On the Bombieri Inequality in Inner Product Spaces

Some Companions of Gruss Inequality in Inner Product Spaces

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

Reverses of the Triangle Inequality in Inner Product Spaces

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.

On the Boas-Bellman Inequality in Inner Product Spaces

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

A Counterpart of Schwarz's Inequality in Inner Product Spaces

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

A Generalisation of an Ostrowski Inequality in Inner Product Spaces

A generalisation of inner product spaces of an inequality due to Ostrowski and applications for sequences and integrals are given.

A Counterpart of Bessel's Inequality in Inner Product Spaces and Some Gruss Type Related Results

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

Genearlizations of Precupanu's Inequality for Orthornormal Families of Vectors in Inner Product Spaces

Some genearlizations 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

Reverses of the Schwarz Inequality in Inner Product Spaces Generalising a Klamkin-McLenaghan Result

New reverses of the Schwarz inequality in inner product spaces that incorporate the classical Klamkin-McLenaghan result for the case of positive n-tuples are given. Applications for Lebesgue integrals are also provided.

Some Reverses of the Cauchy-Bunyakovsky-Schwarz Inequality in 2-Inner Product Spaces

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.

Refinements of Some Reverses of Schwarz's Inequality in 2-Inner Product Spaces and Applications for Integrals

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.

On Bessel and Gruss Inequalities for Orthornormal Families in Inner Product Spaces

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

Some New Results Related to Bessel and Gruss Inequalities for Orthogonal Families in Inner Product Spaces

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

Bounding the Chebychev Functional for a Pair of Sequences in Inner Product Spaces

Some new bounds for the Chebychev functional of a pair of vectors in inner product spaces are pointed out. Reverses for the celebrated Jensen's inequality for convex functions defined on inner product spaces are given as well.

Some Boas-Bellman Type Inequalities in 2-Inner Product Spaces

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.

两种Hornich-Hlawka型及Gram矩阵-based不等式

Two Hornich-Hlawka-type and Gram matrix-based inequalities

本文在实内积空间中建立两种不等式，第一种是对经典Hornich-Hlawka不等式的乘法加强，探讨了等号成立条件；第二种基于Gram矩阵的半正定性，推导出参数不等式，并通过优化参数得到与Gram行列式不等式相关的紧致不等式。

内积空间中 Gruss 型离散不等式再探

Gruss Type Discrete Inequalities in Inner Product Spaces, Revisited

本文重新探讨内积空间中的 Gruss 型离散不等式，得到尖锐结果并应用于凸函数的 Jensen 不等式。

Landau and Gruss type inequalities for inner product type integral transformers in norm ideals

For a probability measure $μ$ and for square integrable fields $(\mathscr{A}_t)$ and $(\mathscr{B}_t)$ ($t\inΩ$) of commuting normal operators we prove Landau type inequality \llu\int_Ω\mathscr{A}_tX\mathscr{B}_tdμ(t)- \int_Ω\mathscr{A}_t\,dμ(t)X \int_Ω\mathscr{B}_t\,dμ(t) \rru \le \llu \sqrt{\,\int_Ω|\mathscr{A}_t|^2\dt-|\int_Ω\mathscr{A}_t\dt|^2}X \sqrt{\,\int_Ω|\mathscr{B}_t|^2 \dt-|\int_Ω\mathscr{B}_t\dt|^2} \rru for all $X\in\mathcalb{B}(\mathcal{H})$ and for all unitarily invariant norms $\lluo\cdot\rruo$. For Schatten $p$-norms similar inequalities are given for arbitrary double square …

Hörmander不等式与de Branges空间中的点评估

Hörmander's Inequality and Point Evaluations in de Branges Space

本文扩展了Hörmander不等式到de Branges空间，研究点评估功能及极值函数，推广了相关研究结果。