Mandelbrot and Julia sets of complex polynomials involving sine and cosine functions via Picard-Mann orbit

DOI10.1007/S11785-022-01312-WOpenAlexW4313450572WikidataQ123123232 ScholiaQ123123232MaRDI QIDQ2677751

Faten Kharbat, Nuha Hamada

Publication date: 6 January 2023

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11785-022-01312-w

zbMATH Keywords

fixed pointsJulia setfractalsMandelbrot setcosinesinePicard-Mann iterationescape criterion

Mathematics Subject Classification ID

Fractals (28A80) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25)

Cites Work

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• Fixed point results in the generation of Julia and Mandelbrot sets
• Julia sets and Mandelbrot sets in Noor orbit
• On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval
• Effect of stochastic noise on superior Julia sets
• Octonionic Julia sets
• The Picard-Mann iteration with \(s\)-convexity in the generation of Mandelbrot and Julia sets
• Tricorns and multicorns of \(S\)-iteration scheme
• On the convergence of fixed point iterations for the moving geometry in a fluid-structure interaction problem
• A Picard-Mann hybrid iterative process

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