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FIXED POINT THEOREMS OF WEAKLY MONOTONE PREŠIĆ TYPE MAPPINGS IN ORDERED CONE METRIC SPACES
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 Title & Authors
FIXED POINT THEOREMS OF WEAKLY MONOTONE PREŠIĆ TYPE MAPPINGS IN ORDERED CONE METRIC SPACES
Khan, Mohammad Saeed; Shukla, Satish; Kang, Shin Min;
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 Abstract
In this paper, we introduce the weakly monotone type mappings in product spaces when the underlying space is an ordered cone metric space. Some fixed point results for such mappings are also proved which generalize and unify several known results in metric and cone metric spaces with normal cone. The results are supported by examples.
 Keywords
type mapping;weakly monotone type mapping;ordered cone metric space;fixed point;
 Language
English
 Cited by
 References
1.
S. Banach, Sur les operations dans les ensembles abstraits et leur applications, Fund. Math. 3 (1922), 133-181.

2.
L. B. Ciric and S. B. Presic, On Presic type generalisation of Banach contraction principle, Acta Math. Univ. Comenian. 76 (2007), no. 2, 143-147.

3.
K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, 1985.

4.
M. Frechet, Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo 22 (1906), 1-74. crossref(new window)

5.
R. George, K. P. Reshma, and R. Rajagopalan, A generalised fixed point theorem of Presic type in cone metric spaces and application to morkov process, Fixed Point Theory Appl. 2011 (2011), no. 85, 8 pages.

6.
L. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), no. 2, 1468-1476. crossref(new window)

7.
G. Jungck, S. Radenovic, S. Radojevic, and V. Rakocevic, Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed Point Theory Appl. 2009 (2009), Article ID 643840, 13 pages.

8.
M. S. Khan, M. Berzig, and B. Samet, Some convergence results for iterative sequences of Presic type and applications, Adv. Difference Equ. 2012 (2012), no. 38, 12 pages.

9.
M. S. Khan and M. Samanipour, Presic type extension in cone metric space, Int. J. Math. Anal. 7 (2013), no. 36, 1795-1802.

10.
D. R. Kurepa, Tableaux ramifies d'ensembles espaces pseudo-distancies, C. R. Acad. Sci. Paris 198 (1934), 1563-1565.

11.
D. R. Kurepa, Free power or width of some kinds of mathematical structure, Publ. Inst. Math. (Beograd) 42(56) (1987), 3-12.

12.
S. Lin, A common fixed point theorem in abstract spaces, Indian J. Pure Appl. Math. 18 (1987), no. 8, 685-690.

13.
N. V. Luong and N. X. Thuan, Some fixed point theorems of Presic-Ciric type, Acta Univ. Apulensis Math. Inform. 30 (2012), 237-249.

14.
S. K. Malhotra, S. Shukla, and R. Sen, A generalization of Banach contraction principle in ordered cone metric spaces, J. Adv. Math. Stud. 5 (2012), no. 2, 59-67.

15.
S. K. Malhotra, S. Shukla, and R. Sen, Some coincidence and common fixed point theorems in cone metric spaces, Bull. Math. Anal. Appl. 4 (2012), no. 2, 64-71.

16.
J. J. Nieto and R. R. Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equation, Order 22 (2005), no. 3, 223-239. crossref(new window)

17.
M. Pacurar, Approximating common fixed points of Presic-Kannan type operators by a multi-step iterative method, An. St. Univ. Ovidius Constanta Ser. Mat. 17 (2009), no. 1, 153-168.

18.
M. Pacurar, A multi-step iterative method for approximating common fixed points of Presic- Rus type operators on metric spaces, Studia Univ. Babes-Bolyai Math. 55 (2010), no. 1, 149-162.

19.
M. Pacurar, Common fixed points for almost Presic type operators, Carpathian J. Math. 28 (2012), no. 1, 117-126.

20.
S. Presic, Sur la convergence des suites, C. R. Acad. Paris 260 (1965), 3828-3830.

21.
A. C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc. 132 (2004), no. 5, 1435-1443. crossref(new window)

22.
S. Rezapour and R. Halbarani, Some notes on the paper, Cone metric spaces and fixed point theorem of contractive mappings, J. Math. Anal. Appl. 345 (2008), no. 2, 719-724. crossref(new window)

23.
B. Rzepecki, On fixed point theorems of Maia type, Publ. Inst. Math. (Beograd) 28(42) (1980), 179-186.

24.
S. Shukla, Presic type results in 2-Banach spaces, Afr. Mat. 25 (2014), no. 4, 1043-1051. crossref(new window)

25.
S. Shukla and B. Fisher, A generalization of Presic type mappings in metric-like spaces, J. Oper. 2013 (2013), Article ID 368501, 5 pages.

26.
S. Shukla and S. Radenovic, A generalization of Presic type mappings in 0-complete ordered partial metric spaces, Chinese J. Math. 2013 (2013), Article ID 859531, 8 pages.

27.
S. Shukla and R. Sen, Set-valued Presic-Reich type mappings in metric spaces, Rev. R. Acad. Cienc. Exactas, Fis. Nat. Ser, A. Mat. 108 (2014), no. 2, 431-440. crossref(new window)

28.
S. Shukla, R. Sen, and S. Radenovic, Set-valued Presic type contraction in metric spaces, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.). http://dx.doi.org/10.2478/aicu-2014-0011. crossref(new window)

29.
P. Zabreiko, K-metric and K-normed spaces: survey, Collect. Math. 48 (1997), no. 4-6, 825-859.