We investigate the relation between the structure of a Moufang loop and its inner mapping group. Moufang loops of odd order with commuting inner mappings have nilpotency class at most two. 6-divisible Moufang loops with commuting inner mappings have nilpotency class at most two. There is a Moufang loop of order 2 with commuting inner mappings and of nilpotency class three.

The concept of 2-metric space is a natural generalization of the metric space. Initially, it has been investigated by Gähler [3] and has been developed broadly by Gähler [4, 5] and more. After this number of fixed point theorems have been proved for 2-metric spaces by introducing compatible mappings, which are more general than commuting and weakly commuting mappings. Jungck and Rhoades defined...

The concept of a 2-metric space is a natural generalization of a metric space. It has been investigated initially by Gähler [4]. Iseki [5] studied the fixed point theorems in 2-metric spaces. Sessa [17] defined weak commutativity and proved common fixed point theorem for weakly commuting maps. In [7] Jungck introduced more generalized commuting mappings, called compatible mappings, which are mo...

Three variants of R-weakly commuting mappings in the realm of uniform spaces are defined. Examples are included to reflect upon the distinctiveness of the notions so defined. Common fixed point theorems concerning these variants of R-weakly commuting mappings in the framework of uniform spaces are obtained. This generalizes several known results in the literature including those of Granas and D...

In this paper, we prove common fixed point theorems for four mappings by using pointwise R-weakly commuting and reciprocally continuous mappings satisfying contractive condition in intuitionistic fuzzy metric spaces. AMS Subject Classification: 47H10, 54H25