Browsing by Author "Ajay Prajapati"

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Fractal surfaces in Lebesgue spaces with respect to fractal measures and associated fractal operators
(Elsevier Ltd, 2024) Rattan Lal; Subhash Chandra; Ajay Prajapati
The goal of this article is to study the fractal surfaces and associated fractal operator on Lebesgue spaces with respect to fractal measures. First, we show that fractal surfaces belongs to Lebesgue spaces under certain conditions. Then, we define a fractal operator on Lebesgue spaces and discuss some analytical properties of it. Moreover, we show the existence of Schauder basis of the associated fractal functions for the space Lq(I×J,μp). In the end, we draw some graph of fractal surfaces for the various scaling factors and mention some future directions. © 2024 Elsevier Ltd
Further analysis of multivariable fractal functions
(Springer Science and Business Media Deutschland GmbH, 2025) Amit Bawalia; Vineeta Basotia; Ajay Prajapati
The aim of this paper is to characterize a fractal operator associated with multivariable fractal interpolation functions and study the several properties of this fractal operator. Further, with the help of this operator, we characterize a latest category of functions and study their approximation aspects. The basic characteristics of this multivariable fractal operator’s are given in several ways in this note. The extension of this fractal operator to the Lp-spaces for p≥1 are also examined. Multivariable continuous fractal functions approximation characteristics are also examined. © The Author(s) 2025.
Non-stationary ϕ -contractions and associated fractals
(Springer Science and Business Media B.V., 2022) Amit; Vineeta Basotia; Ajay Prajapati
In this study we provide several significant generalisations of Banach contraction principle where the Lipschitz constant is substituted by real-valued control function that is a comparison function. We study non-stationary variants of fixed-point. In particular, this article looks into “trajectories of maps defined by function systems” which are regarded as generalizations of traditional iterated function system (IFS). The importance of forward and backward trajectories of general sequences of mappings is analyzed. The convergence characteristics of these trajectories determined a non-stationary variant of the traditional fixed-point theory. Unlike the normal fractals which have self-similarity at various scales, the attractors of these trajectories of maps which defined by function systems that may have various structures at various scales. In this literature we also study the sequence of countable IFS having some generalized contractions on a complete metric space. © 2022, The Author(s), under exclusive licence to The Forum D’Analystes.