In this paper, several weak and strong convergence theorems are established for a new modified iterations with errors for finite family of nonself asymptotically nonexpansive mappings in Banach spaces. Mann-type, Ishikawa-type and Noor-type iterations are covered by the new iteration scheme. Our convergence theorems improve, unify and generalize many important results in the current literatures.

In this paper, the equivalence of the convergence among Mann-Ishikawa and Noor iterations is obtained for uniformly L-Lipschitzian mappings in real Banach spaces. Our results extend and improve the corresponding results in Chang [3] and Ofoedu [4]. Mathematics subject classification (2010): 47H10, 47H09, 46B20..

We consider the relaxed and contraction-proximal point algorithms in Hilbert spaces. Some conditions on the parameters for guaranteeing the convergence of the algorithm are relaxed or removed. As a result, we extend some recent results of Ceng-Wu-Yao and Noor-Yao.

In this paper, we study strong convergence as well as stability results for a pair of nonself mappings using Jungck-SP iterative scheme and a certain contractive condition. Moreover, with the help of computer programs in C++, we show that Jungck-SP iterative scheme converges faster than Jungck-Noor, Jungck-Ishikawa and Jungck-Mann iterative schemes through example. General Terms Computational M...

Summeya Munawar, Muhammad Awais Ghani, Basharat Ali, Azam, Zahid Rashid, Romana Anjum, Sarwar, Tanveer Ahmad, Anam Noor, Qumer Iqbal, Kaiser Latif Cheema, Muzammil Jahangir, Jahanzeb Mehran Abbas