Abstracts

1. The corresponding version for complex-valued functions of a recent refinement of Grüss integral inequality due to Cerone & Dragomir is obtained.

2. In this paper, we give some refinements and generalizations of Jordan's inequality, we also improve some known results.

3. In this note the power-mean generalization of the Erdös - Debrunner inequality is reconsidered and bounds for the maximum order pmax of such an inequality are obtained.

4. In this paper, we extend a variant of Jensen's inequality for convex function.

5. Some inequalities of Cauchy-Bunyakovsky-Schwarz type for sequences of bounded linear operators in Hilbert spaces and some applications are given.

6. Using some techniques developed by S.S. Dragomir in connection to Ostrowski's integral inequality, we point out some approximation results for the Hankel Transform of functions of bounded variation.

7. Some new reverses for the generalised triangle inequality in inner product spaces and applications are given. Applications in connection to the Schwarz inequality are provided as well.

8. Some sharp quadratic reverses for the generalised triangle inequality in inner product spaces and applications are given.

9. Some reverses for the generalised triangle inequality in complex inner product spaces that improve the classical Diaz-Metcalf results and applications are given.

10. Some quadratic reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.

11. Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.

12. Some additive reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.

13. Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in complex Hilbert spaces are given. Applications for complex-valued functions are provided as well.

14. Some reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Banach spaces are given. Applications for complex-valued functions are considered as well.

15. A new reverse of the generalised triangle inequality that complements the classical results of Diaz and Metcalf is obtained. Applications for inner product spaces and for complex numbers are provided.

16. Some additive reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Banach spaces are given. Applications for complex-valued functions are considered as well.

17. Some additive reverses of the generalised triangle inequality in normed linear spaces are given. Applications for complex numbers are provided as well.

18. In this paper, by using some new and innovative techniques, some perturbed iterative algorithms for solving generalized set-valued variational inclusions are suggested and analyzed. Since the generalized set-valued variational inclusions include many variational inclusions, variational inequalities and set-valued operator equation studied by others in recent years, the results obtained in this paper continue to hold for them and represent a significant refinement and improvement of the previously known results in this area.

19. Some new refinements of the Schwarz inequality in inner product spaces are given. Applications for discrete and integral inequalities including the Heisenberg inequality for vector-valued functions in Hilbert spaces are provided.

20. Some reverses of the Cauchy-Bunyakovsky-Schwarz integral inequality for vector-valued functions in Hilbert spaces and applications for the Heisenberg inequality are provided.

21. Some new reverses of the Cauchy-Bunyakovsky-Schwarz integral inequality for vector-valued functions in Hilbert spaces that complement the recent results obtained in [1] are given. Applications for the Heisenberg inequality are provided.

22. Some new refinements of the Schwarz inequality in inner product spaces and applications for vector-valued sequences and integrals are given.

23. A generalisation of Kurepa's inequality in inner product spaces that extends in its turn the de Bruijn refinement of the Cauchy-Buniakovsky-Schwarz inequality for sequences of real and complex numbers is given.

24. Refinements of Buzano's and Kurepa's inequalities in inner product spaces and applications for discrete and integral inequalities improving the celebrated Cauchy-Buniakovsky-Schwarz result are given.

25. Some inequalities for families of orthornormal vectors in inner product spaces that are related with Buzano's, Richard's and Kurepa's results are given.

26. Some generalisations of Precupanu's inequality for orthornormal families of vectors in real or complex inner product spaces and applications related to Buzano's, Richard's and Kurepa's results are given.