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Open AccessCauchy type means for some generalized convex functions
In this paper, we establish Jensen’s inequality for s-convex functions in the first sense. By using Jensen’s inequalities, we obtain some Cauchy type means for p-convex and s-convex functions in the first sense. ...
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Article
Open AccessHermite–Hadamard integral inequalities on coordinated convex functions in quantum calculus
At first, we recall the q-operators in the context of q-calculus and by examining these operators we will introduce new definitions of the partial q-operators. Then, we investigate some new refinements inequaliti...
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Open AccessHermite–Hadamard and Hermite–Hadamard–Fejer type inequalities for p-convex functions via conformable fractional integrals
In this paper, we obtain the Hermite–Hadamard and Hermite–Hadamard–Fejer type inequalities for p-convex functions via conformable fractional integrals. We also discuss some special cases.
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Open AccessOn some Hermite–Hadamard type inequalities for \(tgs\)-convex functions via generalized fractional integrals
In this research article, we establish some Hermite–Hadamard type inequalities for tgs\(tgs\)-convex functions via Katugampola fractional integrals and ψ-Riemann–Liouville fractional integrals. Through these result...
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Open AccessOn applications of Caputo k-fractional derivatives
This research explores Caputo k-fractional integral inequalities for functions whose nth order derivatives are absolutely continuous and possess Grüss type variable bounds. Using Chebyshev inequality (Waheed et a...
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Article
Open AccessHermite–Hadamard type inequalities for exponentially p-convex functions and exponentially s-convex functions in the second sense with applications
In this paper, we introduce the notion of exponentially p-convex function and exponentially s-convex function in the second sense. We establish several Hermite–Hadamard type inequalities for exponentially p-conve...
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Open AccessIntegral inequalities for some convex functions via generalized fractional integrals
In this paper, we obtain the Hermite–Hadamard type inequalities for s-convex functions and m-convex functions via a generalized fractional integral, known as Katugampola fractional integral, which is the generali...
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Article
Open AccessJessen’s type inequality and exponential convexity for positive \(C_{0}\) -semigroups
In this paper a Jessen’s type inequality for normalized positive
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Open AccessCauchy Means of the Popoviciu Type
We discuss log-convexity for the differences of the Popoviciu inequalities and introduce some mean value theorems and related results. Also we give the Cauchy means of the Popoviciu type and we show that these...
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Article
Open AccessNew Means of Cauchy's Type
We will introduce new means of Cauchy's type defined, for example, as ...
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Article
Open AccessOn Logarithmic Convexity for Ky-Fan Inequality
We give an improvement and a reversion of the well-known Ky-Fan inequality as well as some related results.
