Let C be a closed convex subset of a uniformly smooth Banach space E, and T : C → E a nonexpansive nonself-mapping satisfying the weakly inwardness condition such that F(T) = ∅, and f : C → C a fixed contractive mapping. For t ∈ (0,1), the implicit iterative sequence {xt} is defined by xt = P(t f (xt) + (1− t)Txt), the explicit iterative sequence {xn} is given by xn+1 = P(αn f (xn) + (1−αn)Txn)...

*Correspondence: [email protected] 4Department of Mathematics, Kyungnam University Masan, Kyungnam, 631-701, Korea Full list of author information is available at the end of the article Abstract A fixed point theorem is obtained for a monotone self-map in a 0-complete ordered partial metric space under Hardy-Rogers-type contractive condition. This result improves some recently obtained on...

Let E be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. Let J {T t : t ≥ 0} be a family of uniformly asymptotically regular generalized asymptotically nonexpansive semigroup of E, with functions u, v : 0,∞ → 0,∞ . Let F : F J ∩t≥0F T t / ∅ and f : K → K be a weakly contractive map. For some positive real numbers λ and δ satisfying δ λ > 1, let G ...

Recently the author [Proc. Amer. Math. Soc. 103(1988), 11291135] proved random versions of an interesting theorem of Ky Fan [Theorem 2, Math. Z. 112 (1969), 234-240] for continuous condensing random maps and nonexpansive random maps defined on a closed convex bounded subset in a separable Hilbert space. In this paper, we prove that it is still true for (more general) continuous 1-set-contractiv...

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...

The influence of fixed point theorems for contractive and nonexpansive mappings see 1, 2 on fixed point theory is so huge that there are many results dealing with fixed points of mappings satisfying various types of contractive and nonexpansive conditions. On the other hand, it is also huge that well-known Brouwer’s and Schauder’s fixed point theorems for set-contractive mappings exert an influ...

in this paper, we prove some coupled coincidence point theorems for mappings satisfying generalized contractive conditions under a new invariant set in ordered cone metric spaces. in fact, we obtain sufficient conditions for existence of coupled coincidence points in the setting of cone metric spaces. some examples are provided to verify the effectiveness and applicability of our results.