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
Shahid Bahonar University of Kerman
Journal of Mahani Mathematical Research Center
2251-7952
7
1
2018
07
23
A TAXICAB VERSION OF A TRIANGLE' S APOLLONIUS CIRCLE
25
36
EN
Temel
ERMİŞ
Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Eskişehir Osmangazi University, Eskişehir, TURKEY
termis@ogu.edu.tr
Ozcan
Gelişgen
Deparment of Mathematics and Computer Sciences, Faculty of Art and Sciences, Eskişehir Osmangazi University, Eskişehir, TURKEY
gelisgen@ogu.edu.tr
Aybuke
Ekici
Deparment of Mathematics and Computer Sciences, Faculty of Art and Sciences, Eskişehir Osmangazi University, Eskişehir, TURKEY
aybkekici@gmail.com
10.22103/jmmrc.2018.2073
One of the most famous problems of classical geometry is the Apollonius' problem asks construction of a circle which is tangent to three given objects. These objects are usually taken as points, lines, and circles. This well known problem was posed by Apollonius of Perga ( about 262 - 190 B.C.) who was a Greek mathematician known as the great geometer of ancient times after Euclid and Archimedes. The Apollonius' problem can be reduced specically to the question Is there the circle that touches all three excircles of given triangle and encompasses them? " when all three objects are circles. In literature, altough there are a lot of works on the solution of this question in the Euclidean plane, there is not the work on this question in different metric geometries. In this paper, we give that the conditions of existence of Apollonius taxicab circle for any triangle.
Taxicab distance,Distance Functions,Taxicab geometry,Apollonius circle
http://jmmrc.uk.ac.ir/article_2073.html
http://jmmrc.uk.ac.ir/article_2073_c7f14ca1b6a6c894e370b7160e394b3a.pdf