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Generalizations of some ordinary and extreme connectedness properties of topological spaces to relator spaces
Existence of best proximity points satisfying two constraint inequalities
1. | Department of Mathematics, Bharathidasan University, Trichirapalli, Tamilnadu, India |
2. | University of Banja Luka, Faculty of Electrical Engineering, Patre 5, 78000 Banja Luka, Bosnia and Herzegovina |
3. | Department of Mathematics, Ege University, Bornova, 35100, Izmir, Turkey |
In this paper, we prove the existence of best proximity point and coupled best proximity point on metric spaces with partial order for weak proximal contraction mappings such that these critical points satisfy some constraint inequalities.
References:
[1] |
M. A. Alghamdi, N. Shahzad and F. Vetro, Best proximity points for some classes of proximal contractions, Abstr. Appl. Anal., 2013 (2013), 713252, 10PP.
doi: 10.1155/2013/713252. |
[2] |
D. Balraj and V. Piramanantham, Best proximity points for generalized proximal cyclic coupled mappings, Int. J. Res. Anal. Rev., 6 (2019), 869-880. Google Scholar |
[3] |
S. K. Chatterjea,
Fixed-point theorems, C. R. Acad. Bulgare Sci., 25 (1972), 727-730.
|
[4] |
B. S. Choudhury and P. Maity, Cyclic coupled fixed point result using Kannan type contractions, J. Operators, 2014 (2014), 876749, 1–5.
doi: 10.1155/2014/876749. |
[5] |
L. B. Ciric,
Generalized contractions and fixed point theorem, Publ. Inst. Math., 12 (1971), 19-26.
|
[6] |
A. A. Eldred and P. Veeramani,
Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001-1006.
doi: 10.1016/j.jmaa.2005.10.081. |
[7] |
M. Jleli and B. Samet,
A fixed point problem under two constraint inequalities, Fixed Point Theory Appl., 2016 (2016), 1-14.
doi: 10.1186/s13663-016-0504-9. |
[8] |
J. G. Kadwin and M. Marudai,
Fixed point and best proximity point results for generalised cyclic coupled mappings, Thai J. Math., 14 (2016), 431-441.
|
[9] |
R. Kannan,
Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76.
|
[10] |
P. Kumam, V. Pragadeeswarar, M. Marudai and K. Sitthithakerngkiet,
Coupled best proximity points in ordered metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-13.
doi: 10.1186/1687-1812-2014-107. |
[11] |
V. Lakshmikantham and L. B. Ciric,
Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341-4349.
doi: 10.1016/j.na.2008.09.020. |
show all references
References:
[1] |
M. A. Alghamdi, N. Shahzad and F. Vetro, Best proximity points for some classes of proximal contractions, Abstr. Appl. Anal., 2013 (2013), 713252, 10PP.
doi: 10.1155/2013/713252. |
[2] |
D. Balraj and V. Piramanantham, Best proximity points for generalized proximal cyclic coupled mappings, Int. J. Res. Anal. Rev., 6 (2019), 869-880. Google Scholar |
[3] |
S. K. Chatterjea,
Fixed-point theorems, C. R. Acad. Bulgare Sci., 25 (1972), 727-730.
|
[4] |
B. S. Choudhury and P. Maity, Cyclic coupled fixed point result using Kannan type contractions, J. Operators, 2014 (2014), 876749, 1–5.
doi: 10.1155/2014/876749. |
[5] |
L. B. Ciric,
Generalized contractions and fixed point theorem, Publ. Inst. Math., 12 (1971), 19-26.
|
[6] |
A. A. Eldred and P. Veeramani,
Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001-1006.
doi: 10.1016/j.jmaa.2005.10.081. |
[7] |
M. Jleli and B. Samet,
A fixed point problem under two constraint inequalities, Fixed Point Theory Appl., 2016 (2016), 1-14.
doi: 10.1186/s13663-016-0504-9. |
[8] |
J. G. Kadwin and M. Marudai,
Fixed point and best proximity point results for generalised cyclic coupled mappings, Thai J. Math., 14 (2016), 431-441.
|
[9] |
R. Kannan,
Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76.
|
[10] |
P. Kumam, V. Pragadeeswarar, M. Marudai and K. Sitthithakerngkiet,
Coupled best proximity points in ordered metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-13.
doi: 10.1186/1687-1812-2014-107. |
[11] |
V. Lakshmikantham and L. B. Ciric,
Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341-4349.
doi: 10.1016/j.na.2008.09.020. |
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