Fixed point to fixed circle and activation function in partial metric space
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Abstract
We familiarize a notion of a fixed circle in a partial metric space, which is not necessarily the same as a circle in a Euclidean space. Next, we establish novel fixed circle theorems and verify these by illustrative examples with geometric interpretation to demonstrate the authenticity of the postulates. Also, we study the geometric properties of the set of non-unique fixed points of a discontinuous self-map in reference to fixed circle problems and responded to an open problem regarding the existence of a maximum number of points for which there exist circles. This paper is concluded by giving an application to activation function to exhibit the feasibility of results, thereby providing a better insight into the analogous explorations.
Acknowledgements
The authors are grateful to the anonymous referees for their precise remarks and suggestions, which led to the improvement of the paper.
References
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Articles in the same Issue
- Frontmatter
- L 1-solutions of the initial value problems for implicit differential equations with Hadamard fractional derivative
- On tangential approximations of the solution set of set-valued inclusions
- Stabilization of the wave equation with a nonlinear delay term in the boundary conditions
- Fixed point to fixed circle and activation function in partial metric space
- A note on the validity of the Schrödinger approximation for the Helmholtz equation
- Certain classes of analytic functions defined by Hurwitz–Lerch zeta function
- A new factor theorem on absolute matrix summability method
- On a solution to a functional equation
- Hydromagnetic effects on non-Newtonian Hiemenz flow
- Stability of a class of entropies based on fractional calculus
- Asymptotic behavior of solution of Whitham–Broer–Kaup type equations with negative dispersion
- Numerical study of time delay singularly perturbed parabolic differential equations involving both small positive and negative space shifts
- Weak solutions to the time-fractional g-Navier–Stokes equations and optimal control
- On the asymptotic formulas for perturbations in the eigenvalues of the Stokes equations due to the presence of small deformable inclusions
- Extended homogeneous balance conditions in the sub-equation method
Articles in the same Issue
- Frontmatter
- L 1-solutions of the initial value problems for implicit differential equations with Hadamard fractional derivative
- On tangential approximations of the solution set of set-valued inclusions
- Stabilization of the wave equation with a nonlinear delay term in the boundary conditions
- Fixed point to fixed circle and activation function in partial metric space
- A note on the validity of the Schrödinger approximation for the Helmholtz equation
- Certain classes of analytic functions defined by Hurwitz–Lerch zeta function
- A new factor theorem on absolute matrix summability method
- On a solution to a functional equation
- Hydromagnetic effects on non-Newtonian Hiemenz flow
- Stability of a class of entropies based on fractional calculus
- Asymptotic behavior of solution of Whitham–Broer–Kaup type equations with negative dispersion
- Numerical study of time delay singularly perturbed parabolic differential equations involving both small positive and negative space shifts
- Weak solutions to the time-fractional g-Navier–Stokes equations and optimal control
- On the asymptotic formulas for perturbations in the eigenvalues of the Stokes equations due to the presence of small deformable inclusions
- Extended homogeneous balance conditions in the sub-equation method
