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In this paper, a novel class of rational cubic fractal interpolation function (RCFIF) has been proposed, which is characterized by one shape parameter and a linear denominator. In interpolation for shape preservation, the proposed rational cubic fractal interpolation function provides a simple but effective approach. The nature of shape preservation of the proposed rational cubic fractal interpolation function makes them valuable in the field of data visualization, as it is crucial to maintain the original data shape in data visualization. Furthermore, we discussed the upper bound of error and explored the mathematical framework to ensure the convergence of RCFIF. Shape parameters and scaling factors are constraints to obtain the desired shape-preserving properties. We further generalized the proposed RCFIF by introducing the concept of signature, giving its construction in the form of a zipper-rational cubic fractal interpolation function (ZRCFIF). The positivity conditions for the rational cubic fractal interpolation function and zipper-rational cubic fractal interpolation function are found, which required a detailed analysis of the conditions where constraints on shape parameters and scaling factor lead to the desired shape-preserving properties. In the field of shape preservation, the proposed rational cubic fractal interpolation function and zipper fractal interpolation function both represent significant advancement by offering a strong tool for data visualization. [ABSTRACT FROM AUTHOR]

The intent of this paper is to study the fractal patterns of one dimensional complex logistic map by finding the optimum values of the control parameter using Ishikawa iterative scheme. The logistic map is shown to have bounded and stable behaviour for larger values of the control parameter. This is well depicted via time series analysis and interesting fractal patterns as well are presented

The goal of this work was to undertake a systematic evaluation of recently published e-commerce research and amalgamate any lessons learned for e-commerce system headway from a quality standpoint. Using Google Scholar, a systematic review of 8 shortlisted papers was done. The following were discovered as a result of the review: The tremendous rise of the e-commerce industry in 2020 cannot be overlooked. As situational requirements evolved and differed throughout countries, demand for diverse types of items increased. Customers' lack of trust and confidence in online transactions, as well as poor rules and regulations to safeguard them, have prevented several countries from properly implementing e-commerce. As a few data suggest, several theories such as Maslow's stratified needs and Ajzen's planned reasoned action and planned etiquette may relate to customer aspirations for online purchase. On the second side, numerous digital equipment have been employed to expedite product presentation, safety information, e-ordering, and payment mechanisms, and new ways are being tested. In this regard, international organisations such as the World Health Organization, the World Bank, the European Union, and international consulting firms such as McKinsey have issued reports and guidance. One clear credence is that the pandemic's new normal in all strands of work and life will persist even after the threat has passed. From the standpoint of e-commerce system development quality, this research suggests that the system should have the coterie characteristics: acquire client faith and confidence by aligning the system with best practices in online transactions; employ appropriate automated technology to expedite product exhibit, safety guidance, ordering online, and payment; and make sure there is enough product supply. [ABSTRACT FROM AUTHOR]