Fixed point theorems for uniformly generalized Kannan type semigroup of self-mappings

In this paper, we consider a new uniformly generalized Kannan type semigroup of self-mappings defined on a closed convex subset of a real Banach space equipped with uniform normal structure and employ the same to show that such semigroup of self-mappings admits a common fixed point provided the underlying semigroup of self-mappings has a bounded orbit.

A fixed point theorem for uniformly Lipschitzian mappings in modular vector spaces

We give a fixed point theorem for uniformly Lipschitzian mappings defined in modular vector spaces which have the uniform normal structure property in the modular sense. We also discuss this result in the variable exponent space lp(.) = {(xn) ? RN; ?? n=0 ??xn?p(n) < ? for some ? > 0.