Abstract
We introduce a relational generalized Meir–Keeler contraction and a relational generalized Meir–Keeler contraction with rational terms in non-complete relational b-metric like spaces in order to establish non-unique fixed point results for a discontinuous single-valued map. Also, we provide an illustrative example to demonstrate that a relational generalized Meir–Keeler contraction with rational terms in a relational b-metric like space admits discontinuity at the fixed point. Thereby, we provide a novel explanation via a binary relation to the question of the existence of a contractive map admitting a fixed point at the point of discontinuity. Finally, we give applications to solve an initial value problem and a non-linear matrix equation which demonstrate the usability and effectiveness of our results.
Acknowledgements
The authors are grateful to the anonymous referees for their precise remarks and suggestions which led to the improvement of this paper.
References
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Estimates for a beam-like partial differential operator and applications
- Stabilization of polynomial systems in ℝ3 via homogeneous feedback
- Analyzing the existence of solution of a fractional order integral equation: A fixed point approach
- Existence of solution to a nonlocal biharmonic problem with dependence on gradient and Laplacian
- Global existence and exponential decay for a viscoelastic equation with not necessarily decreasing kernel
- Solving fractal differential equations via fractal Laplace transforms
- Minimum energy control of degenerate Cauchy problem with skew-Hermitian pencil
- Splines in vibration analysis of non-homogeneous circular plates of quadratic thickness
- The weak eigenfunctions of boundary-value problem with symmetric discontinuities
- Some subclasses of analytic functions involving certain integral operator
- Relation theoretic contractions and their applications in b-metric like spaces
- A new conservative finite difference scheme for 1D Cahn–Hilliard equation coupled with elasticity
- An improved proximal method with quasi-distance for nonconvex multiobjective optimization problem
Artikel in diesem Heft
- Frontmatter
- Estimates for a beam-like partial differential operator and applications
- Stabilization of polynomial systems in ℝ3 via homogeneous feedback
- Analyzing the existence of solution of a fractional order integral equation: A fixed point approach
- Existence of solution to a nonlocal biharmonic problem with dependence on gradient and Laplacian
- Global existence and exponential decay for a viscoelastic equation with not necessarily decreasing kernel
- Solving fractal differential equations via fractal Laplace transforms
- Minimum energy control of degenerate Cauchy problem with skew-Hermitian pencil
- Splines in vibration analysis of non-homogeneous circular plates of quadratic thickness
- The weak eigenfunctions of boundary-value problem with symmetric discontinuities
- Some subclasses of analytic functions involving certain integral operator
- Relation theoretic contractions and their applications in b-metric like spaces
- A new conservative finite difference scheme for 1D Cahn–Hilliard equation coupled with elasticity
- An improved proximal method with quasi-distance for nonconvex multiobjective optimization problem