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. ...

in this article, we apply two new fixed point theorems to investigate the existence of mild solutions for a nonlocal fractional cauchy problem with an integral initial condition in banach spaces.

In this paper, we first study a hierarchical problem of Baillon’s type, and we study a strong convergence theorem of this problem. For the special case of this convergence theorem, we obtain a strong convergence theorem for the ergodic theorem of Baillon’s type. Our result of the ergodic theorem of Baillon’s type improves and generalizes many existence theorems of this type of problem. Two nume...

Motivated by the recent work of Moudafi (Inverse Problem, 26 (2010), 587-600 ), Chang et al. (Appl. Math. Comput. 219, (2013), 1041610424 ), Tang Jinfang (Acta Mathematicae Applicatae Sinica, Vol. 37, (2014), 119-126 ), Wu et al. (Journal of Inequalities and Applications 2014, 2014:428 ) and Chidume et al. (J. Nonlinear Analysis and Optimization (to appear)), we investigate a Krasnoselskii-type...