]>
2021
7
1
46
Fixed points of generalized \(F-H-\phi-\psi-\varphi-\) weakly contractive mappings
Fixed points of generalized \(F-H-\phi-\psi-\varphi-\) weakly contractive mappings
en
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.
1
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
[
[1]
Ya. I. Alber, S. Guerre-Delabriere, Principles of weakly contractive maps in Hilbert spaces New results in Operator theory, Adv. Appl., 98 (1997), 7-22
##[2]
A. H. Ansari, Note on φ-ψ-contractive type mappings and related fixed point, The 2nd Regional Conference on Mathematics and Applications, Payame Noor University Tehran, 2014 (2014), 377-380
##[3]
A. H. Ansari, D. Dolicanin-Djekic, T. Dosenovic, S. Radenovic, Coupled coincidence point theorems for (α − µ − ψ − H − F)−two sided contractive type mappings in partially ordered metric spaces using compatible mappings, Filomat, 31 (2017), 2657-2673
##[4]
A. H. Ansari, H. Isik, S. Radenovic, Coupled fixed point theorems for contractive mappings involving new function classes and applications, Filomat, 31 (2017), 1893-1907
##[5]
A. H. Ansari, J. Kaewcharoen, C−class functions and fixed point theorems for generalized α − η − ψ − φ − F−contraction type mappings in α − η complete metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 4177-4190
##[6]
G. V. R. Babu, P. D. Sailaja, A fixed point theorem of generalized weakly contractive maps in orbitally complete metric space, Thai J. Math., 9 (2011), 1-10
##[7]
S. Cho, Fixed point theorems for generalized weakly contractive mappings in metric spaces with application, Fixed Point Theory Appl., 2018 (2018), 1-18
##[8]
B. S. Choudhury, Unique fixed point theorems for weakly C−Contractive mappings, Khatmandu University J. Sci. Tech., 5 (2009), 6-13
##[9]
B. S. Choudhury, P. Konar, B. E. Rhoades , N. Metiya, Fixed point theorems for generalized weakly contractive mappings, Nonlinear Anal., 74 (2011), 2116-2126
##[10]
D. Doric, Common fixed point for generalized (ψ, φ)− weak contractions, Appl. Math. Lett., 22 (2009), 1896-1900
##[11]
P. N. Dutta, B. S. Choudhury, A generalization of contraction principle in metric spaces, Fixed Point Theory Appl., 2008 (2008), 1-8
##[12]
J. Hasanzade Asl, S. Rezapour, N. Shahzad, On fixed points of α − ψ−contractive multifunctions, Fixed Point Theory Appl., 2012 (2012), 1-6
##[13]
N. Hussain, M. A. Kutbi, P. Salimi, Fixed point theory in α−complete metric spaces with applications, Abstr. Appl. Anal., 2014 (2014), 1-11
##[14]
R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 10 (1968), 71-76
##[15]
E. Karapinar, P. Kumam, P. Salimi, On α − ψ− Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 1-12
##[16]
H. Qawagneh, M. S. M. Noorani, W. Shatanawt, H. Alsamir, Common fixed points for pairs of triangular α−admissible mappings, J. Nonlinear Sci. Appl., 10 (2017), 6192-6204
##[17]
B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226 (1977), 257-290
##[18]
B. E. Rhoades, Some theorems on weakly contractive mappings, Nonlinear Anal., 47 (2001), 2683-2693
##[19]
P. Salimi, A. Latif, N. Hussain, Modified α − ψ− contractive mappings with applications, Fixed Point Theory Appl., 2013 (2013), 1-19
##[20]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for α − ψ−contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
##[21]
Q. Zhang,Y. Song, Fixed point theory for generalized ϕ−weak contractions, App. Math. Letters, 22 (2009), 75-78
]
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
en
en
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.
16
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
[
[1]
O. Adebimpe, K. A. Bashiru, T. A. Ojurongbe, Stability analysis of an SIR epidemic with non-linear incidence rate and treatment, Open J. Model. Simul., 3 (2015), 104-110
##[2]
E. Balcı, İ. Öztürk, S. Kartal, Dynamical behaviour of fractional order tumor model with Caputo and conformable fractional derivative, Chaos Solitons Fractals, 123 (2019), 43-51
##[3]
M. V. Barbarossa, M. Polner, G. Röst, Stability switches induced by immune system boosting in an SIRS model with discrete and distributed delays, SIAM J. Appl. Math., 77 (2017), 905-923
##[4]
E. Beretta , Y. Takeuchi, Global stability of an SIR epidemic model with time delays, J. Math. Biol., 33 (1995), 250-260
##[5]
E. Beretta, T. Hara, W. Ma, Y. Takeuchi, Global asymptotic stability of an SIR epidemic model with distributed time delay, Nonlinear Anal., 47 (2001), 4107-4115
##[6]
F. Brauer, C. Castillo-Chavez, Mathematical models in population biology and epidemiology: second edition, Springer, New York (2012)
##[7]
H. Cao, Y. Zhou, B. Song, https://www.hindawi.com/journals/ddns/2011/653937/, Discrete Dyn. Nat. Soc., 2011 (2011), 1-21
##[8]
E. B. Cox, M. A. Woodbury, L. E. Myers, A new model for tumor growth analysis based on a postulated inhibitory substance, Comp. Biomed. Res., 13 (1980), 437-445
##[9]
W. E. Diewert, K. Spremann, F. Stehling, Mathematical modelling in economics: Essays in Honor of Wolfgang Eichhorn, Springer, Berlin (1993)
##[10]
P. V. D. Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48
