Shahid Bahonar University of Kerman
Journal of Mahani Mathematical Research Center
2251-7952
7
1
2018
03
01
Nonlinear oscillation of certain third-order neutral differential equation with distributed delay
1
12
EN
Sathish Kumar
Marappan
Paavai Engineering College (Autonomous)
Paavai Institutions,
Paavai Nagar, NH-7,
Pachal -637 018.
Namakkal Dist. Tamilnadu,
India.
msksjv@gmail.com
Ganesan
V
Department of Mathematics,
Aringar Anna Government Arts College, Namakkal-637002,
Tamilnadu, India.
ganesan_vgp@rediffmail.com
Janaki
S
Deputy Directorate of statistics,
Government of Tamil Nadu,
Namakkal-637003, Tamil Nadu, India.
janakisms@gmail.com
Osama
Moaaz
Department of Mathematics,
Faculty of Science,
Mansoura University,
Mansoura, 35516, Egypt.
o_moaaz@mans.edu.eg
10.22103/jmmrc.2018.11248.1052
The authors obtain necessary and sufficient conditions for the existence of oscillatory solutions with a specified asymptotic behavior of solutions to a nonlinear neutral differential equation with distributed delay of third order. We give new theorems which ensure that every solution to be either oscillatory or converges to zero asymptotically. Examples dwelling upon the importance of applicability of these results.
Nonlinear,Oscillation,Distributed delay,Neutral differential equation
http://jmmrc.uk.ac.ir/article_1952.html
http://jmmrc.uk.ac.ir/article_1952_fdc230aad0e65c21c4a52d14c10d29ff.pdf
Shahid Bahonar University of Kerman
Journal of Mahani Mathematical Research Center
2251-7952
7
1
2018
03
01
Some results on convergence and existence of best proximity points
13
24
EN
Marzieh
Ahmadi Baseri
Yazd University
m.ahmadi@stu.yazd.ac.ir
H.
Mazaheri
Yazd University
hmazaheri@yazd.ac.ir
T. D
Narang
Guru Nanak Dev University
tdnarang1948@yahoo.co.in
10.22103/jmmrc.2018.10747.1045
In this paper, we introduce generalized cyclic φ-contraction maps in metric spaces and give some results of best proximity points of such mappings in the setting of a uniformly convex Banach space. Moreover, we obtain convergence and existence results of proximity points of the mappings on reflexive Banach spaces
Best proximity point,Generalized cyclic φ-contraction map.Best proximity point,Proximal property,Generalized cyclic φ-contraction map
http://jmmrc.uk.ac.ir/article_2055.html
http://jmmrc.uk.ac.ir/article_2055_6bcf15495105392fcbe4e154e8350936.pdf