Solving Existence Problems via F-Reich Contraction

Mudasir Younis, Deepak Singh and Anil Goyal
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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

Chapter Chapter 35 in Integral Methods in Science and Engineering, 2019, pp 451-463 from Springer

Abstract: 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.

Date: 2019
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DOI: 10.1007/978-3-030-16077-7_35

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