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2021
7
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Fixed points of generalized \(F-H-\phi-\psi-\varphi-\) weakly contractive mappings
Fixed points of generalized \(F-H-\phi-\psi-\varphi-\) weakly contractive mappings
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en
We introduce the notion of generalized \(F-H-\phi-\psi-\varphi-\) weakly contractive mappings and prove the existence of fixed points of such mappings in complete metric spaces. We draw some corollaries and provide examples in support of our main results. Our results extend the results of Cho [S. Cho, Fixed Point Theory Appl., \({\bf 2018} (2018)\), 18 pages] and Choudhury, Konar, Rhoades and Metiya [B. S. Choudhury, P. Konar, B. E. Rhoades, N. Metiya, Nonlinear Anal., \({\bf 74} (2011)\), 2116--2126] in the sense that the control function that we used in our results need not have monotonicity property.
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15
G. V.
Ravindranadh Babu
Department of Mathematics
Andhra University
India
gvr_babu@hotmail.com
M.
Vinod Kumar
Department of Mathematics
Anil Neerukonda Institute of Technology and Sciences
India
dravinodvivek@gmail.com
\(\alpha-\)admissible
\(\mu-\)subadmissible
\(C-\)class function, the pair \((F,H)\) is upclass of type I
the pair \((F,H)\) is special upclass of type I
Article.1.pdf
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On the stability analysis of solutions of an integral equation with an application in epidemiology
On the stability analysis of solutions of an integral equation with an application in epidemiology
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This paper concerns a nonlinear integral equation modeling the spread of
epidemics in which immunity does not occur after recovery. The model is
mainly based on the return of some of the individuals who have been exposed
to the pathogen and who have completed the incubation period, into the
susceptible class. We first prove the uniqueness of the global solution of
the model with the given initial conditions. After determining the
positively invariant region for the model, using LaSalle invariance
principle [J. P. LaSalle, IRE Trans. CT, \({\bf 7} (1960)\), 520--527] and the concept of persistence we present some
results about the stability analysis of the solutions according to the case
of the reproduction number \(\mathcal{R}_{0}\) which is a vital threshold in the spread of diseases.
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25
Ümit
Çakan
Department of Mathematics
İnönü University
Turkey
umitcakan@gmail.com
Global stability analysis
Lyapunov function
LaSalle invariance principle
mathematical epidemiology
persistence
Article.2.pdf
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