uzair Awan
author_facet	Sadia Talib Muhammad Uzair Awan
author_sort	Sadia Talib
title	Estimations of Upper Bounds for n-th Order Differentiable Functions Involving χ-Riemann–Liouville Integrals via γ-Preinvex Functions
title_short	Estimations of Upper Bounds for n-th Order Differentiable Functions Involving χ-Riemann–Liouville Integrals via γ-Preinvex Functions
title_full	Estimations of Upper Bounds for n-th Order Differentiable Functions Involving χ-Riemann–Liouville Integrals via γ-Preinvex Functions
title_fullStr	Estimations of Upper Bounds for n-th Order Differentiable Functions Involving χ-Riemann–Liouville Integrals via γ-Preinvex Functions
title_full_unstemmed	Estimations of Upper Bounds for n-th Order Differentiable Functions Involving χ-Riemann–Liouville Integrals via γ-Preinvex Functions
title_sort	estimations of upper bounds for n-th order differentiable functions involving χ-riemann–liouville integrals via γ-preinvex functions
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/13defcb21ac84ac6806a3728077aabac
work_keys_str_mv	AT sadiatalib estimationsofupperboundsfornthorderdifferentiablefunctionsinvolvingchriemannliouvilleintegralsviagpreinvexfunctions AT muhammaduzairawan estimationsofupperboundsfornthorderdifferentiablefunctionsinvolvingchriemannliouvilleintegralsviagpreinvexfunctions
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Estimations of Upper Bounds for n-th Order Differentiable Functions Involving χ-Riemann–Liouville Integrals via γ-Preinvex Functions

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