Some generalized Hermite–Hadamard–Fejér inequality for convex functions

Published on Dec 1, 2021in Advances in Difference Equations2.803
· DOI :10.1186/S13662-021-03351-7
Miguel Jose Vivas-Cortez1
Estimated H-index: 1
(Pontificia Universidad Católica del Ecuador),
Péter Kórus5
Estimated H-index: 5
(University of Szeged),
Juan E. Nápoles Valdés4
Estimated H-index: 4
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Abstract
In this paper, we have established some generalized inequalities of Hermite–Hadamard–Fejer type for generalized integrals. The results obtained are applied for fractional integrals of various type and therefore contain some previous results reported in the literature.
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#1Saima Rashid (GCUF: Government College University, Faisalabad)H-Index: 20
#2İmdat İşcan (Giresun University)H-Index: 20
Last. Yu-Ming Chu (CSUST: Changsha University of Science and Technology)H-Index: 28
view all 4 authors...
The celebrated Hermite–Hadamard and Ostrowski type inequalities have been studied extensively since they have been established. We find novel versions of the Hermite–Hadamard and Ostrowski type inequalities for the n-polynomial s-type convex functions in the frame of fractional calculus. Taking into account the new concept, we derive some generalizations that capture novel results under investigation. We present two different general techniques, for the functions whose first and second derivativ...
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#1Péter Kórus (University of Szeged)H-Index: 5
#2Luciano M. LugoH-Index: 1
Last. Juan E. Nápoles ValdésH-Index: 4
view all 3 authors...
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#1Miguel J. Vivas-Cortez (Facultad de Ciencias Exactas y Naturales)H-Index: 7
#2Thabet Abdeljawad (PRC: China Medical University (PRC))H-Index: 55
Last. Yenny Rangel-Oliveros (Facultad de Ciencias Exactas y Naturales)H-Index: 3
view all 4 authors...
Integral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In the present research article, we obtain new inequalities of Simpson’s integral type based on the - convex and - quasiconvex functions in the second derivative sense. In the last sections, some applications on special functions are provided and shown via two figures to demonstrate the explanation of the readers.
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#2Luciano M. LugoH-Index: 1
Last. Miguel J. Vivas-CortezH-Index: 7
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In this paper, we present a general definition of a generalized integral operator which contains as particular cases, many of the well-known, fractional and integer order integrals.
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#1Dumitru Baleanu (Çankaya University)H-Index: 106
#2Pshtiwan Othman Mohammed (University of Sulaymaniyah)H-Index: 16
Last. Shengda Zeng (Jagiellonian University)H-Index: 21
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Abstract During the last years several fractional integrals were investigated. Having this idea in mind, in the present article, some new generalized fractional integral inequalities of the trapezoidal type for λ φ –preinvex functions, which are differentiable and twice differentiable, are established. Then, by employing those results, we explore the new estimates on trapezoidal type inequalities for classical integral and Riemann–Liouville fractional integrals, respectively. Finally, we apply o...
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Last. Dumitru BaleanuH-Index: 106
view all 3 authors...
Integral inequality plays a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods (numerically or analytically) and to dedicate the convergence and stability of the methods. Unfortunately, mathematical methods are useless if the method is not convergent or stable. Thus, there is a present day need for accurate inequalities in proving the existence and uniqueness of the mathematical methods. Convexity play a c...
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#1Shilpi JainH-Index: 16
#2Khaled MehrezH-Index: 10
Last. Praveen AgarwalH-Index: 30
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In this paper, we discuss various estimates to the right-hand (resp. left-hand) side of the Hermite–Hadamard inequality for functions whose absolute values of the second (resp. first) derivatives to positive real powers are log-convex. As an application, we derive certain inequalities involving the q-digamma and q-polygamma functions, respectively. As a consequence, new inequalities for the q-analogue of the harmonic numbers in terms of the q-polygamma functions are derived. Moreover, several in...
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#1Yenny Carolina Rangel-Oliveros (Pontificia Universidad Católica del Ecuador)H-Index: 1
#2Miguel Jose Vivas-Cortez (Pontificia Universidad Católica del Ecuador)H-Index: 1
In this paper, we establish some new results related to the left-hand of the Hermite-Hadamard type inequalities for the class of functions whose second derivatives are s\varphiconvex functions.
#1Kamel Saoudi (UoD: University of Dammam)H-Index: 10
#2Praveen Agarwal (Hodges University)H-Index: 30
Last. Phatiphat Thounthong (King Mongkut's University of Technology North Bangkok)H-Index: 32
view all 5 authors...
We aim to investigate the following nonlinear boundary value problems of fractional differential equations: $\begin{aligned} (\mathrm{P}_{\lambda}) \left \{ \textstyle\begin{array}{l} -_{t}D_{1}^{\alpha} ( \vert {}_{0}D_{t}^{\alpha}(u(t)) \vert ^{p-2} {}_{0}D_{t}^{\alpha}u(t) ) \\ \quad=f(t,u(t))+\lambda g(t) \vert u(t) \vert ^{q-2}u(t)\quad (t\in(0,1)),\\ u(0)=u(1)=0, \end{array}\displaystyle \right . \end{aligned} where λ is a positive parameter, \(2< r< p< q\), \(\frac{1}{2}<\alpha < 1\), ...
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