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Coupled Fixed Points for Hardy-Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions

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  • S. Kabaivanov
  • V. Zhelinski
  • B. Zlatanov

Abstract

In this paper we generalize Hardy-Rogers maps in the context of coupled fixed points. We generalizes with the help of the obtained main theorem some known results about existence and uniqueness of market equilibrium in duopoly markets. We investigate some recent results about market equilibrium in duopoly markets with the help of the main theorem and we enrich them. We define a generalized response function including production and surpluses. Finally we illustrate a possible application of the main result in the investigation of market equilibrium, when the pay off functions are non differentiable.

Suggested Citation

  • S. Kabaivanov & V. Zhelinski & B. Zlatanov, 2021. "Coupled Fixed Points for Hardy-Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions," Papers 2110.01496, arXiv.org.
    • Handle: RePEc:arx:papers:2110.01496
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    References listed on IDEAS

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    1. Udhayanan, Prateksha & Mishra, Swasti S. & Rao, Shrisha, 2021. "Firm dynamics and employee performance management in duopoly markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    2. Fazli, Hossein & Nieto, Juan J., 2018. "Fractional Langevin equation with anti-periodic boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 332-337.
    3. Akio Matsumoto & Ferenc Szidarovszky, 2018. "Dynamic Oligopolies with Time Delays," Springer Books, Springer, number 978-981-13-1786-6, June.
    4. Yulia Dzhabarova & Stanimir Kabaivanov & Margarita Ruseva & Boyan Zlatanov, 2020. "Existence, Uniqueness and Stability of Market Equilibrium in Oligopoly Markets," Administrative Sciences, MDPI, vol. 10(3), pages 1-32, September.
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