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On Krasnoselskii Fixed Point Theorem and fractal

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  • Kashyap, Sunil Kumar
  • Sharma, Birendra Kumar
  • Banerjee, Amitabh
  • Shrivastava, Subhash Chandra

Abstract

We show that Φ has a fixed point, if S is convex and Φ is convex and closed valued (Sehgal and Singh, 1978) [2], (Wu, 1997 ) [3], in addition Φ is convex-closed under σ(Φ) approximation continuous, this is the fixed (invariant) set. We use these invariants in fractals (in the grab of a self-similar set). We generate the Fractal Set from Krasnoselskii’s Fixed Point Theorem (Sehgal and Singh, 1978) [2], (Wu, 1997) [3].

Suggested Citation

  • Kashyap, Sunil Kumar & Sharma, Birendra Kumar & Banerjee, Amitabh & Shrivastava, Subhash Chandra, 2014. "On Krasnoselskii Fixed Point Theorem and fractal," Chaos, Solitons & Fractals, Elsevier, vol. 61(C), pages 44-45.
    • Handle: RePEc:eee:chsofr:v:61:y:2014:i:c:p:44-45
    DOI: 10.1016/j.chaos.2014.02.003
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    Cited by:

    1. Prithvi, B.V. & Katiyar, S.K., 2023. "Revisiting fractal through nonconventional iterated function systems," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Ullah, Kifayat & Katiyar, S.K., 2023. "Generalized G-Hausdorff space and applications in fractals," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).

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