CONVERGENCE THEOREMS ON ASYMPTOTICALLY GENERALIZED $\PHI-$ PSEUDOCONTRACTIVE MAPPINGS IN THE INTERMEDIATE SENSE

Abstract

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 L-Lipschitzian mappings, Nonlinear Analysis 71 (2009) 2833-2838] and several others.