APPROXIMATION OF FIXED POINTS OF STRONGLY PSEUDOCONTRACTIVE MAPPINGS IN UNIFORMLY SMOOTH BANACH SPACES

Let E be a real uniformly smooth Banach space, and K a nonempty closed convex subset of E. Assume that T 1 + T 2 : K → K is a continuous and strongly pseudocontractive mapping, where T 1 : K → K is Lipschitz and T 2 : K → K has the bounded range mapping. Then the Ishikawa iterative sequence converges strongly to the unique fixed point of T 1 + T 2

APPROXIMATION OF FIXED POINTS OF STRONGLY PSEUDOCONTRACTIVE MAPPINGS IN UNIFORMLY SMOOTH BANACH SPACES

Let E be a real uniformly smooth Banach space, and K a nonempty closed convex subset of E. Assume that T 1 + T 2 : K → K is a continuous and strongly pseudocontractive mapping, where T 1 : K → K is Lipschitz and T 2 : K → K has the bounded range mapping. Then the Ishikawa iterative sequence converges strongly to the unique fixed point of T 1 + T 2

APPROXIMATION OF FIXED POINTS OF SOME CLASSES OF NONLINEAR MAPPINGS

We introduce a new class of nonlinear mappings, the class of generalized strongly successively Phi- hemicontractive mappings in the intermediate sense and prove the convergence of Mann type iterative scheme with errors to their fixed points. This class of nonlinear mappings is more general than those defined by several authors. In particular, the class of generalized strongly successively Phi- hemicontractive mappings in the intermediate sense introduced in this study is more general than the class defined by Liu et al. [Z. Liu, J. K. Kim and K. H. Kim, Convergence theorems and stability problems of the modified Ishikawa iterative sequences for strictly successively hemicontractive mappings, Bull. Korean Math. Soc. 39 (2002), No. 3, pp. 455-469]

Convergence theorems for common fixed point of the family of nonself and nonexpansive mappings in real Banach spaces

In this paper, we construct cyclic-Mann type of iterative method for approximating a common fixed point of the finite family of nonself and nonexpansive mappings satisfying inward condition on a non-empty, closed and convex subset of a real uniformly convex Banach space . We also construct the averaging algorithm to the class of nonexpansive mappings in 2-uniformly smooth Banach space. We prove weak and strong convergence results for the iterative method. The results of this work extend results in the literature

Approximation of common fixed points of a countable family of continuous pseudocontractions in a uniformly smooth Banach space

AbstractIn this paper, we introduce a new implicit iterative algorithm for finding a common element of a countable family of continuous pseudocontractions in a uniformly smooth Banach space. We obtain some strong convergence theorems under suitable conditions. Our results extend the recent results announced by many others

Convergence Theorems on Generalized Strongly Successively Phi-pseudocontractive Mappings in the Intermediate Sense

We introduce a new class of nonlinear mappings, the class of generalized strongly successively Phi-pseudocontractive mappings in the intermediate sense and prove the convergence of Mann type iterative scheme to their fixed points. Our results improves and generalizes several other results in literature

Convergence theorems on asymptotically demicontractive and hemicontractive mappings in the intermediate sense

In this study, we introduce two classes of nonlinear mappings, the class of asymptotically demicontractive mappings in the intermediate sense and asymptotically hemicontractive mappings in the intermediate sense and prove the convergence of Mann-type and Ishikawa-type iterative schemes to their respective fixed points. Our results are improvements and generalizations of the results of several authors in the literature