Let H be a Hilbert space and let C be a closed convex nonempty subset of H and a non-self nonexpansive mapping. A map defined by . Then, for a fixed and for , Krasnoselskii–Mann algorithm is defined by where . Recently, Colao and Marino (Fixed Point Theory Appl 2015:39, 2015) have proved both weak and strong convergence theorems when C is a strictly convex set and T is an inward mapping. Meanwhile, they proposed a open question for a countable family of non-self nonexpansive mappings. In this article, authors will give an answer and will prove the further generalized results with the examples to support them.

The purpose of this article is to evaluate the definition of a class of intuitionistic fuzzy metric space which was presented by Park [J. H. Park, Chaos Solitons Fractals, 22 (2004), 1039-1046]. This review is also appropriate to the definition of a class of intuitionistic fuzzy normed space which was presented by

In finite set, Choquet fuzzy integral with respect to fuzzy measures can be transferred into linear combination of product, based on this fact we can choose standard optimization technical to determine fuzzy measures. This paper present linear programming and quadratic programming to determine fuzzy measures, the experiments demonstrate that classification accuracy of fuzzy integral with respect to fuzzy measure is better than the classification accuracies of majority voting and weighted average.

The purpose of this paper is to the best proximity point theorems for the proximal nonexpansive mapping on the starshaped sets by using a clever and simple method. The results improve and extend the recent results of Chen et al. (Fixed Point Theory Appl 2015:19, 2015). It should be noted that, the complex method is used by Jianren Chen et al. can be replaced by the clever and simple method presented in this paper.

In this article, a new multidirectional monotone hybrid iteration algorithm for finding a solution to the split common fixed point problem is presented for two countable families of quasi-nonexpansive mappings in Banach spaces. Strong convergence theorems are proved. The application of the result is to consider the split common null point problem of maximal monotone operators in Banach spaces. Strong convergence theorems for finding a solution of the split common null point problem are derived. This iteration algorithm can accelerate the convergence speed of iterative sequence. The results of this paper improve and extend the recent results of Takahashi and Yao (Fixed Point Theory Appl 2015:87, 2015) and many others .