THE EQUIVALENCE OF JUNGCK-TYPE ITERATIONS FOR GENERALIZED CONTRACTIVE-LIKE OPERATORS IN A BANACH SPACE

We show that the convergences of Jungck, Jungck- Mann, Jungck-Ishikawa, Jungck-Noor and Jungck-multistep itera- tion processes are equivalent for a class of generalized contractive- like operators defined on a Banach space. Our results are general- izations and extensions of the work of Soltuz [20, 21], Zhiqun [23] and some other numerous ones 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

On Convergence and Stability of the Generalized Noor Iterations for a General Class of Operators

In this paper, we establish some strong convergence and stability results of multistep iterative scheme for a general class of operators introduced by Bosede and Rhoades [5] in a Banach space. As corollaries, some convergence and stability results for the Noor, Ishikawa, Mann and Picard iterative schemes are also established. Our convergence results generalize and extend the results of Berinde [3], Bosede [4], Olaleru [16], Rafiq [21, 22] among others, while our stability results are extensions and generalizations of multitude of results in the literature, including the results of Berinde [1], Bosede and Rhoades [5], Imoru and Olatinwo [9] and Osilike [18]

COMMON FIXED POINTS OF A THREE-STEP ITERATION WITH ERRORS OF ASYMPTOTICALLY QUASI-NONEXPANSIVE NONSELF-MAPPINGS IN THE INTERMEDIATE SENSE IN BANACH SPACES

In this paper, we extend the results of Inprasit and Wattanataweekul [7] to the class of asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense. We prove some strong convergence theorems for asymptotically quasi-nonexpansive nonself-mappings in the intermediate sense using a three-step iterative method for finding a common element of the set of solutions of a generalized mixed equilibrium problem and the set of common fixed points of a finite family of nonexpansive mappings in a real Hilbert space. Our results extends, improves, unifies and generalizes the results of [13], [25] and [27]

Convergence Theorems for Asymptotically Pseudocontractive Mappings in the Intermediate Sense for the Modified Noor Iterative Scheme

We study the convergence of the modi�ed Noor iterative scheme for the class of asymptotically pseudocontractive mappings in the intermediate sense which is not necessarily Lipschitzian. Our results improves, extends and unifies the results of [Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, Mathematical Analysis and Applications, 158 (2) (1991) 407-413] and [Qin et al.Convergence theorems on asymptotically pseudocontractive mappings in the intermediate sense, Fixed Point Theory and Applications, 2010, Article ID 186874, 14 pages, (2010)]

Modified Noor iterations with errors for nonlinear equations in Banach spaces

We introduce a new three step iterative scheme with errors to approximate the unique common fixed point of a family of three strongly pseudocontractive (accretive) mappings on Banach spaces. Our results are generalizations and improvements of results obtained by several authors in literature. In particular, they generalize and improve the results of Mogbademu and Olaleru [A. A. Mogbademu and J. O. Olaleru, Bull. Math. Anal. Appl., 3 (2011), 132-139], Xue and Fan [Z. Xue and R. Fan, Appl. Math. Comput., 206(2008), 12-15] which is in turn a correction of Rafiq [A. Rafiq, Appl. Math. Comput., 182 (2006), 589-595]

THE CONVERGENCE OF JUNGCK-TYPE ITERATIVE SCHEMES FOR GENERALIZED CONTRACTIVE-LIKE OPERATORS

We introduce the Jungck-multistep iteration and show that it converges strongly to the unique common fxed point of a pair of weakly compatible generalized contractive-like opera-tors defined on a Banach space. As corollaries, the results show that the Jungck-Mann, Jungck-Ishikawa and Jungck-Noor itera- tions can also be used to approximate the common fixed points of such maps. The results are improvements, generalizations and ex- tensions of the work of Olatinwo and Imoru [13], Olatinwo [14-15]. Consequently, several results in literature are generalized

On Multistep Iterative Scheme for Approximating the Common Fixed Points of Contractive-Like Operators

We introduce the Jungck-multistep iteration and show that it converges strongly to the unique common fixed point of a pair of weakly compatible generalized contractive-like operators defined on a Banach space. As corollaries, the results show that the Jungck-Mann, Jungck-Ishikawa, and Jungck-Noor iterations can also be used to approximate the common fixed points of such maps. The results are improvements, generalizations, and extensions of the work of Olatinwo and Imoru (2008), Olatinwo (2008). Consequently, several results in literature are generalized

Strong Convergence Theorems for Asymptotically Pseudocontractive Mappings in the Intermediate Sense

In this study, we prove a strong convergence of Noor type scheme for a uniformly L-Lipschitzian and asymptotically pseudocontractive mappings in the intermediate sense without assuming any form of compactness. Consequently, we also obtain a convergence result for the class of asymptotically strict pseudocontractive mappings in the intermediate sense. Our results are improvements and extensions of some of the results in literature