Relationships between singular expansions of real numbers

Singular functions, Cantor functions, functions with other special properties (26A30) Functional equations for real functions (39B22) Metric theory of other algorithms and expansions; measure and Hausdorff dimension (11K55) Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives (26A27) Systems of functional equations and inequalities (39B72) Irrationality; linear independence over a field (11J72) Representation functions (11B34)

Cites Work

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On the duality of aggregation operators and \(k\)-negations
The singularity spectrum of some non-regularity Moran fractals
Systems of functional equations and generalizations of certain functions
On the structures and dimensions of Moran sets
A Salem generalised function
On one fractal property of the Minkowski function
The singularity spectrum \(f(\alpha)\) of some Moran fractals
A multifractal formalism
An explicit formula of the exponential sums of digital sums
De Rham's singular function and related functions
On certain maps defined by infinite sums
On the mutual singularity of Hewitt-Stromberg measures
Rational numbers defined in terms of certain generalized series
Local dimensions and quantization dimensions in dynamical systems
A note on expansions of rational numbers by certain series
Generalizations of certain representations of real numbers
A review on multifractal analysis of Hewitt-Stromberg measures
Certain singular distributions and fractals
Some fractal properties of sets having the Moran structure
On the mutual singularity of multifractal measures
Multifractal analysis of Bernoulli measures on a class of homogeneous Cantor sets
A class of polynomials and connections with Bernoulli's numbers
Large and moderate deviation principles for alternating Engel expansions
A multifractal formalism for Hewitt-Stromberg measures
The generalized shifts and rational numbers
Some types of numeral systems and their modeling
Techniques in fractal geometry
Beta-Expansions with Negative Bases
Representations for real numbers and their ergodic properties
New bounds on the length of finite pierce and Engel series
One distribution function on the Moran sets
Lüroth-type alternating series representations for real numbers
THE MULTIFRACTAL DIMENSION FUNCTIONS OF HOMOGENEOUS MORAN MEASURE
Physical models of fractal functions
Most Monotone Functions are Singular
On one class of functions with complicated local structure
Continuous Functions with Complicated Local Structure Defined in Terms of Alternating Cantor Series Representation of Numbers
Another example of the mutual singularity of multifractal measures
The mutual singularity of multifractal measures for some non-regular Moran fractals
Non-Differentiable Functions Defined in Terms of Classical Representations of Real Numbers
On One Application of Infinite Systems of Functional Equations in Function Theory
Multifractal spectra of Moran measures without local dimension
Continuous Functions without Derivatives
On Some Singular Monotonic Functions Which Are Strictly Increasing
Certain Functions Defined in Terms of Cantor Series
The relative multifractal analysis, review and examples
On an algorithm and its use in approximating roots of algebraic equations.
The derivative of Minkowski's \(?(x)\) function
On the mutual singularity of Hewitt-Stromberg measures for which the multifractal functions do not necessarily coincide
Singular modifications of a classical function
A certain modification of classical singular function
On hyper complex numbers with higher order Pell numbers components
One example of singular representations of real numbers from the unit interval
General fractal dimensions of graphs of products and sums of continuous functions and their decompositions
Generation of fractals via iterated function system of Kannan contractions in controlled metric space
Cantor series expansions of rational numbers
Functional equations, alternating expansions, and generalizations of the Salem functions
Octonions and hyperbolic octonions with the \(k\)-balancing and \(k\)-Lucas balancing numbers
The generalized Salem functions defined in terms of certain Cantor expansions
A Pillai-Catalan-type problem involving Fibonacci numbers

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