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

• Published in: AIMS 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
• Language: English
• Published: AIMS Press 01.01.2021
• Subjects: h⋅h inequality; iv convex function; ψk−rl fractional integrals
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021273

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.