On the existence of sulutions of the equation Lx ∞ Nx and a coincidence degree theory

The coincidence degree for the pair (L, N) developed by Mawhin (1972) provides a method for proving the existence of solutions of the equation Lx = Nx where L: dom L ⊂ X → Z is a linear Fredholm mapping of index zero and is a (possiblv nonlinear) mapping and Ω is a bounded open subset of X, X and Z being normed linear spaces over the reals. In this paper we have extended the coincidence degree for the pair (L, N) to solve the equation , where L: dom L ⊂ X → Z is a linear Fredholm mapping of index zero, and X, Z and Ω are as above, CK(Z) being the set of compact convex subsets of Z.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 47 H 15, 47 A 50; secondary 47 H 10, 47 A 55.

A common fixed point theorm for six expansive mappings in G-metric spaces

In this paper we obtain a unique common fixed point theorem for six expansive mappings in G –metric spaces. AMS 2000 Subject classification : 47 H 10; 54 H 25. Key words : Expansive mappings; G –metric space; Weakly compatible mappings DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5428 KUSET 2011; 7(1): 113-120

Remarks on Certain Selected Fixed Point Theorems - II

Recent common fixed point theorems due to Kumar et al and Jungck are used to derive two common fixed point theorems for four finite families of mappings in complete and compact metric spaces respectively. AMS (MOS) Subject Classification(2000) : Primary 54 H 25; Secondary 47 H 10. Key Words and phrases: Compatible mapping; coincidentally commuting mappings; coincidence point; fixed point; common fixed point. DOI: 10.3126/kuset.v3i2.2894 Kathmandu University Journal of Science, Engineering and Technology Vol.3, No.2, August 2007, pp 27-30