Novel fixed point results for a class of enriched nonspreading mappings in real Banach spaces

Abstract

A modified Halpern-type iterative technique, having weak and strong convergence results for approximating invariant points of a new class of enriched nonspreading operators subject to some standard mild conditions in the setting of real Banach spaces, was presented in this work. It was demonstrated with an example that the class of enriched nonspreading mappings includes the class of nonspreading mappings. Again, it was demonstrated with nontrivial examples that the class of enriched nonspreading mappings and the class of enriched nonexpansive mappings are independent. Some basic properties of the class of enriched nonspreading mappings were established. The results obtained solve the open question raised in Nonlinear Analysis 73 (2010): 1562–1568 for nonspreading-type mappings incorporating an averaged mapping. Moreover, we studied the estimation of common invariant points of this new class of mappings and the class of enriched nonexpansive operators and provided a strong convergence theorem for these mappings.