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1
2-point left Radau-type inequalities via s-convexity
Meftah Badreddine, Lakhdari Abdelghani, Saleh Wedad
Journal of Applied Analysis
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2023
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Vol. 29, nr 2
341--346
EN
Convexity is a fundamental concept in analysis. Over the past few decades, many significant error bounds have been established for various quadrature rules using different types of convexity. This paper focuses on the Gauss-Radau quadrature formula. Initially, we introduce a novel identity related to 2-point left Radautype rule. Next, we derive several integral inequalities for functions whose first derivatives are s-convex in the second sense. Finally, we present applications to special means to demonstrate the effectiveness of our results.
2
Content available remote On Ostrowski type inequalities
Agarwal R. P., Luo M.-J., Raina R. K.
Fasciculi Mathematici
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2016
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Nr 56
5--27
EN
In this paper, new forms of Ostrowski type inequalities are established for a general class of fractional integral operators. The main results are used to derive Ostrowski type inequalities involving the familiar Riemann-Liouville fractional integral operators and other important integral operators. We further obtain similar types of inequalities for the integral operators whose kernels are the Fox-Wright generalized hypergeometric function. Several consequences and special cases of some of the results including applications to Stolarsky's means are also pointed out.
3
Content available remote On Hermite-Hadamard type inequalities for s-convex mappings via fractional integrals of a function with respect to another function
Budak H., Sarikaya M. Z.
Fasciculi Mathematici
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2016
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Nr 57
25--36
EN
In this paper, we obtain some Hermite-Hadamard type inequalities for s-convex function via fractional integrals with respect to another function which generalize the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. The results presented here provide extensions of those given in earlier works.
4
Content available remote More on Ostrowski type inequalities for some s-convex functions in the second sense
Liu Z.
Demonstratio Mathematica
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2016
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Vol. 49, nr 4
398--412
EN
Some Ostrowski type inequalities for functions whose second derivatives in absolute value at certain powers are s-convex in the second sense are established. Two mistakes in a recently published paper are pointed out and corrected.
5
Content available remote Some Ostrowski’s type inequalities for functions whose second derivatives are s-convex in the second sense
Set E., Sarikaya M. Z., Ozdemir M. E.
Demonstratio Mathematica
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2014
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Vol. 47, nr 1
37--47
EN
Some new inequalities of the Ostrowski type for twice differentiable mappings whose derivatives in absolute value are s-convex in the second sense are given.
6
Content available remote On some new inequalities of Hermite-Hadamard-Fejer type involving convex functions
Tseng K., Hwang S., Dragomir S.
Demonstratio Mathematica
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2007
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Vol. 40, nr 1
51-64
EN
In this paper, we establish some inequalities of Hermite-Hadamard-Fejér type for m-convex functions and s-convex functions.
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