# Search Results

## You are looking at 1 - 2 of 2 items for :

- Author or Editor: H. Tan x

- Mathematics and Statistics x

- Refine by Access: All Content x

## Summary

Some stability and convergence theorems of the modified Ishikawa iterative sequences with errors for asymptotically nonexpansive mapping in the intermediate sense and asymptotically pseudo contractive and uniformly Lipschitzian mappings in Banach spaces are obtained.

We prove that

$\sum _{k=1}^{n}\frac{\mathrm{sin}\text{k}\theta}{k}}\le \frac{\pi -\theta}{\pi}{\displaystyle {\int}_{o}^{\pi}\frac{\mathrm{sin}t}{t}}dt+\frac{1}{2}\mathrm{sin}\theta +\frac{1}{2}\left(\frac{1}{\pi}{\displaystyle {\int}_{0}^{\pi}\frac{\mathrm{sin}t}{t}dt-\frac{1}{2}}\right)\mathrm{sin}2\theta $

for all integers n ≥ 1 and ɵ ≤ 8 ≤ π. This result refines inequalities due to Jackson (1911) and Turán (1938).