Fixed Point Theorems for Generalized ( ?? - ? )-Contractions in F -Metric Spaces with Applications

Saleh Abdullah Al-Mezel, Jamshaid Ahmad and Giuseppe Marino
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Saleh Abdullah Al-Mezel: Department of Mathematics, University of Jeddah, P.O.Box 80327, Jeddah 21589, Saudi Arabia
Jamshaid Ahmad: Department of Mathematics, University of Jeddah, P.O.Box 80327, Jeddah 21589, Saudi Arabia
Giuseppe Marino: Department of Mathematics and Computer Science, University of Calabria, Via P. Bucci, 87036 Arcavacata di Rende (CS), Italy

Mathematics, 2020, vol. 8, issue 4, 1-14

Abstract: The purpose of this paper is to define generalized ( α β - ψ ) -contraction in the context of F -metric space and obtain some new fixed point results. As applications, we solve a nonlinear neutral differential equation with an unbounded delay ϑ / ( ι ) = − ρ 1 ( ι ) ϑ ( ι ) + ρ 2 ( ι ) L ( ϑ ( ι − ς ( ι ) ) ) + ρ 3 ( ι ) ϑ / ( ι − ς ( ι ) ) , where ρ 1 ( ι ) , ρ 2 ( ι ) are continuous, ρ 3 ( ι ) is continuously differentiable and ς ( ι ) > 0 , for all ι ∈ R and is twice continuously differentiable.

Keywords: nonlinear neutral differential equation; fixed point; generalized ( ??-? )-contraction; ?-metric spaces (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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