Abstracts

  1. In the present paper we establish some new integral inequalities analogous to the well known Hadamard’s inequality by using a fairly elementary analysis.

  2. For any nonnegative integer $ k$ and natural numbers $ n$ and $ m$, we have the following inequalities on the ratio for the geometric means of a positive arithmetic sequence with unit difference:

    $\displaystyle \frac{n+k+1+\alpha}{n+m+k+1+\alpha} <\frac{\left[\prod_{i=k+1}^{n... ...m+k}(i+\alpha)\right]^{1/(n+m)}} \leq \sqrt{\frac{n+k+\alpha}{n+m+k+\alpha}}\,,$    
    where $ \alpha\in[0,1]$ is a constant. The equality above is valid for $ n=1$ and $ m=1$. Moreover, some monotonicity results for the sequences involving $ \sqrt[n]{\prod_{i=k+1}^{n+k}(i+\alpha)}$ are obtained, and the related inequalities are generalized.

     

  3. An extension of the Cauchy-Buniakowski-Schwartz inequality due to Wagner for sequences of vectors in inner product spaces is given.

  4. Some majorisation type discrete inequalities for convex functions are established. Two applications are also provided.

  5. In this paper we point out an Ostrowski type inequality for convex functions which complement in a sense the recent results for functions of bounded variation and absolutely continuous functions. Applications in connection with the Hermite-Hadamard inequality are also considered.

  6. A version of Ostrowski's inequality in complex inner product spaces is given. Applications for complex sequences and integrals are also provided.

  7. Some new Grüss type inequalities in inner product spaces and applications for integrals are given.

  8. Some companions of Grüss inequality in inner product spaces and applications for integrals are given.

  9. Some Ostrowski type inequalities via Cauchy's mean value theorem and applications for certain particular instances of functions are given.

  10. A counterpart of the famous Bessel's inequality for orthornormal families in real or complex inner product spaces is given. Applications for some Grüss type inequalities are also provided.

  11. An inequality providing some bounds for the integral mean via Pompeiu's mean value theorem and applications for quadrature rules and special means are given.

  12. A new counterpart of Bessel's inequality for orthornormal families in real or complex inner product spaces is obtained. Applications for some Grüss type results are also provided.

  13. Some new counterparts of Bessel's inequality for orthornormal families in real or complex inner product spaces are pointed out. Applications for some Grüss type inequalities are also emphasized.

  14. New results related to the Boas-Bellman generalisation of Bessel's inequality in inner product spaces are given.

 

  1. Companion results to the Bombieri generalisation of Bessel's inequality in inner product spaces are given.

  2. Some related results to Pecaric's inequality in inner product spaces that generalises Bombieri's inequality, are given.

  3. A new counterpart of Schwarz's inequality in inner product spaces and applications for isotonic functionals, integrals and sequences are provided.

  4. Reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces that improve some earlier results are pointed out. They are applied to obtain new Grüss type inequalities in inner product spaces. Some natural applications for integral inequalities are also pointed out.

  5. New reverses of the Schwarz, triangle and Bessel inequalities in inner product spaces are pointed out. These results complement the recent ones obtained by the author in the earlier paper [13]. Further, they are employed to establish new Grüss type inequalities. Finally, some natural integral inequalities are stated as well.

  6. A new counterpart of Bessel's inequality for orthornormal families in real or complex 2-inner product spaces is obtained. Applications for some Grüss type results with applications for determinantal integral inequalities are also provided.

  7. A reverse of Bessel's inequality in 2-inner product spaces and companions of Grüss inequality with applications for determinantal integral inequalities are given.

  8. Some companions of Grüss inequality in 2-inner product spaces and applications for determinantal integral inequalities are given.

  9. Some new reverses of Bessel's inequality for orthonormal families in real or complex inner product spaces are pointed out. Applications for some Grüss type inequalities and for determinantal integral inequalities are given as well.

  10. Some results related to the Pecaric's type generalisation of Bessel's inequality in 2-inner product spaces are given. Applications for determinantal integral inequalities are also provided.

  11. Two methods in approximating the fiber refractive index profile that have been recently obtained are reviewed. Two new methods based on the approximation of Stieltjes integral via mid-point and trapezoidal rule are also examined.

  12. Some new Grüss type inequalities in 2-inner product spaces are given. Using this framework, some determinantal integral inequalities for synchronous functions are also derived.

  13. Refinements of some recent reverse inequalities for the celebrated Cauchy -Bunyakovsky -Schwarz inequality in $2-$inner product spaces are given. Using this framework, applications for determinantal integral inequalities are also provided.

  14. Some inequalities in 2-inner product spaces generalizing Bessel's result that are similar to the Boas-Bellman inequality from inner product spaces, are given. Applications for determinantal integral inequalities are also provided.

  15. In this paper, some new Gronwall type inequalities involving iterated integrals are given.

  16. The main objective of the present paper is to establish some new Gronwall type inequalities involving iterated integrals.

  17. Norm estimates are developed between the Bochner integral of a vector-valued function in Banach spaces having the Radon-Nikodym property and the convex combination of function values taken on a division of the interval [a,b] .

  18. In this paper, some reverses of the Cauchy-Bunyakovsky-Schwarz inequality in 2-inner product spaces are given. Using this framework, some applications for determinantal integral inequalities are also provided.

  19. Some results related to the Bombieri type generalisation of Bessel's inequality in 2-inner product spaces are given. The corresponding versions for Selberg and Heilbronn inequalities for 2-inner products and applications for determinantal integral inequalities are also pointed out.