Fixed Point Iterations of a Pair of Hemirelatively Nonexpansive Mappings

Fixed Point Iterations of a Pair of Hemirelatively Nonexpansive Mappings

where 〈·, ·〉 denotes the generalized duality pairing. A Banach space E is said to be strictly convex if ‖ x y /2‖ < 1 for all x, y ∈ E with ‖x‖ ‖y‖ 1 and x / y. It is said to be uniformly convex if limn→∞‖xn − yn‖ 0 for any two sequences {xn} and {yn} in E such that ‖xn‖ ‖yn‖ 1 and limn→∞‖ xn yn /2‖ 1. Let UE {x ∈ E : ‖x‖ 1} be the unit sphere of E. Then the Banach space E is said to be smooth ...

Ishikawa Iterations for Equilibrium and Fixed Point Problems for Nonexpansive Mappings in Hilbert Spaces

In this paper, we introduce an iterative scheme Ishikawa-type for finding a common element of the set EP (G) of the equilibrium points of a bifunction G and the set Fix(T ) of fixed points of a nonexpansive mapping T in a Hilbert space H. We prove that the method converges strongly to an element z ∈ Fix(T ) T EP (G) which is the unique solution of the variational inequality 〈(A− γf)z, x− z〉 ≥ 0...

Common fixed point theorem for nonexpansive type single valued mappings

The aim of this paper is to prove a common fixed point theorem for nonexpansive type single valued mappings which include both continuous and discontinuous mappings by relaxing the condition of continuity by weak reciprocally continuous mapping. Our result is generalize and extends the corresponding result of Jhade et al. [P.K. Jhade, A.S. Saluja and R. Kushwah, Coincidence and fixed points of ...

Approximating fixed points of generalized nonexpansive mappings

On Fixed Point Theorems of Nonexpansive Mappings in Product Spaces

We prove some fixed point theorems for nonexpansive selfand non-self-mappings in product spaces; in particular, we provide a constructive proof of a result of Kirk and Martinez and a partial answer to a question of Khamsi. Our proofs are elementary in the sense that we do not use any universal (or ultra) nets.