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...

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.

*Correspondence: [email protected] 3Department of Mathematics, Sari Branch, Islamic Azad University, Sari, Iran Full list of author information is available at the end of the article Abstract In this paper, we introduce and consider a new system of generalized nonlinear mixed variational inequalities involving six different nonlinear operators and discuss the existence and uniqueness of s...

*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 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...

Let C be a nonempty convex subset of a real Banach space E in which the normalized duality map is norm-to-norm uniformly continuous on bounded subsets of E. Let T be a nearly uniformly L−Lipschitzian asymptotically generalized Φ-hemicontractive map in the intermediate sense. An iterative process of the Manntype is proved to converge strongly to the unique fixed point of T . Under this setting, ...

* Correspondence: [email protected] Department of Mathematics Education and RINS, Gyeongsang National University, Chinju 660-701, Korea Full list of author information is available at the end of the article Abstract The purpose of this paper is to introduce a new system of general nonlinear regularized nonconvex variational inequalities and verify the equivalence between the proposed system and f...

We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.

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.