zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Some common fixed point theorems for a pair of tangential mappings in symmetric spaces. (English) Zbl 1213.54066
In this note the authors consider two common fixed point theorems proved by R. P. Pant [J. Math. Anal. Appl. 240, No. 1, 280–283 (1999; Zbl 0933.54031)] and by K. P. R. Sastry and J. S. R. Krishma Murthy [ibid. 250, No. 2, 731–734 (2000; Zbl 0977.54037)] and prove their analogues in a symmetric space setting. Let us recall that a notion of a symmetric on a non-empty set was introduced by Menger in 1928 and it denotes a function d:X×X[0,+) such that d(y,x)=d(x,y) and d(x,x)=0 (for all x,yX ).

MSC:
54H25Fixed-point and coincidence theorems in topological spaces
54E25Semimetric spaces
References:
[1]Galvin, F.; Shore, S. D.: Completeness in semi-metric spaces, Pacific J. Math. 113, 67-75 (1984) · Zbl 0558.54019
[2]Wilson, W. A.: On semi-metric spaces, Amer. J. Math. 53, 361-373 (1931) · Zbl 0001.22804 · doi:10.2307/2370790
[3]Aliouche, A.: A common fixed point theorem for weakly compatible mappings in symmetric spaces satisfying a contractive condition of integral type, J. math. Anal. appl. 322, 796-802 (2006) · Zbl 1111.47046 · doi:10.1016/j.jmaa.2005.09.068
[4]Burke, D. K.: Cauchy sequences in semi-metric spaces, Proc. amer. Math. soc. 33, 161-164 (1972) · Zbl 0233.54015 · doi:10.2307/2038192
[5]Pant, R. P.: Common fixed points of non-commuting mappings, J. math. Anal. appl. 188, 436-440 (1994) · Zbl 0830.54031 · doi:10.1006/jmaa.1994.1437
[6]Pant, R. P.: R-weak commutativity and common fixed points of non-compatible maps, Ganita 49, 19-27 (1998) · Zbl 0977.54039
[7]Aamri, M.; El Moutawakil, D.: Some new common fixed point theorems under strict contractive conditions, J. math. Anal. appl. 270, 181-188 (2002) · Zbl 1008.54030 · doi:10.1016/S0022-247X(02)00059-8
[8]Sastry, K. P. R.; Murthy, I. S. R. Krishna: A common fixed points of two partially commuting tangential selfmaps on a metric space, J. math. Anal. appl. 250, 731-734 (2000) · Zbl 0977.54037 · doi:10.1006/jmaa.2000.7082
[9]Jungck, G.: Common fixed points for non-continuous non-self maps on non-metric spaces, Far east J. Math. sci. 4, No. 2, 199-215 (1996) · Zbl 0928.54043
[10]Jungck, G.; Rhoades, B. E.: Fixed point theorems for occasionally weakly compatible mappings, Fixed point theory 7, No. 2, 287-296 (2006) · Zbl 1118.47045
[11]Pant, R. P.: Common fixed points of Lipschitz type mapping pairs, J. math. Anal. appl. 248, 280-283 (1999) · Zbl 0933.54031 · doi:10.1006/jmaa.1999.6559