Abstract
We extend the application of nearly contraction mapping principle introduced by Sahu (2005) for existence of fixed points of demicontinuous mappings to certain hemicontinuous nearly Lipschitzian nonlinear mappings in Banach spaces. We have applied certain results due to Sahu (2005) to obtain conditions for existence—and to introduce an asymptotic iterative process for construction—of fixed points of these hemicontractions with respect to a new auxiliary operator.
Highlights
In this paper, we have applied certain results due to Sahu [1] on nearly contraction mapping principle to obtain conditions for existence of fixed points of certain hemicontinuous mappings and introduced an asymptotic iterative process for construction of fixed points of these hemicontinuous mappings with respect to a new auxiliary operator
We extend the application of nearly contraction mapping principle introduced by Sahu (2005) for existence of fixed points of demicontinuous mappings to certain hemicontinuous nearly Lipschitzian nonlinear mappings in Banach spaces
(i) demicontinuous if whenever a sequence {xn} ⊂ X converges strongly to x ∈ X it implies that the sequence {Txn} converges weakly to Tx ∈ Y; (ii) hemicontinuous if whenever a sequence {xn} ⊂ X converges stronly on a line to x ∈ X it implies that the sequence {Txn} converges weakly to Tx ∈ Y, that is, T(x0 + tnx) ⇀ Tx0 as tn → 0
Summary
We have applied certain results due to Sahu [1] on nearly contraction mapping principle to obtain conditions for existence of fixed points of certain hemicontinuous mappings and introduced an asymptotic iterative process for construction of fixed points of these hemicontinuous mappings with respect to a new auxiliary operator. We extend the application of nearly contraction mapping principle introduced by Sahu (2005) for existence of fixed points of demicontinuous mappings to certain hemicontinuous nearly Lipschitzian nonlinear mappings in Banach spaces.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
