Kohlenbach and Leuştean have shown in 2010 that any asymptotically nonexpansive self-mapping of a bounded nonempty UCW-hyperbolic space has fixed point. In this paper, we adapt construction due to Moloney order provide sequence converges strongly such

We first consider an auxiliary problem for the generalized mixed vector equilibrium problem with a relaxed monotone mapping and prove the existence and uniqueness of the solution for the auxiliary problem. We then introduce a new iterative scheme for approximating a common element of the set of solutions of a generalized mixed vector equilibrium problem with a relaxed monotone mapping and the s...

We introduce a new composite iterative scheme by the viscosity approximation method for nonexpansive mappings andmonotone mappings in a Hilbert space. It is proved that the sequence generated by the iterative scheme converges strongly to a common point of set of fixed points of nonexpansive mapping and the set of solutions of variational inequality for an inversestrongly monotone mappings, whic...

and Applied Analysis 3 If θ ≡ 0, the problem 1.4 reduces into the minimize problem, denoted by arg min φ , which is to find x ∈ C such that φ ( y ) − φ x ≥ 0, ∀y ∈ C. 1.7 The above formulation 1.5 was shown in 11 to covermonotone inclusion problems, saddle point problems, variational inequality problems, minimization problems, optimization problems, variational inequality problems, vector equil...

and Applied Analysis 3 Very recently, Qin et al. 16 proposed the composite Halpern type iterative scheme in a uniformly smooth Banach space as follows: x0 x, u ∈ C, zn γnxn ( 1 − γn ) Txn, yn βnxn ( 1 − βn ) Tzn, xn 1 αnu 1 − αn yn, n ≥ 0, 1.6 and showed strong convergence of the sequence {xn} generated by 1.6 under the following control conditions: i ∑∞ n 0αn ∞; ii limn→∞αn 0, limn→∞βn 0 and 0...

In this paper, we first introduce the class of generalized nonexpansive mappings in Banach spaces. This class contains both the classes of nonexpansive and ̨-nonexpansive mappings. In addition, we obtain some fixed point and coincidence point theorems for generalized nonexpansive mappings in uniformly convex Banach spaces. Our results extend some wellknown results in literature. 2010 Mathematic...

Let K be a nonempty closed convex subset of a reflexive and strictly convex Banach space E with a uniformly Gâteaux differentiable norm, F {T h : h ≥ 0} a generalized asymptotically nonexpansive self-mapping semigroup of K, and f : K → K a fixed contractive mapping with contractive coefficient β ∈ 0, 1 . We prove that the following implicit and modified implicit viscosity iterative schemes {xn}...

We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E. Keywords—Common fixed point, Mann iteration, Multivalued mapping, weak convergence.

Let E be a real reflexive Banach space which has uniformly Gâteaux differentiable norm. Let K be aclosed convex subset of E which is also a sunny nonexpansive retract of E, and T : K → E be nonexpansive mapping satisfying the weakly inward condition and F (T ) = {x ∈ K, Tx = x} 6= ∅, and f : K → K be a contractive mapping. Suppose that x0 ∈ K, {xn} is defined by { xn+1 = αnf(xn) + (1− αn)((1− δ...

Recently, S. Reich and S. Simons provided a novel proof of the Kirszbraun-Valentine extension theorem using Fenchel duality and Fitzpatrick functions. In the same spirit, we provide a new proof of an extension result for firmly nonexpansive mappings with an optimally localized range. Throughout this paper, we assume that X is a real Hilbert space, with inner product p = 〈· | ·〉 and induced norm...