We propose a Generalized Dantzig Selector (GDS) for linear models, in which any norm encoding the parameter structure can be leveraged for estimation. We investigate both computational and statistical aspects of the GDS. Based on conjugate proximal operator, a flexible inexact ADMM framework is designed for solving GDS. Thereafter, non-asymptotic high-probability bounds are established on the e...

Let ? be an open connected subset of the complex plane C and let T be a bounded linear operator on a Hilbert space H. For ? in ? let e the orthogonal projection onto the null-space of T-?I . We discuss the necessary and sufficient conditions for the map ?? to b e continuous on ?. A generalized Gram- Schmidt process is also given.

in this paper‎, ‎first we propose a new method to approximate the solution of two-dimensional linear fuzzy fredholm integral equations of the second kind based on the fuzzy wavelet like operator‎. ‎then‎, ‎we discuss and investigate the convergence and error analysis of the proposed method‎. ‎finally‎, ‎to show the accuracy of the proposed method‎, ‎we present two numerical ‎examples.‎

we investigate a class of fourth-order differential operators with eigenparameter dependent boundary conditions and transmission conditions. a self-adjoint linear operator a is defined in a suitable hilbert space h such that the eigenvalues of such a problem coincide with those of a . we discuss asymptotic behavior of its eigenvalues and completeness of its eigenfunctions. finally, we obtain th...

The main purpose of this article is to give a relationship between Fredholm multivalued linear operators and the demicompact relation; we provide some sufficient conditions on inputs closable block operator matrix ensure generalized demicompactness its closure. Our results generalize many known ones in literature.

in this paper we obtain coefficient characterization‎, ‎extreme points and‎ ‎distortion bounds for the classes of harmonic $p-$valent functions‎ ‎defined by certain modified operator‎. ‎some of our results improve‎ ‎and generalize previously known results‎.

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...

In this paper, we defined two classes $S_{p}^{ast }(n,lambda ,A,B)$ and\ $ K_{p}(n,lambda ,A,B)$ of meromorphic $p-$valent functions associated with a new linear operator. We obtained convolution properties for functions in these classes.

The papers [21], [8], [23], [25], [24], [5], [7], [6], [19], [4], [1], [2], [18], [10], [22], [13], [3], [20], [16], [15], [9], [12], [11], [14], and [17] provide the terminology and notation for this paper. Let X be a non empty set and let f , g be elements of X . Then g · f is an element of X . One can prove the following propositions: (1) Let X, Y , Z be real linear spaces, f be a linear ope...