Cite this article:
Koparde and Waghmode (1993). Study of commuting mappings in Hilbert space. Journal of Ravishankar University (Part-B: Science), 6(1), pp. 53-56.
J. Ravishaokar University. Vol.6, No. 8 (Science) 1993 PP. 53-56.
Study of commuting
mappings in Hilbert space
P.V. Koparde and B.B. Waghmode
Department of Mathematics, Shivaji
University, Kolhapur-416004
MS: Received:
22.6.90, Accepted: 11.10.93.
Abstract. In this paper we have obtained
unique common fixed point for two mappings S
and T which are e6ntinuous. Commuting self mappings on a dosed subset X of a Hilbert space
H and
saatisfy the conditions,
(i)
S(X) < T(X)
(ii)
|| Sx- Sy ||2 < a ||Tx - Sx||2 +b || Ty - Sy ||2
+c || Tx – Ty ||2
For
all x, y in X where a,b,c are non-negative real numbers satisfying
(iii)
0 < a + b + c < 1
Key words: Fixed point,
Commuting mappings, Recursive iteration.
NOTE: Full version of this manuscript is
available in PDF.