Existence of Picard operator and iterated function system


  • Medha Garg Thapar Institute of Engineering & Technology
  • Sumit Chandok Thapar Institute of Engineering & Technology




Picard operator, fixed point, weak θm− contraction, iterated function system


In this paper, we define weak θm− contraction mappings and give a new class of Picard operators for such class of mappings on a complete metric space. Also, we obtain some new results on the existence and uniqueness of attractor for a weak θm− iterated multifunction system. Moreover, we introduce (α, β, θm)− contractions using cyclic (α, β)− admissible mappings and obtain some results for such class of mappings without the continuity of the operator. We also provide an illustrative example to support the concepts and results proved herein.


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Author Biographies

Medha Garg, Thapar Institute of Engineering & Technology

School of Mathematics

Sumit Chandok, Thapar Institute of Engineering & Technology

School of Mathematics


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How to Cite

M. Garg and S. Chandok, “Existence of Picard operator and iterated function system”, Appl. Gen. Topol., vol. 21, no. 1, pp. 57–70, Apr. 2020.



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