Harmonic Mapping Problem and Affine Capacity

A unified theoretical harmonic analysis approach to the cyclic wavelet transform (CWT) for periodic signals of prime dimensions

The article introduces cyclic dilation groups and finite affine groups for prime integers, and  as an application of this theory it presents a unified group theoretical approach for the  cyclic wavelet transform (CWT) of prime dimensional periodic signals.

General Approach to Regions of Variability via Subordination of Harmonic Mappings

A planar harmonic mapping in a simply connected domain D ⊂ C is a complex-valued function f u iv defined in D for which both u and v are real harmonic in D, that is, Δf 4fzz 0, where Δ represents the Laplacian operator. The mapping f can be written as a sum of an analytic and antianalytic functions, that is, f h g. We refer to 1 and the book of Duren 2 for many interesting results on planar har...

Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings

Recommended by Narendra Kumar Govil We first obtain the relations of local univalency, convexity, and linear connectedness between analytic functions and their corresponding affine harmonic mappings. In addition, the paper deals with the regions of variability of values of affine harmonic and biharmonic mappings. The regions their boundaries are determined explicitly and the proofs rely on Schw...

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

A new perspective to the Mazur-Ulam problem in $2$-fuzzy $2$-normed linear spaces

In this paper, we introduce the concepts of $2$-isometry, collinearity, $2$%-Lipschitz mapping in $2$-fuzzy $2$-normed linear spaces. Also, we give anew generalization of the Mazur-Ulam theorem when $X$ is a $2$-fuzzy $2$%-normed linear space or $Im (X)$ is a fuzzy $2$-normed linear space, thatis, the Mazur-Ulam theorem holds, when the $2$-isometry mapped to a $2$%-fuzzy $2$-normed linear space...