AIMS Mathematics, 2019, 4(5): 1403-1415. doi: 10.3934/math.2019.5.1403.

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Some inequalities via Ψ-Riemann-Liouville fractional integrals

School of Natural Sciences, National University of Sciences and Technology, H-12 Islamabad, Pakistan

In this paper, we establish some Hermite-Hadamard type inequalities via $\psi$-Riemann-Liouville fractional integrals for $s$-convex functions in second sense and the functions belongs to the class $P(I)$ $($that is, a class of non-negative functions $\curlyvee:I\rightarrow\mathbb{R}$ which satisfies the condition $\curlyvee(ra_1+(1-r)a_2)\leq \curlyvee(a_1)+\curlyvee(a_2)$, for all $a_1,a_2\in I$ and $r\in[0,1])$. Some applications to special means are also investigated.
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Keywords Hermite-Hadamard inequalities; s-convex functions in second sense; non-negative functions P(I)

Citation: Naila Mehreen, Matloob Anwar. Some inequalities via Ψ-Riemann-Liouville fractional integrals. AIMS Mathematics, 2019, 4(5): 1403-1415. doi: 10.3934/math.2019.5.1403


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This article has been cited by

  • 1. Naila Mehreen, Matloob Anwar, On some Hermite–Hadamard type inequalities for tgs$tgs$-convex functions via generalized fractional integrals, Advances in Difference Equations, 2020, 2020, 1, 10.1186/s13662-019-2457-x
  • 2. Naila Mehreen, Matloob Anwar, Hermite–Hadamard and Hermite–Hadamard–Fejer type inequalities for p-convex functions via conformable fractional integrals, Journal of Inequalities and Applications, 2020, 2020, 1, 10.1186/s13660-020-02363-3
  • 3. Yong Zhao, Haiwei Sang, Weicheng Xiong, Zhongwei Cui, Hermite–Hadamard-type inequalities involving ψ-Riemann–Liouville fractional integrals via s-convex functions, Journal of Inequalities and Applications, 2020, 2020, 1, 10.1186/s13660-020-02389-7

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