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Solving Existence Problems via F-Reich Contraction

In: Integral Methods in Science and Engineering

Author

Listed:
  • Mudasir Younis

    (UIT-Rajiv Gandhi Technological University (University of Technology of M.P.), Department of Applied Mathematics)

  • Deepak Singh

    (NITTTR, Under Ministry of HRD, Government of India, Department of Applied Sciences)

  • Anil Goyal

    (UIT-Rajiv Gandhi Technological University (University of Technology of M.P.), Department of Applied Mathematics)

Abstract

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.

Suggested Citation

  • Mudasir Younis & Deepak Singh & Anil Goyal, 2019. "Solving Existence Problems via F-Reich Contraction," Springer Books, in: Christian Constanda & Paul Harris (ed.), Integral Methods in Science and Engineering, chapter 0, pages 451-463, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-16077-7_35
    DOI: 10.1007/978-3-030-16077-7_35
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