On modified convex interval valued functions and related inclusions via the interval valued generalized fractional integrals in extended interval space

In this paper, we propose a new family of interval valued ($\mathrm{IV}$) convex functions termed as generalized modified $(p,h)$-convex $\mathrm{IV}$ functions. We obtain the counterpart of Hermite-Hadamard $H\cdot H$ inequality by extending the $\mathrm{IV}$ fractional integral to the $\mathrm{IV}...

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Published inAIMS mathematics Vol. 6; no. 5; pp. 4638 - 4663
Main Authors Alqudah, Manar A., Kashuri, Artion, Mohammed, Pshtiwan Othman, Raees, Muhammad, Abdeljawad, Thabet, Anwar, Matloob, Hamed, Y. S.
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
h⋅h inequality
iv convex function
ψk−rl fractional integrals
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Abstract In this paper, we propose a new family of interval valued ($\mathrm{IV}$) convex functions termed as generalized modified $(p,h)$-convex $\mathrm{IV}$ functions. We obtain the counterpart of Hermite-Hadamard $H\cdot H$ inequality by extending the $\mathrm{IV}$ fractional integral to the $\mathrm{IV}$ $\psi_{k}$-Riemann-Liouville ($\psi_{k}-RL$) fractional integrals. Also, several inequalities using extended operations on the newly defined class of convex $\mathrm{IV}$ functions are given.
AbstractList In this paper, we propose a new family of interval valued ($\mathrm{IV}$) convex functions termed as generalized modified $(p,h)$-convex $\mathrm{IV}$ functions. We obtain the counterpart of Hermite-Hadamard $H\cdot H$ inequality by extending the $\mathrm{IV}$ fractional integral to the $\mathrm{IV}$ $\psi_{k}$-Riemann-Liouville ($\psi_{k}-RL$) fractional integrals. Also, several inequalities using extended operations on the newly defined class of convex $\mathrm{IV}$ functions are given.
Author Raees, Muhammad
Mohammed, Pshtiwan Othman
Abdeljawad, Thabet
Anwar, Matloob
Kashuri, Artion
Hamed, Y. S.
Alqudah, Manar A.
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CorporateAuthor Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, 9400, Vlora, Albania
School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq
Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O.Box 84428, Riyadh 11671, Saudi Arabia
Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan
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SubjectTerms h⋅h inequality
iv convex function
ψk−rl fractional integrals
Title On modified convex interval valued functions and related inclusions via the interval valued generalized fractional integrals in extended interval space
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