In Orlicz-Bochner sequence spaces endowed with Orlicz norm and Luxemburg norm, points of lower monotonicity, upper monotonicity, lower local uniform monotonicity and upper local uniform monotonicity are characterized.

The purpose of the present paper is to introduce a new subclass of $p$−valent meromorphic functions by using certain integral operator and to investigate various properties for this subclass.

This paper is devoted to problems stated by Z. Zhou and F. Li in 2009. They concern relations between almost periodic, weakly almost periodic, and quasi-weakly almost periodic points of a continuous map $f$ and its topological entropy. The negative answer follows by our recent paper. But for continuous maps of the interval and other more general one-dimensional spaces we give more results; in some cases the answer is positive.

The paper considers the Krylov-Lanczos and the Eckhoff approximations for recovering a bivariate function using limited number of its Fourier coefficients. These approximations are based on certain corrections associated with jumps in the partial derivatives of the approximated function. Approximation of the exact jumps is accomplished by solution of systems of linear equations along the idea of Eckhoff. Asymptotic behaviors of the approximate jumps and the Eckhoff approximation are studied. Exact constants of the asymptotic errors are computed. Numerical experiments validate theoretical investigations.

Making use of Wright operator we introduce a new class of complex-valued harmonic functions with respect to symmetric points which are orientation preserving, univalent and starlike. We obtain coefficient conditions, extreme points, distortion bounds, and convex combination.

In this paper, we give the exact lower density of Hausdorff measure of a class of symmetric perfect sets.

In this paper, the notion of $p$-wavelet packets on the positive half-line $\mathbb{R}^+$ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet subspaces directly instead of using the low-pass and high-pass filters associated with the multiresolution analysis as used in the classical theory of wavelet packets. Further, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation factor $p > 2$.