##[11]
N. Farajzadeh Tehrani, M. R. Razvan, S. Yasaman, Global analysis of a delay SVEIR epidemiological model, Iran. J. Sci. Technol. Trans. A Sci., 37 (2013), 483-489
##[12]
A. D. Freed, K. Diethelm, Y. Luchko, Fractional-order viscoelasticity (FOV): Constitutive developments using the fractional calculus: First annual report, Technical Memorandum, TM-2002-211914, NASA Glenn Research Center, Cleveland (2002)
##[13]
M. Golgeli, A mathematical model of Hepatitis B transmission in Turkey, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 68 (2019), 1586-1595
##[14]
G. Gripenberg, On some epidemic models, Quart. Appl. Math., 39 (1981), 317-327
##[15]
H. W. Hethcote, D. W. Tudor, Integral equation models for endemic infectious diseases, J. Math. Biol., 9 (1980), 37-47
##[16]
S. Hu, M. Khavanin, W. Zhuang, Integral equations arising in the kinetic theory of gases, Appl. Anal., 34 (1989), 261-266
##[17]
W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Part I Proc. Roy. Soc. A, 115 (1927), 700-721
##[18]
I. Koca, Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators, Eur. Phys. J. Plus, 133 (2018), 1-11
##[19]
A. Korobeinikov, Lyapunov functions and global properties for SEIR and SEIS epidemic models, Math. Med. Biol., 21 (2004), 75-83
##[20]
Y. Kuang, Delay differential equations: with applications in population dynamics, Academic Press, Boston (1993)
##[21]
J. P. LaSalle, Some extensions of Liapunov’s second method, IRE Trans. CT, 7 (1960), 520-527
##[22]
Z. Lu, X. Chi, L. Chen, The effect of constant and pulse vaccination on SIR epidemic model with horizontal and vertical transmission, Math. Comput. Modelling, 36 (2002), 1039-1057
##[23]
W. Ma, M. Song, Y. Takeuchi, Global stability of an SIR epidemic model with time delay, Appl. Math. Lett., 17 (2004), 1141-1145
##[24]
W. Ma, Y. Takeuchi, T. Hara, E. Beretta, Permanence of an SIR epidemic model with distributed time delays, Tohoku Math. J., 54 (2002), 581-591
##[25]
C. C. McCluskey, Complete global stability for an SIR epidemic model with delay distributed or discrete, Nonlinear Anal. Real World Appl., 11 (2010), 55-59
##[26]
M. M. Ojo, F. O. Akinpelu, Lyapunov functions and global properties of SEIR epidemic model, IJCMP, 1 (2017), 11-16
##[27]
S. Side, Y. M. Rangkuti, D. G. Pane, M. S. Sinaga, Stability analysis susceptible, exposed, infected, recovered (SEIR) model for spread model for spread of dengue fever in medan, J. Phys.: Conf. Ser., 954 (2018), 1-11
##[28]
H. L. Smith, H. R. Thieme, Dynamical systems and population persistence, American Mathematical Society,, 118 (2011), 1-10
##[29]
P. J. Torvik, R. L. Bagley, On the appearance of the fractional derivative in the behavior of real materials, J. Appl. Mech., 51 (1984), 294-298
##[30]
B. Yang, Stochastic dynamics of an SEIS epidemic model, Adv. Difference Equ., 226 (2016), 1-11
]
Existence and global behaviour of solutions of a nonlinear system modelling some epidemic diseases
Existence and global behaviour of solutions of a nonlinear system modelling some epidemic diseases
en
en
In this study, we introduce a new mathematical model with a vaccination
strategy in which different levels of susceptibility of individuals to an
epidemic are considered. This model, which also takes into account
the latent period, consists of a delay differential equation system.
After showing the uniqueness of solution of the system, we present the equilibrium points of the model and the reproduction
number \(\mathcal{R}_{0}\) which is a vital threshold in spread of diseases.
Then by using Lyapunov function and LaSalle Invariance Principle \cite
LaSalle, we give some results about the global stabilities of the equilibrium
points ofthe model according to \(\mathcal{R}_{0}\).
26
40
U.
Cakan
Inonu University
Department of Mathematics
Turkey
umitcakan@gmail.com
E.
Laz
Ministry of Education,
Turkey
erkanco1905@gmail.com
Global stability analysis
Lyapunov function
LaSalle invariance principle
Mathematical epidemiology
Vaccination strategy
Covid 19
Article.3.pdf
[
]
Proposing a Developed Gram-Schmidt Algorithm to Construct Orthogonal Unit Vectors
Proposing a Developed Gram-Schmidt Algorithm to Construct Orthogonal Unit Vectors
en
en
The Gram-Schmidt method is among the most well-known approaches for the orthogonalization of vectors; however, the accuracy of this algorithm might decline when it is implemented on large-scale vectors. This paper proposes a Developed Gram-Schmidt Algorithm (DGSA). The Schmidt vectors obtained from the proposed algorithm are prone to a lower error rate than those resulting from the Gram-Schmidt algorithm.
41
47
H.
Jafari
Young Researchers and Elite Club, Arak Branch
Islamic Azad University
Iran
hossein_jafari_123@yahoo.com
K.
Salehi
Department of Industrial Engineering, Aliabad Katoul Branch,
Islamic Azad University
Iran
kiyanasalehi11@yahoo.com
A.
Etebari
Department of Industrial Engineering, Aliabad Katoul Branch
Islamic Azad University
Iran
asma.etebari@gmail.com
Gram-Schmidt Algorithm
Orthogonalization of Vectors
Article.4.pdf
[
]