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 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