The propose of this paper is to present a modified block iterative algorithm for finding a common element between the set of solutions of the fixed points of two countable families of asymptotically relatively nonexpansive mappings and the set of solution of the system of generalized mixed equilibrium problems in a uniformly smooth and uniformly convex Banach space. Our results extend many know...

some algorithms for nding common xed point of a family of mappings isconstructed. indeed, let c be a nonempty closed convex subset of a uniformlyconvex banach space x whose norm is gateaux dierentiable and let {tn} bea family of self-mappings on c such that the set of all common fixed pointsof {tn} is nonempty. we construct a sequence {xn} generated by the hybridmethod and also we give the ...

Throughout this paper, we assume that X is a uniformly convex Banach space and X∗ is the dual space of X. Let J denote the normalized duality mapping form X into 2 ∗ given by J x {f ∈ X∗ : 〈x, f〉 ‖x‖2 ‖f‖2} for all x ∈ X, where 〈·, ·〉 denotes the generalized duality pairing. It is well known that if X is uniformly smooth, then J is single valued and is norm to norm uniformly continuous on any b...

Let A be a unital, commutative and finitely generated ring. We prove that if n ≥ 4, then the group G = ELn(A) has a fixed point property for affine isometric actions on B. Here B stands for any L space or any Banach space isomorphic to a Hilbert space. We also verify that the comparison map Ψ : H b (G,B) → H(G,B) from bounded to ordinary cohomology is injective, where G and B are as in above. F...

In this paper, we prove that for a unital commutative and finitely generated ring A, the group G = ELn(A) has a fixed point property for affine isometric actions on B if n ≥ 4. Here B stands for any L space or any Banach space isomorphic to a Hilbert space. We also verify that the comparison map Ψ : H b (G,B) → H (G,B) from bounded to usual cohomology is injective, where G and B are same as in ...

Let E be a real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E∗, and K be a nonempty closed convex subset of E. Suppose that T, S : K → K are two nonexpansive mappings such that F := F (ST ) = F (T ) ∩ F (S) = ∅. For arbitrary initial value x0 ∈ K and fixed anchor u ∈ K, define iteratively a sequence {xn} as follows: { yn = βnxn + (1− βn)Txn xn+...

Let A be a unital, commutative and finitely generated ring. We prove that if n ≥ 4, then the group G = ELn(A) has a fixed point property for affine isometric actions on B. Here B stands for any L space or any Banach space isomorphic to a Hilbert space. We also verify that the comparison map Ψ : H b (G,B) → H(G,B) from bounded to ordinary cohomology is injective, where G and B are as in above. F...

*Correspondence: [email protected]; [email protected] Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300387, China Abstract Let E be a uniformly convex and uniformly smooth Banach space, let C be a nonempty closed convex subset of E, let {Tn} : C→ C be a countable family of weak relatively nonexpansive mappings such that F = ⋂∞ n=1 F(Tn) = ∅. For any given gauss x0 ∈ C,...