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Fixed points of nonexpansive and quasi-nonexpansive mappings

Original Research Paper
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Abstract

In the paper Krasnoselskii–Mann method for non-self mappings in the journal of Fixed Point Theory and Applications, Colao and Marino proved strong convergence of Krasnoselskii–Mann algorithm defined by \(x_{n+1}=\alpha _nx_n+(1-\alpha _n)Tx_n\) for a non-expansive non-self mapping in a Hilbert space and they proposed three open questions. In this paper we have proved theorems that are answers to all the open questions raised in that paper by relaxing the space, involved map and inward condition to be uniformly convex Banach space, quasi-nonexpansive and weakly inward condition respectively. An application of non-linear parabolic partial differential equation is discussed.We also provide numerical example to verify our main result.

Keywords

Uniformly convex Banach space Quasi-nonexpansive Weakly inward 

Mathematics Subject Classification

58J20 47H09 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

  1. 1.Department of MathematicsThe Gandhigram Rural Institute (Deemed to be University)GandhigramIndia
  2. 2.Department of MathematicsBharathidasan UniversityTiruchirappalliIndia

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