CONVERGENCE THEOREMS ON ASYMPTOTICALLY GENERALIZED Phi-PSEUDOCONTRACTIVE MAPPINGS IN THE INTERMEDIATE SENSE

In this study, we introduce the class of asymptotically generalized 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 the results of Kim et al. [J. K. Kim, D. R. Sahu, Y. M. Nam, Convergence theorem for fixed points of nearly LLipschitzian mappings, Nonlinear Analysis 71 (2009) 28332838] and several others

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]

Strong convergence and stability of Kirk-multistep-type iterative schemes for contractive-type operators

In this paper, we introduce Kirk-multistep and Kirk-multistep-SP iterative schemes and prove their strong convergences and stabilities for contractive-type operators in normed linear spaces. By taking numerical examples, we compare the convergence speed of our schemes (Kirk-multistep-SP iterative schemes) with the others (Kirk-SP,Kirk-Noor, Kirk-Ishikawa, Kirk-Mann and Kirk iterative schemes) for this class of operators. Our results generalize and extend most convergence and stability results in the literature

Existence of Fixed Points of Some Classes of Nonlinear Mappings in Spaces with Weak Uniform Normal Structure

In this paper, we prove some �xed point results for some classes of nonlinear mappings recently introduced by Okeke and Olaleru [5]. Our results improves several other known results in literature, including the results of Sahu et al. [8] and Sahu [7]

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

Some new coupled fixed point theorems on partial metric spaces

In this paper, we obtain some new coupled fixed point theorems for mappings satisfying some contractive conditions on complete partial metric space. Our results unify, extend and generalize the results of [3] and [12]

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 and almost sure T-stability for a random iterative sequence generated by a generalized random operator

The aim of this paper is to introduce the concept of generalized φ-weakly contraction random operators and then to prove the convergence and almost sure T-stability of Mann and Ishikawa-type random iterative schemes. We also prove that a random fixed point of such operators is Bochner integrable. Our results generalize, extend and improve various results in the existing literature including the results in Berinde (Bul. ¸Stiin¸t. - Univ. Baia Mare, Ser. B Fasc. Mat.-Inform. 18(1):7-14, 2002), Olatinwo (J. Adv. Math. Stud. 1(1):5-14, 2008), Rhoades (Trans. Am. Math. Soc. 196:161-176, 1974; Indian J. Pure Appl. Math. 21(1):1-9, 1990; Indian J. Pure Appl. Math. 24(11):691-703, 1993) and Zhang et al. (Appl. Math. Mech. 32(6):805-810, 201

Existence of Fixed Points of Some Classes of Nonlinear Mappings in Spaces with Weak Uniform Normal Structure

In this paper, we prove some fixed point results for some classes of nonlinear mappings recently introduced by Okeke and Olaleru [5]. Our results improves several other known results in literature, including the results of Sahu et al. [8] and Sahu [7]

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]