Convergence for a Fixed Point of Evolution Families in Banach Space via Iterative Process

On iterative fixed point convergence in uniformly convex Banach space and Hilbert space

Some fixed point convergence properties are proved for compact and demicompact maps acting over closed, bounded and convex subsets of a real Hilbert space. We also show that for a generalized nonexpansive mapping in a uniformly convex Banach space the Ishikawa iterates converge to a fixed point. Finally, a convergence type result is established for multivalued contractive mappings acting on clo...

Convergence of Approximating Fixed Point Sequences for Nonexpansive Mappings in a Banach Space

In this paper, a strong convergence theorem for nonexpansive mappings in a uniformly convex and smooth Banach space is proved without using Bruck’s result, see RE Bruck (Bruck 1981). This theorem is different from the recent strong convergence theorems due to S Matsushita and W Takahashi (Matsushita and Takahashi 2008) and HK Xu (Xu 2006).

A composite explicit iterative process with a viscosity method for Lipschitzian semigroup in a smooth Banach space

Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces

and Applied Analysis 3 Recall that the Bregman projection [13] of x ∈ int domf onto the nonempty, closed, and convex subset C of domf is the necessarily unique vector projf C (x) ∈ C satisfying D f (projf C (x) , x) = inf{D f (y, x) : y ∈ C} . (12) Let f : E → (−∞, +∞] be a convex and Gâteaux differentiable function. The function f is said to be totally convex at x ∈ int domf if its modulus of ...

Fixed Point Theorems in Banach Space

In this paper,we establish fixed points theorems in Banach space using Mann Iteration for nonexpansive and asymtotically nonexpansive mappings . Iteration scheme is defined by (2.1) and (2.2). We extended the work of Mann.