Some fixed point theorems in Banach spaces
The aim of this paper is to introduce the concepts of compatible mappings and compatible mappings of type in non-Archimedean Menger probabilistic normed spaces and to study the existence problems of common fixed points for compatible mappings of type , also, we give an applications by using the main theorems.
A generalization is obtained for some of the fixed point theorems of Khan, Swaleh and Sessa, Pathak and Rekha Sharma, and Sastry and Babu for a self-map on a metric space, which involve the idea of alteration of distances between points.
The Fixed Point Theory for nonexpansive mappings is strongly based upon the geometry of the ambient Banach space. In section 1 we state the role which is played by the multidimensional convexity and smoothness in this theory. In section 2 we study the computation of the normal structure coefficient in finite dimensional lp-spaces and its connection with several classic geometric problems.