A. K. B. Chand
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View article: Fractal cubic multiquadric quasi-interpolation
Fractal cubic multiquadric quasi-interpolation Open
View article: Solutions of differential equations using fractal multiquadric RBF networks
Solutions of differential equations using fractal multiquadric RBF networks Open
In this article, we introduce a novel class of self-referential fractal multiquadric (MQ) functions that exhibit symmetry about the origin. To ensure the differentiability of the original classical multiquadric function, we carefully limit…
View article: Fixed-Point and Random Fixed-Point Theorems in Preordered Sets Equipped with a Distance Metric
Fixed-Point and Random Fixed-Point Theorems in Preordered Sets Equipped with a Distance Metric Open
This paper explores fixed points for both contractive and non-contractive mappings in traditional b-metric spaces, preordered b-metric spaces, and random b-metric spaces. Our findings provide insights into the behavior of mappings under va…
View article: Approximation with fractal radial basis functions
Approximation with fractal radial basis functions Open
The article reports on the construction of a general class of fractal radial basis functions (RBFs) in the literature. The fractal RBFs is defined through fractal perturbation of a RBF through suitable choice of iterated function system (I…
View article: Shape preserving fractal multiquadric quasi-interpolation
Shape preserving fractal multiquadric quasi-interpolation Open
In this article, we construct a novel self-referential fractal multiquadric function which is symmetric about the origin. The scaling factors are suitably restricted to preserve the differentiability and the convexity of the underlying cla…
View article: An Exploratory Study on Self-Reported Auditory Symptoms and Hearing Loss among Workers in a Small-Scale LPG Plant
An Exploratory Study on Self-Reported Auditory Symptoms and Hearing Loss among Workers in a Small-Scale LPG Plant Open
Background: Occupational noise is considered a factor contributing to acquired hearing loss (HL) in adults. Frequent noise exposure can cause cochlear damage, leading to sensorineural HL, tinnitus, vertigo, and other non auditory effects a…
View article: Convexity-Preserving Rational Cubic Zipper Fractal Interpolation Curves and Surfaces
Convexity-Preserving Rational Cubic Zipper Fractal Interpolation Curves and Surfaces Open
A class of zipper fractal functions is more versatile than corresponding classes of traditional and fractal interpolants due to a binary vector called a signature. A zipper fractal function constructed through a zipper iterated function sy…
View article: Iterative Schemes Involving Several Mutual Contractions
Iterative Schemes Involving Several Mutual Contractions Open
In this paper, we introduce the new concept of mutual Reich contraction that involves a pair of operators acting on a distance space. We chose the framework of strong b-metric spaces (generalizing the standard metric spaces) in order to ad…
View article: Multivariate Zipper Fractal Functions
Multivariate Zipper Fractal Functions Open
View article: Approximation by Quantum Meyer-König-Zeller Fractal Functions
Approximation by Quantum Meyer-König-Zeller Fractal Functions Open
In this paper, a novel class of quantum fractal functions is introduced based on the Meyer-König-Zeller operator Mq,n. These quantum Meyer-König-Zeller (MKZ) fractal functions employ Mq,nf as the base function in the iterated function syst…
View article: Multivariate Zipper Fractal Functions
Multivariate Zipper Fractal Functions Open
A novel approach to zipper fractal interpolation theory for functions of several variables is proposed. We develop multivariate zipper fractal functions in a constructive manner. We then perturb a multivariate function to construct its zip…
View article: Approximation by Quantum Meyer König and Zeller-Fractal Functions
Approximation by Quantum Meyer König and Zeller-Fractal Functions Open
In this paper, a novel class of quantum fractal functions is introduced based on the Meyer-König-Zeller operator $M_{q,n}$. These quantum Meyer-König-Zeller (MKZ) fractal functions employ $M_{q,n} f$ as the base function in the iterated fu…
View article: Zipper Fractal Functions with Variable Scalings
Zipper Fractal Functions with Variable Scalings Open
Zipper fractal interpolation function (ZFIF) is a generalization of fractal interpolation function through an improved version of iterated function system by using a binary parameter called a signature. The signature allows the horizontal …
View article: Binary Operations in Metric Spaces Satisfying Side Inequalities
Binary Operations in Metric Spaces Satisfying Side Inequalities Open
