In this paper, we prove strong convergence results for a modified Mann iterative process for a new class of I- nearly weak uniformly L-Lipschitzian mappings in a real Banach space. The class of I-nearly weak uniformly L-Lipschitzian mappings is an interesting generalization of the class of nearly weak uniformly L-Lipschitzian mappings which inturn is a generalization of the class of nearly unif...

*Correspondence: [email protected] Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand Abstract We prove a convergence theorem of the Mann iteration scheme for a uniformly L-Lipschitzian asymptotically demicontractive mapping in a CAT(κ ) space with κ > 0. We also obtain a convergence theorem of the Ishikawa iteration scheme for a uniformly L-Lipsc...

in this paper, we obtained the convergence of modified noor iterative scheme for nearly lipschitzian maps in real banach spaces. our results contribute to the literature in this area of re- search.

Suppose that C is a nonempty closed convex subset of a real uniformly convex Banach space X . Let T : C→ C be an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that if T is uniformly L-Lipschitzian and completely continuous, then the iterative scheme converges strongly to some fixed point...

In this paper, we show that the modified Mann iteration with errors converges strongly to fixed point for uniformly L-Lipschitzian asymptotically Φ-pseudocontractive mappings in real Banach spaces. Meanwhile, it is proved that the convergence of Mann and Ishikawa iterations is equivalent for uniformly L-Lipschitzian asymptotically Φpseudocontractive mappings in real Banach spaces. Finally, we o...

In this paper, under some new appropriate conditions imposed on the parameters and mappings involved in proximal mapping associated with a general H-monotone operator, its Lipschitz continuity is proved an estimate of constant computed. The main contribution work establishment equivalence relationship between graph convergence sequence strongly their mappings, respectively, to given by using no...

* Correspondence: [email protected]. edu.cn School of Computer and Information Engineering, Zhejiang Gongshang University, Hangzhou 310018, People’s Republic of China Full list of author information is available at the end of the article Abstract In this article, we introduce the concept of nonself uniformly quasi-Lipschitzian mapping and consider a new iterative scheme with errors to converge t...

We consider another class of generalized Lipschitzian type mappings and utilize the same to prove fixed point theorems for asymptotically regular and uniformly generalized Lipschitzian one-parameter semigroups of self-mappings defined on bounded metric spaces equipped with uniform normal structure which yield corresponding results in respect of semigroup of iterates of a self-mapping as corolla...