Abstract
We connect the F iteration process with the class of generalized α -nonexpansive mappings. Under some appropriate assumption, we establish some weak and strong convergence theorems in Banach spaces. To show the numerical efficiency of our established results, we provide a new example of generalized α -nonexpansive mappings and show that its F iteration process is more efficient than many other iterative schemes. Our results are new and extend the corresponding known results of the current literature.
Highlights
Introduction and PreliminariesOnce an existence of a solution for an operator equation is established in many cases, such solution cannot be obtained by using ordinary analytical methods
To show the numerical efficiency of our established results, we provide a new example of generalized α-nonexpansive mappings and show that its F iteration process is more efficient than many other iterative schemes
We apply the most suitable iterative algorithm on the fixed point equation, and the limit of the sequence generated by this most suitable algorithm is the value of the desired fixed point for the fixed point equation and the solution for the operator equation
Summary
Introduction and PreliminariesOnce an existence of a solution for an operator equation is established in many cases, such solution cannot be obtained by using ordinary analytical methods. To show the numerical efficiency of our established results, we provide a new example of generalized α-nonexpansive mappings and show that its F iteration process is more efficient than many other iterative schemes. In 2008, Suzuki [20] showed that the class of maps endowed with condition ðCÞ is weaker than the notion of nonexpansive maps and proved some related fixed point theorems in Banach spaces.
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