6 papers
Weaker quantization dimension results for self-similar measures
Saurabh Verma, Shivam Dubey
In this paper, we investigate the quantization dimension of self-similar measures, particularly when the IFS does not satisfy the separation condition, but the sub-IFS at some leve…
Some results on Lower Assouad and quantization dimensions
Saurabh Verma, Ekta Agrawal, Shivam Dubey
In this paper, we first show that the collection of all subsets of \( \mathbb{R} \) having lower dimension \( γ\in [0,1] \) is dense in \( Π(\mathbb{R}) \), the space of compact su…
Dimension Of Inhomogeneous Sub-Self-Similar Sets
Shivam Dubey, Saurabh Verma
In this paper, we introduce the concept of Inhomogeneous sub-self-similar (ISSS) sets, building upon the foundations laid by Falconer (Trans. Amer. Math. Soc. 347 (1995) 3121-3129)…
Quantization for a condensation system
Shivam Dubey, Mrinal Kanti Roychowdhury, Saurabh Verma
For a given , the quantization dimension of order , if it exists, denoted by , represents the rate at which the th quantization error of order …
Quantization dimension for a generalized inhomogeneous bi-Lipschitz iterated function system
Shivam Dubey, Mrinal Kanti Roychowdhury, Saurabh Verma
For a given , the quantization dimension of order , if it exists, denoted by , of a Borel probability measure on represents the sp…
Fractal dimension for Inhomogeneous graph-directed attractors
Shivam Dubey, Saurabh Verma
In this paper, we define inhomogeneous Graph-Directed (GD) separation conditions for a given inhomogeneous GD Iterated Function Systems (IFS), and estimate the upper box dimension…