The theory of metric spaces is a convenient and very powerful way of examining the behavior of numerous mathematical models. In a previous paper, a new operation between functions on a compact real interval called fractal convolution has b…
View article: Iterated Functions Systems Composed of Generalized θ-Contractions
Iterated Functions Systems Composed of Generalized θ-Contractions Open
The theory of iterated function systems (IFSs) has been an active area of research on fractals and various types of self-similarity in nature. The basic theoretical work on IFSs has been proposed by Hutchinson. In this paper, we introduce …
View article: Cyclic Meir-Keeler Contraction and Its Fractals
Cyclic Meir-Keeler Contraction and Its Fractals Open
In present times, there has been a substantial endeavor to generalize the classical notion of iterated function system (IFS). We introduce a new type of non-linear contraction namely cyclic Meir-Keeler contraction, which is a generalizatio…
View article: Generalized Bivariate Hermite Fractal Interpolation Function
Generalized Bivariate Hermite Fractal Interpolation Function Open
Fractal interpolation provides an efficient way to describe a smooth or non-smooth structure associated with nature and scientific data. The aim of this paper is to introduce a bivariate Hermite fractal interpolation formula that generaliz…
View article: Cubic spline fractal solutions of two-point boundary value problems with a non-homogeneous nowhere differentiable term
Cubic spline fractal solutions of two-point boundary value problems with a non-homogeneous nowhere differentiable term Open
View article: MULTIVARIATE AFFINE FRACTAL INTERPOLATION
MULTIVARIATE AFFINE FRACTAL INTERPOLATION Open
Fractal interpolation functions capture the irregularity of some data very effectively in comparison with the classical interpolants. They yield a new technique for fitting experimental data sampled from real world signals, which are usual…
View article: A New Class of Monotone/Convex Rational Fractal Function
A New Class of Monotone/Convex Rational Fractal Function Open
This paper presents a description and analysis of a rational cubic spline FIF (RCSFIF) that has two shape parameters in each subinterval when it is defined implicitly. To be precise, we consider the iterated function system (IFS) with $q_n…
View article: Parameter Identification of Constrained Data by a New Class of Rational Fractal Function
Parameter Identification of Constrained Data by a New Class of Rational Fractal Function Open
This paper sets a theoretical foundation for the applications of the fractal interpolation functions (FIFs). We construct rational cubic spline FIFs (RCSFIFs) with quadratic denominator involving two shape parameters. The elements of the i…
View article: Generalized trigonometric interpolation
Generalized trigonometric interpolation Open
View article: Constrained shape preserving rational cubic fractal interpolation functions
Constrained shape preserving rational cubic fractal interpolation functions Open
In this paper, we discuss the construction of $\\mathcal {C}^1$-rational cubic fractal interpolation function (RCFIF) and its application in preserving the constrained nature of a given data set. The $\\mathcal {C}^1$-RCFIF is the fractal …
View article: On Weak Separation Property for Affine Fractal Functions
On Weak Separation Property for Affine Fractal Functions Open
We show that a fractal affine function $f(x)$ defined by a system $\mathcal S$ which does not satisfy weak separation property is a quadratic function.
View article: TOWARDS A MORE GENERAL TYPE OF UNIVARIATE CONSTRAINED INTERPOLATION WITH FRACTAL SPLINES
TOWARDS A MORE GENERAL TYPE OF UNIVARIATE CONSTRAINED INTERPOLATION WITH FRACTAL SPLINES Open
Recently, in [Electron. Trans. Numer. Anal. 41 (2014) 420–442] authors introduced a new class of rational cubic fractal interpolation functions with linear denominators via fractal perturbation of traditional nonrecursive rational cubic sp…
View article: FRACTAL BASES FOR BANACH SPACES OF SMOOTH FUNCTIONS
FRACTAL BASES FOR BANACH SPACES OF SMOOTH FUNCTIONS Open
This article explores the properties of fractal interpolation functions with variable scaling parameters, in the context of smooth fractal functions. The first part extends the Barnsley–Harrington theorem for differentiability of fractal f…
View article: Shape Preserving Rational Cubic Spline Fractal Interpolation
Shape Preserving Rational Cubic Spline Fractal Interpolation Open
Fractal interpolation functions (FIFs) developed through iterated function systems (IFSs) prove more versatile than classical interpolants. However, the applications of FIFs in the domain of `shape preserving interpolation' are not fully a…