2018
7
1
0
0
Nonlinear oscillation of certain thirdorder neutral differential equation with distributed delay
2
2
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.
1

1
12


Sathish Kumar
Marappan
Paavai Engineering College (Autonomous)
Paavai Institutions,
Paavai Nagar, NH7,
Pachal 637 018.
Namakkal Dist. Tamilnadu,
India.
Paavai Engineering College (Autonomous)
Paavai
Iran
msksjv@gmail.com


Ganesan
V
Department of Mathematics,
Aringar Anna Government Arts College, Namakkal637002,
Tamilnadu, India.
Department of Mathematics,
Aringar Anna
Iran
ganesan_vgp@rediffmail.com


Janaki
S
Deputy Directorate of statistics,
Government of Tamil Nadu,
Namakkal637003, Tamil Nadu, India.
Deputy Directorate of statistics,
Government
Iran
janakisms@gmail.com


Osama
Moaaz
Department of Mathematics,
Faculty of Science,
Mansoura University,
Mansoura, 35516, Egypt.
Department of Mathematics,
Faculty of Science,
Man
Iran
o_moaaz@mans.edu.eg
Nonlinear
Oscillation
Distributed delay
Neutral differential equation
Some results on convergence and existence of best proximity points
2
2
In this paper, we introduce generalized cyclic φcontraction 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
1

13
24


Marzieh
Ahmadi Baseri
Yazd University
Yazd University
Iran
m.ahmadi@stu.yazd.ac.ir


H.
Mazaheri
Yazd University
Yazd University
Iran
hmazaheri@yazd.ac.ir


T. D
Narang
Guru Nanak Dev University
Guru Nanak Dev University
Iran
tdnarang1948@yahoo.co.in
Best proximity point
Generalized cyclic φcontraction map.Best proximity point
Proximal property
Generalized cyclic φcontraction map
A TAXICAB VERSION OF A TRIANGLE' S APOLLONIUS CIRCLE
2
2
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.
1

25
36


Temel
ERMİŞ
Department of Mathematics and Computer Sciences, Faculty of Arts and Sciences, Eskişehir Osmangazi University, Eskişehir, TURKEY
Department of Mathematics and Computer Sciences,
Iran
termis@ogu.edu.tr


Ozcan
Gelişgen
Deparment of Mathematics and Computer Sciences, Faculty of Art and Sciences, Eskişehir Osmangazi University, Eskişehir, TURKEY
Deparment of Mathematics and Computer Sciences,
Iran
gelisgen@ogu.edu.tr


Aybuke
Ekici
Deparment of Mathematics and Computer Sciences, Faculty of Art and Sciences, Eskişehir Osmangazi University, Eskişehir, TURKEY
Deparment of Mathematics and Computer Sciences,
Iran
aybkekici@gmail.com
Taxicab distance
Distance Functions
Taxicab geometry
Apollonius circle