Modified multistep iteration for approximating a general class
of functions in locally convex spaces
Received: November 29, 2012; Accepted: September 18, 2013
Abstract. In this paper, we study the convergence of modified multistep iteration and use the scheme to approximate the fixed point of a general class of functions introduced by Bosede and Rhoades in a complete metrisable locally convex space. As corollaries, the convergence results for SP and Mann iterations are also established. Moreover, most convergence results in Banach spaces are generalized to complete metrisable locally convex spaces. Our convergence results generalize and extend the results of Berinde, Olaleru, Phuengrattana and Suantai, Rafiq among others.
Keywords: Strong convergence; modified multistep iteration; general class of functions; fixed point.
AMS Subject classification: Primary: 47H10
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