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SOME FIXED POINT THEOREMS VIA COMMON LIMIT RANGE PROPERTY IN NON-ARCHIMEDEAN MENGER PROBABILISTIC METRIC SPACES
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 Title & Authors
SOME FIXED POINT THEOREMS VIA COMMON LIMIT RANGE PROPERTY IN NON-ARCHIMEDEAN MENGER PROBABILISTIC METRIC SPACES
Nashine, Hemant Kumar; Kadelburg, Zoran;
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 Abstract
We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized -contractive conditions i Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.
 Keywords
t-norm;non-Archimedean Menger PM-space;weakly compatible mappings;common limit range property;fixed point;
 Language
English
 Cited by
1.
Implicit relations related to ordered orbitally complete metric spaces and applications, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2017, 111, 2, 403  crossref(new windwow)
 References
1.
M. Aamri and D. El. Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002), no. 1, 181-188. crossref(new window)

2.
R. Bellman and E. S. Lee, Functional equations in dynamic programming, Aequationes Math. 17 (1978), no. 1, 1-18. crossref(new window)

3.
T. C. Bhakta and S. Mitra, Some existence theorems for functional equations arising in dynamic programming, J. Math. Anal. Appl. 98 (1984), no. 2, 348-362. crossref(new window)

4.
S. S. Chang, Fixed point theorems for single-valued and multi-valued mappings in Non-Archimedean Menger probabilistic metric spaces, Math. Japon. 35 (1990), no. 5, 875-885.

5.
S. S. Chang, Y. J. Chom, and S. M. Kang, Nonlinear Operator Theory in Probabilistic Metric Spaces, Nova Science Publishers, New York, 2001.

6.
S. Chauhan and S. Kumar, Fixed point theorems in Non-Archimedean Menger PM-spaces using common property (E.A), Asian-Eur. J. Math. 5 (2012), no. 4, 13 pages.

7.
S. Chauhan, S. Radenovic, M. Imdad, and C. Vetro, Some integral type fixed point theorems in Non-Archimedean Menger PM-Spaces with common property (E.A) and application to functional equations in dynamic programming, Rev. R. Acad. Cienc. Ex- actas Fis. Nat. Ser. A Math. 108 (2014), no. 2, 795-810. crossref(new window)

8.
S. Chauhan and J. Vujakovic, Some fixed point theorems for weakly compatible map- pings in Non-Archimedean Menger probabilistic metric spaces via common limit range property, Matematiche (Catania) 68 (2013), no. 2, 77-90.

9.
Y. J. Cho, S. M. Kang, and S. S. Chang, Coincidence point theorems for nonlinear hybrid contractions in Non-Archimedean Menger probabilistic metric spaces, Demonstratio Math. 28 (1995), no. 1, 19-32.

10.
Y. J. Cho, S. M. Kang, and S. S. Chang, Common fixed point theorems for compatible mappings of type (A) in Non- Archimedean Menger PM-spaces, Math. Japon. 46 (1997), no. 1, 169-179.

11.
R. C. Dimri and B. D. Pant, Fixed point theorems in non-Archimedean Menger spaces, Kyungpook Math. J. 31 (1991), no. 1, 89-95.

12.
M. Grabiec, Y. J. Cho, and V. Radu, On Nonsymmetric Topological and Probabilistic Structures, Nova Science Publishers, New York, 2006.

13.
O. Hadzic, A note on Istratescu's fixed point theorems in non-Archimedean probabilistic metric spaces, Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 24(72) (1980), no. 4, 359-362.

14.
M. Imdad, J. Ali, and M. Tanveer, Coincidence and common fixed point theorems for nonlinear contractions in Menger PM spaces, Chaos Solitons Fractals 42 (2009), no. 5, 3121-3129. crossref(new window)

15.
M. Imdad, S. Chauhan, and Z. Kadelburg, Fixed point theorems for mappings with common limit range property satisfying generalized (${\psi},{\varphi}$)-weak contractive conditions, Math. Sci. (Springer) 7 (2013), Art. 16, 8 pp.

16.
M. Imdad, S. Chauhan, Z. Kadelburg, and C. Vetro, Fixed point theorems for non-self mappings in symmetric spaces under $\varphi$-weak contractive conditions and an application to functional equations in dynamic programming, Appl. Math. Comput. 227 (2014), 469-479. crossref(new window)

17.
M. Imdad, B. D. Pant, and S. Chauhan, Fixed point theorems in Menger spaces using the ($CLR_ST$) property and applications, J. Nonlinear Anal. Optim. 3 (2012), no. 2, 225-237.

