Fixed Point of Modified F-Contraction with an Application

Wang, Min; Saleem, Naeem; Bashir, Shahid; Zhou, Mi

doi:10.3390/axioms11080413

Axioms

2022

DOI: 10.3390/axioms11080413

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Fixed Point of Modified F-Contraction with an Application

Min Wang

Naeem Saleem

Shahid Bashir

et al.

Abstract: In this paper, we prove the existence of fixed points for every 2-rotative continuous mapping in Banach spaces to answer an open question raised by Goebel and Koter. Further, we modify F-contraction by developing F-rotative mapping and establish some fixed-point theorems. Finally, we apply our results to prove the existence of a solution of a non-linear fractional differential equation.

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2023

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Cited by 2 publications

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Lyapunov Functionals in Integral Equations

Raffoul

2023

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Lyapunov functions/functionals have found their footing in Volterra integro-differential equations. This is not the case for integral equations, and it is therefore further explored in this paper. In this manuscript, we utilize Lyapunov functionals combined with Laplace transform to qualitatively analyze the solutions of the integral equation In addition, we extend our method to nonlinear integral equations, integral equations with infinite delay, and integral equations with several kernels. We mention that Laplace transform has been used to solve integral equations of convolution types but has never been applied directly to integral equations that are not of the convolution type. In addition, our method allows us to find the upper estimates, and our necessary conditions are easy to verify.

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Lyapunov Functionals in Integral Equations

Raffoul

2023

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Fixed Points of (α, β, F*) and (α, β, F**)-Weak Geraghty Contractions with an Application

2023

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This study aims to provide some new classes of (α,β,F*)-weak Geraghty contraction and (α,β,F**)-weak Geraghty contraction, which are self-generalized contractions on any metric space. Furthermore, we find that the mappings satisfying the definition of such contractions have a unique fixed point if the underlying space is complete. In addition, we provide an application showing the uniqueness of the solution of the two-point boundary value problem.

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Fixed Point of Modified F-Contraction with an Application

Cited by 2 publications

References 18 publications

Lyapunov Functionals in Integral Equations

Lyapunov Functionals in Integral Equations

Fixed Points of (α, β, F*) and (α, β, F**)-Weak Geraghty Contractions with an Application

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