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

Manar A. Alqudah; Artion Kashuri; Pshtiwan Othman Mohammed; Muhammad Raees; Thabet Abdeljawad; Matloob Anwar; Y. S. Hamed; Manar A. Alqudah; Artion Kashuri; Pshtiwan Othman Mohammed; Muhammad Raees; Thabet Abdeljawad; Matloob Anwar; Y. S. Hamed

doi:10.3934/math.2021273

AIMS Mathematics

2021, Volume 6, Issue 5: 4638-4663. doi: 10.3934/math.2021273

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Research article

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

1.
Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O.Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, 9400, Vlora, Albania
3.
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq
4.
School of Natural Sciences, National University of Sciences and Technology, Islamabad, Pakistan
5.
Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, Riyadh 11586, Saudi Arabia
6.
Department of Medical Research, China Medical University, Taichung 40402, Taiwan
7.
Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan
8.
Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia

Received: 05 January 2021 Accepted: 18 February 2021 Published: 24 February 2021
MSC : 26A51, 26A33, 26D07, 26D10, 26D15

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.
- $ H\cdot H $ inequality,
- $ \psi_{k}-RL $ fractional integrals,
- $ \mathrm{IV} $ convex function
Citation: Manar A. Alqudah, Artion Kashuri, Pshtiwan Othman Mohammed, Muhammad Raees, Thabet Abdeljawad, Matloob Anwar, Y. S. Hamed. On modified convex interval valued functions and related inclusions via the interval valued generalized fractional integrals in extended interval space[J]. AIMS Mathematics, 2021, 6(5): 4638-4663. doi: 10.3934/math.2021273

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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.

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