Let C be a nonempty closed convex subset of a complete CAT (0) space and T: C®C be a generalized NONEXPANSIVE mapping with F (T)={x Î C: T (x)=x} ¹Æ. Suppose {xn} is generated iteratively by x1 Î C,xn+1=tnT[snTxn Å (1-sn) xn] Å (1-tn) xn,for all n ³ 1, where {tn} and {sn} are real sequences in [0, 1] such that one of the following two conditions is satisfied: (i)tn Î [a, b] and sn Î [0, 1], for some a, b with 0<a £ b<1, (ii)tn Î [a, 1] and sn Î [a, b], for some a, b with 0<a £ b<1.Then, the sequence{xn}, D-converges to a fixed point of T. Our results extend the ones in Laokul and Panyanak.

In this paper, we present some common fixed point theorems for two generalized NONEXPANSIVE multivalued MAPPINGS in CAT (0) spaces as well as in UCED Banach spaces. Moreover, we prove the existence of fixed points for generalized NONEXPANSIVE multivalued MAPPINGS in complete geodesic metric spaces with con- vex metric for which the asymptotic center of a bounded sequence in a bounded closed convex subset is nonempty and singleton. The results obtained in this paper extend and improve some recent results.

We  rst obtain some properties of a fundamentally NONEXPANSIVE self-mapping on a nonempty subset of a Banach space and next show that if the Banach space is having the Opial condition, then the  xed points set of such a mapping with the convex range is nonempty. In particular, we establish that if the Banach space is uniformly convex, and the range of such a mapping is bounded, closed and convex, then its the  xed points set is nonempty, closed and convex.

In this paper, we propose a generalized iterative method for finding a common element of the set of fixed points of a single nonexpannsive mapping and the set of solutions of two variational inequalities with inverse STRONGLY monotone MAPPINGS and strictly pseudo-contractive of Browder-Petryshyn type mapping. Our results improve and extend the results announced by many others.

X. Qin and Y. Su proved a strong convergence theorems of modified Ishikawa iteration by CQ method for relatively NONEXPANSIVE MAPPINGS in a Banach space [Xiao long Qin, Yongfu Su, Nonlinear Anal. 67 (2007), no. 6, 1958–1965]. The result of this paper extends and improves the result of X. Qin and Y. Su in the two respects: (1). By using the monotone CQ method to modify the CQ method, so that the new method of proof is used. (2). Relax the restriction on T from uniformly continuous to continuous. The result of this paper also extends and improves the recent ones announced by Nakajo, Takahashi, Kim, Martinez-Yanes, Xu and some others.

In this paper, motivated by [F. Vetro, Filomat, 29: 9 (2015), 2011– 2020] we present some fixed point results for a class ofNONEXPANSIVE self-MAPPINGS and multi-valued MAPPINGS in theframework of $b$-metric spaces. Our results generalize and improvethe consequences of [ Khojasteh et al. Abstract and AppliedAnalysis, vol. 2014, Article ID 325840, 5 pages, 2014. ] and [F. Vetro, Filomat, 29: 9 (2015), 2011– 2020]. Some examples are provided to illustrate our results.

A normed space X is said to have the  xed point property, if for each NONEXPANSIVE mapping T: E 􀀀 ! E on a nonempty bounded closed convex subset E of X has a  xed point. In this paper, we  rst show that if X is a locally compact Hausdor space then the following are equivalent: (i) X is in nite set, (ii) C0(X) is in nite dimensional, (iii) C0(X) does not have the  xed point property. We also show that if A is a commutative complex C? {algebra with nonempty carrier space, then the following statements are equivalent: (i) Carrier space of A is in nite, (ii) A is in nite dimensional, (iii) A does not have the  xed point property. Moreover, we show that if A is an in nite dimensional complex C? {algebra (not necessarily commutative), then A does not have the  xed point property.

The aim of this paper is to prove a common  xed 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  xed points of NONEXPANSIVE type multivalued and single valued maps, European J. Pure Appl. Math., 4 (2011) 330-339].

A new approximation method for the set of common fixed points of NONEXPANSIVE MAPPINGS and the set of solutions of systems of variational inequalities is introduced and studied. More-over, we apply our main result to obtain strong convergence theorem to a common fixed point of a NONEXPANSIVE mapping and solutions of a system of variational inequalities of an inverse STRONGLY mono-tone mapping and strictly pseudo-contractive mapping of Browder-Petryshyn type.