FIXED POINT THEOREMS VIA FAMILY OF MAPS IN WEAK NON-ARCHIMEDEAN MENGER PM-SPACES

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2013, v.20 no.3, pp.181-198

https://doi.org/10.7468/jksmeb.2013.20.3.181

Singh, Deepak (Department of Applied Sciences, NITTTR (Ministry of HRD, Govt. of India))
Ahmed, Amin (Bansal Institute of Science & Technology)

Singh, Deepak, & Ahmed, Amin. (2013). FIXED POINT THEOREMS VIA FAMILY OF MAPS IN WEAK NON-ARCHIMEDEAN MENGER PM-SPACES. 한국수학교육학회지시리즈B:순수및응용수학, 20(3), 181-198, https://doi.org/10.7468/jksmeb.2013.20.3.181

복사

Abstract

C. Vetro [4] gave the concept of weak non-Archimedean in fuzzy metric space. Using the same concept for Menger PM spaces, Mishra et al. [22] proved the common fixed point theorem for six maps, Also they introduced semi-compatibility. In this paper, we generalized the theorem [22] for family of maps and proved the common fixed point theorems using the pair of semi-compatible and reciprocally continuous maps for one pair and R-weakly commuting maps for another pair in Menger WNAPM-spaces. Our results extends and generalizes several known results in metric spaces, probabilistic metric spaces and the similar spaces.

keywords: non-Archimedean Menger PM-spaces, weak non-Archimedean Menger PM-space, R-weakly commuting maps, semi-compatible and reciprocally continuous maps, common fixed point

참고문헌

(1979). On the completion on non-Archimedean probabilistic metric spaces . Seminar de spatii metrice probabiliste, Universitatea Timisoara Nr..

(1977). On non-Archimedean probabilistic metric space. An. Univ. Timisoara Ser. Sti. Mat., 12(2), 115-118.

(1978). Fixed point theorems for some classes of contraction mappings on non-Archimedean probablistic spaces. Publ. Math. (Debrecen), 25, 29-34.

(1975). On some fixed point theorems with applications to the non-Archimedean Menger spaces. Attidella Acad. Naz. Lincei, 58, 374-379.

(1972). Fixed points of contraction mappings on probabilistic metric spaces. Math. Systems Theory, 6, 97-102. 10.1007/BF01706080.

(1997). Remarks on R-weakly commuting maps and common fixed point theorems. Bull. Korean Math. Soc., 34, 247-257.

(1997). Common fixed point theorems for compatible mappings of type(A) in non-Archimedean Menger PM-spaces. Math. Japon., 46, 169-179.

(1998). Compatible mappings of type (C) and common fixed point theorems of Gregus type. Demonstratio Math., 31, 499-518.

(1982). On a weak commutativity condition of mappings in fixed point considerations. Publications de I'Institute Mathematique (Beograd), 32, 149-153.

10.

(1974). On some classes of non-Archimedean probabilistic metric spaces . Seminar de spatii metrice probabiliste, Universitatea Timisoara, Nr..

11.

(1996). Compatible mappings of type (P) and fixed point theorems in metric spaces and probabilistic metric spaces. Novi Sad J. Math., 26, 87-109.

12.

(1971). Complete probabilistic metric spaces. Z. Wahrsch, Verw Gebiete, 20, 117-128. 10.1007/BF00536289.

13.

(1983). Fixed point theorems for a class of mappings on non-Archimedean probablistic metric spaces. Mathematica, 25, 5-9.

14.

(2009). A common fixed point theorem in non-Archimedean Menger PM-space. Novi Sad J. Math., 39, 81-87.

15.

(2008). A common fixed point theorem in 2 non-Archimedean Menger PM-space for R-weakly commuting maps of type (p). Novi Sad J. Math., 38, 145-152.

16.

(2009). Fixed point theorems for expansion mappings in 2 Non-Archimedean Menger PM-spaces. Novi Sad J. Math., 39(2), 51-60.

17.

(2012). A common fixed point theorem in non- Archimedean Menger PM-spaces. Bull. of Int. Math. Virtual Inst., 2, 141-152.

18.

(1994). Common fixed points of non-commuting mappings. J. Math. Anal. Appl., 188, 436-440. 10.1006/jmaa.1994.1437.

19.

(1999). Common fixed points for R-weakly commuting maps in fuzzy metric spaces. Indian J. Pure and Applied Math., 30, 419-423.

20.

(2012). Fixed point theorems in non-Archimedean Menger PM-spaces. J. Non-linear Anal. Opti., 3(2), 153-160.

21.

(1990). Fixed point theorems for single-valued and multivalued mappings in non-archimedean Menger probabilistic metric spaces. Math. Japon., 35, 875-885.

22.

(1977). Semi-compatible and reciprocally con- tinuous maps in weak non-Archimedean Menger Pm-spaces. Filomat, 26(4), 783-792.

23.

(2011). A common fixed point theorem for weakly compatible mappings in non-Archimedean Menger PM-spaces. Mat. Vesnik, 63(4), 285-294.

24.

(2005). Semi-compatibility, compatibility and fixed point theorems in fuzzy metric space. J. Chungcheong Math. Soc., 18, 1-22.

25.

(1960). Statistical metric spaces. Pacific J. Math., 10, 313-334. 10.2140/pjm.1960.10.313.

26.

(2011). Fixed points in weak non-Archimedean fuzzy metric spaces. Fuzzy Sets and Systems, 162, 84-90. 10.1016/j.fss.2010.09.018.

27.

(1988). Fixed point for set valued functions without continuity. Indian J. Pure Appl. Math., 29, 227-238.

28.

(1986). Compatible mappings and common fixed points. Internat. J. Math. Math. Sci., 9, 771-779. 10.1155/S0161171286000935.

29.

(1993). Compatible mappings of type (A) and common fixed points. Math. Japon., 38, 381-391.

30.

(1965). Compatible mappings of type (B) and common fixed point theorems of Gregus type. Czech. Math. J., 45, 685-698.

바로가기메뉴

논문 상세

Vol.20 No.3

FIXED POINT THEOREMS VIA FAMILY OF MAPS IN WEAK NON-ARCHIMEDEAN MENGER PM-SPACES

FIXED POINT THEOREMS VIA FAMILY OF MAPS IN WEAK NON-ARCHIMEDEAN MENGER PM-SPACES

Abstract

참고문헌

한국수학교육학회지시리즈B:순수및응용수학