A FAMILY of inequalities concerning inner products of vectors and functions began with Cauchy. The extensions and generalizations later led to the inequalities of Schwarz, Minkowski and Holder. The well known Holder inequality involves the inner product of vectors measured by Minkowski norms. In this paper, another step of extension is taken so that a Holder type inequality may apply to general...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

In this paper, we propose a new iteration method based on the hybrid steepest descent method and Ishikawa-type method for seeking a solution of a variational inequality involving a Lipschitz continuous and strongly monotone mapping on the set of common fixed points for a finite family of Lipschitz continuous and quasi-pseudocontractive mappings in a real Hilbert space. MSC: Primary 41A65; 47H17...

In this paper, we present a Tseng-type self-adaptive algorithm for solving variational inequality and fixed point problem involving pseudomonotone pseudocontractive operators in Hilbert spaces. A weak convergent result such is proved under weaker assumption than sequentially weakly continuous imposed on the operator. Some corollaries are also included.

The classical Lojasiewicz inequality and its extensions for partial differential equation problems (Simon) and to o-minimal structures (Kurdyka) have a considerable impact on the analysis of gradient-like methods and related problems: minimization methods, complexity theory, asymptotic analysis of dissipative partial differential equations, tame geometry. This paper provides alternative charact...

It is well-known that Kolmogorov’s inequality is the particular case bk = 1, for all k and n = 1 in (1.1). Afterwards this inequality was extended to real valued martingales (see [4]). Since then, this inequality has been studied by many authors. For the case of R-valued random variables, Sung [22] obtained the Hájek-Rényi inequality for the associated sequence. Liu et al. [19] considered the n...

We study the efficiency of greedy algorithms with regard to redundant dictionaries in Hilbert spaces. We obtain upper estimates for the errors of the Pure GreedyAlgorithm and the Orthogonal GreedyAlgorithm in terms of the best m-term approximations. We call such estimates the Lebesgue-type inequalities. We prove the Lebesgue-type inequalities for dictionaries with special structure. We assume t...