Stieltjes integral inequalities of Gronwall type and applications

1990 ◽  
Vol 157 (1) ◽  
pp. 77-97 ◽  
Author(s):  
L. H. Erbe ◽  
QingKai Kong
Keyword(s):  
Integral Inequalities ◽  
Stieltjes Integral

scholarly journals Two Ostrowski type inequalities for the Stieltjes integral of monotonic functions

2007 ◽  
Vol 75 (2) ◽  
pp. 299-311 ◽  
Author(s):  
W.-S. Cheung ◽  
S. S. Dragomir
Keyword(s):  
Numerical Analysis ◽  
Trapezoidal Rule ◽  
Integral Inequalities ◽  
Stieltjes Integral ◽  
Hölder Continuous ◽  
Monotonic Functions ◽  
Dual Case

Two integral inequalities of Ostrowski type for the Stieltjes integral are given. The first is for monotonic integrators and Hölder continuous integrands while the second considers the dual case, that is, for monotonic integrands and Hölder continuous integrators. Applications for the mid-point inequality that are useful in the numerical analysis of Stieltjes integrals are exhibited. Some connections with the generalised trapezoidal rule are also presented.

Some new generalizations for GA-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
Ahmet Akdemir ◽  
Özdemir Emin ◽  
Ardıç Avcı ◽  
Abdullatif Yalçın
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
General Integral ◽  
Second Derivatives ◽  
Derivatives Of

In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity: Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.

scholarly journals Singular Lebesgue-Stieltjes integral equations

1941 ◽  
Vol 74 (0) ◽  
pp. 197-310 ◽  
Author(s):  
W. J. Trjitzinsky
Keyword(s):  
Integral Equations ◽  
Stieltjes Integral

scholarly journals A new generalization of some quantum integral inequalities for quantum differentiable convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yi-Xia Li ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Mujahid Abbas ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Quantum Integral ◽  
Special Cases

AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

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