eng
Shahid Bahonar University of Kerman
Journal of Mahani Mathematical Research Center
2251-7952
2251-7952
2018-03-01
7
1
1
12
10.22103/jmmrc.2018.11248.1052
1952
Nonlinear oscillation of certain third-order neutral differential equation with distributed delay
Sathish Kumar Marappan
msksjv@gmail.com
1
Ganesan V
ganesan_vgp@rediffmail.com
2
Janaki S
janakisms@gmail.com
3
Osama Moaaz
o_moaaz@mans.edu.eg
4
Paavai Engineering College (Autonomous) Paavai Institutions, Paavai Nagar, NH-7, Pachal -637 018. Namakkal Dist. Tamilnadu, India.
Department of Mathematics, Aringar Anna Government Arts College, Namakkal-637002, Tamilnadu, India.
Deputy Directorate of statistics, Government of Tamil Nadu, Namakkal-637003, Tamil Nadu, India.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt.
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.
http://jmmrc.uk.ac.ir/article_1952_fdc230aad0e65c21c4a52d14c10d29ff.pdf
Nonlinear
Oscillation
Distributed delay
Neutral differential equation
eng
Shahid Bahonar University of Kerman
Journal of Mahani Mathematical Research Center
2251-7952
2251-7952
2018-03-01
7
1
13
24
10.22103/jmmrc.2018.10747.1045
2055
Some results on convergence and existence of best proximity points
Marzieh Ahmadi Baseri
m.ahmadi@stu.yazd.ac.ir
1
H. Mazaheri
hmazaheri@yazd.ac.ir
2
T. D Narang
tdnarang1948@yahoo.co.in
3
Yazd University
Yazd University
Guru Nanak Dev University
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
http://jmmrc.uk.ac.ir/article_2055_6bcf15495105392fcbe4e154e8350936.pdf
Best proximity point
Generalized cyclic φ-contraction map.Best proximity point
Proximal property
Generalized cyclic φ-contraction map
eng
Shahid Bahonar University of Kerman
Journal of Mahani Mathematical Research Center
2251-7952
2251-7952
2018-07-23
7
1
25
36
10.22103/jmmrc.2018.2073
2073
A TAXICAB VERSION OF A TRIANGLE' S APOLLONIUS CIRCLE
Temel ERMİŞ
termis@ogu.edu.tr
1
Ozcan Gelişgen
gelisgen@ogu.edu.tr
2
Aybuke Ekici
aybkekici@gmail.com
3
Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Eskişehir Osmangazi University, Eskişehir, TURKEY
Deparment of Mathematics and Computer Sciences, Faculty of Art and Sciences, Eskişehir Osmangazi University, Eskişehir, TURKEY
Deparment of Mathematics and Computer Sciences, Faculty of Art and Sciences, Eskişehir Osmangazi University, Eskişehir, TURKEY
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.
http://jmmrc.uk.ac.ir/article_2073_c7f14ca1b6a6c894e370b7160e394b3a.pdf
Taxicab distance
Distance Functions
Taxicab geometry
Apollonius circle