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Fixed Point Results of Dynamic Process Dˇϒ,μ0 through FIC‐Contractions with Applications

Author

Listed:
  • Amjad Ali
  • Eskandar Ameer
  • Muhammad Arshad
  • Hüseyin Işık
  • Mustafa Mudhesh

Abstract

This article constitutes the new fixed point results of dynamic process D(ϒ, μ0) through FIC‐integral contractions of the Ciric kind and investigates the said contraction to iterate a fixed point of set‐valued mappings in the module of metric space. To do so, we use the dynamic process instead of the conventional Picard sequence. The main results are examined by tangible nontrivial examples which display the motivation for such investigation. The work is completed by giving an application to Liouville‐Caputo fractional differential equations.

Suggested Citation

  • Amjad Ali & Eskandar Ameer & Muhammad Arshad & Hüseyin Işık & Mustafa Mudhesh, 2022. "Fixed Point Results of Dynamic Process Dˇϒ,μ0 through FIC‐Contractions with Applications," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:8495451
    DOI: 10.1155/2022/8495451
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    References listed on IDEAS

    as
    1. A. Branciari, 2002. "A fixed point theorem for mappings satisfying a general contractive condition of integral type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 29, pages 1-6, January.
    2. B. E. Rhoades, 2003. "Two fixed-point theorems for mappings satisfying a general contractive condition of integral type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-7, January.
    3. Ali, Amjad & Uddin, Fahim & Arshad, Muhammad & Rashid, Maliha, 2020. "Hybrid fixed point results via generalized dynamic process for F-HRS type contractions with application," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
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