Solving Existence Problems via F-Reich Contraction

  • Mudasir Younis
  • Deepak Singh
  • Anil Goyal


The main assessment of this article is to furnish a new technique, based on F-Reich contraction, for solving some models of real world problems, viz. “concentration of a diffusing substance in an absorbing medium” and an integral equation. For this purpose, we inaugurate the notation of F-Reich contraction in the context of rectangular b-metric space and establish certain new fixed point results without taking into account the continuity of the mapping involved. Innovative approach of visualizing non-trivial examples gives a new direction especially to nonlinear problems pertinent to geometrical interpretation. Examples are hosted by a series of mappings containing transcendental terms along with nontrivial fixed points. Established results substantially theorize and improve F-contraction version of some prime results in the existing literature. At the end some open problems are also presented for potential readers.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Mudasir Younis
    • 1
  • Deepak Singh
    • 2
  • Anil Goyal
    • 1
  1. 1.Department of Applied MathematicsUIT-Rajiv Gandhi Technological University (University of Technology of M.P.)BhopalIndia
  2. 2.Department of Applied SciencesNITTTR, Under Ministry of HRD, Government of IndiaBhopalIndia

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