18.
I. Istratescu, On some fixed point theorems with applications to the nonarchimedean Menger spaces, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 58 (1975), no. 3, 374-379.

19.
I. Istratescu, Fixed point theorems for some classes of contraction mappings on nonar-chimedean probabilistic metric space, Publ. Math. Debrecen 25 (1978), no. 1-2, 29-34.

20.
I. Istratescu and G. Babescu, On the completion on non-Archimedean probabilistic metric spaces, Seminar de spatii metrice probabiliste, Universitatea Timisoara, Nr. 17, 1979.

21.
I. Istratescu and N. Crivat, On some classes of non-Archimedean probabilistic metric spaces, Seminar de spatii metrice probabiliste, Universitatea Timisoara, Nr. 12, 1974.

22.
I. Istrat. escu and G. Palea, On non-Archimedean probabilistic metric spaces, An. Univ. Timisoara Ser. Sti. Mat. 12 (1974/77), no. 2, 115-118.

23.
G. Jungck, Common fixed points for noncontinuous nonself maps on nonmetric spaces, Far East J. Math. Sci. 4 (1996), no. 2, 199-215.

24.
G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (1998), no. 3, 227-238.

25.
M. A. Khan, Common fixed point theorems in non-Archimedean Menger PM-spaces, Int. Math. Forum 6 (2011), no. 40, 1993-2000.

26.
M. A. Khan and Sumitra, A common fixed point theorem in non-Archimedean Menger PM-space, Novi Sad J. Math. 39 (2009), no. 1, 81-87.

27.
S. Kutukcu and S. Sharma, A common fixed point theorem in non-Archimedean Menger PM-spaces, Demonstratio Math. 42 (2009), no. 4, 837-849.

28.
H. K. Pathak, Y. J. Cho, S. S. Chang, and S. M. Kang, Compatible mappings of type (P) and fixed point theorems in metric spaces and probabilistic metric spaces, Novi Sad J. Math. 26 (1996), no. 2, 87-109.

29.
K. P. R. Rao and E. T. Ramudu, Common fixed point theorem for four mappings in non-Archimedean Menger PM-spaces, Filomat 20 (2006), no. 2, 107-113. crossref(new window)

30.
B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 313-334. crossref(new window)

31.
V. M. Sehgal and A. T. Bharucha-Reid, Fixed points of contraction mappings on prob- abilistic metric spaces, Math. Systems Theory 6 (1972), 97-102. crossref(new window)

32.
B. Singh, A. Jain, and P. Agarwal, Semi-compatibility in non-Archimedean Menger PM-space, Comment. Math. 49 (2009), no. 1, 15-25.

33.
B. Singh, A. Jain, and M. Jain, Compatible maps and fixed points in non-Archimedean Menger PM-spaces, Int. J. Contemp. Math. Sci. 6 (2011), no. 37-40, 1895-1905.

34.
S. L. Singh and B. D. Pant, Common fixed points of weakly commuting mappings on non-Archimedean Menger PM-spaces, Vikram J. Math. 6 (1987), 27-31.

35.
S. L. Singh, B. D. Pant, and S. Chauhan, Fixed point theorems in non-Archimedean Menger PM-spaces, J. Nonlinear Anal. Optim. 3 (2012), no. 2, 153-160.

36.
B. Singh, R. K. Sharma, and M. Sharma, Compatible maps of type (P) and common fixed points in non-Archimedean Menger PM-spaces, Bull. Allahabad Math. Soc. 25 (2010), no. 1, 191-200.

37.
W. Sintunavarat and P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math. 2011, Article ID 637958, 14 pages, 2011.

38.
W. Sintunavarat and P. Kumam, Common fixed points for R-weakly commuting in fuzzy metric spaces, Ann. Univ. Ferrara Sez. VII Sci. Mat. 58 (2012), no. 2, 389-406. crossref(new window)

39.
C. Vetro, S. Chauhan, E. Karapinar, and W. Shatanawi, Fixed points of weakly com- patible mappings satisfying generalized $\varphi$-weak contractions, Bull. Malaysian Math. Sci. Soc. (2014), in press.