Hossein Dehghan

Approximating fixed points of asymptotically nonexpansive mappings in Banach spaces by metric projections

Abstract In this paper, a strong convergence theorem for asymptotically nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem extends and improves the recent strong convergence theorem due to Matsushita and Takahashi [S. Matsushita, W. Takahashi, Approximating fixed points of nonexpansive mappings in a Banach space by metric projections, Appl. Math. Comput. 196 (2008) 422–425] which was established for nonexpansive mappings.

Approximating Fixed Points of Non-Lipschitzian Mappings by Metric Projections

We define and study a new iterative algorithm inspired by Matsushita and Takahashi (2008). We establish a strong convergence theorem of the proposed algorithm for asymptotically nonexpansive in the intermediate sense mappings in uniformly convex and smooth Banach spaces by using metric projections. This theorem generalizes and refines Matsushita and Takahashis strong convergence theorem which was established for nonexpansive mappings.

Strong convergence of a CQ method for k-strictly asymptotically pseudocontractive mappings

Let E be a real q-uniformly smooth Banach space, which is also uniformly convex (for example, Lp or ℓp spaces, 1<p<∞), and C be a nonempty bounded closed convex subset of E. Let T:C→C be a k-strictly asymptotically pseudocontractive map with a nonempty fixed point set. A hybrid algorithm is constructed to approximate fixed points of such maps. Furthermore, strong convergence of the proposed algorithm is established.

Comment on ‘Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory and Applications, doi:10.1186/1687-1812-2011-93, 20 pages’

In this paper, we provide an example to show that some results obtained in [Mongkolkeha et al. in Fixed Point Theory Appl. 2011, doi:10.1186/1687-1812-2011-93] are not valid.MSC:47H09, 47H10.

Some Monotonicity Properties of Convex Functions with Applications

We mainly establish a monotonicity property between some special Riemann sums of a convex function f on [a, b], which in particular yields that

A Characterization of Metric Projection in CAT(0) Spaces

{\frac{b-a}{n+1} \sum_{i=0}^n f\left(a+i\frac{b-a}{n} \right)}

A New Three-Step Mean Value Iterations with Errors for Asymptotically Nonexpansive Mappings in Banach Spaces

b-an+1∑i=0nfa+ib-an is decreasing while