The Journal of the Indian Mathematical Society

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Implicit Mann Iteration Scheme for Hemicontractive Mappings


Affiliations
1 Hajvery University, 43-52 Industrial Area, Gulberg-III, Lahore, Pakistan
2 Department of Mathematics, Aligarh Muslim University, Aligarh - 202 002, India
     

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The purpose of this paper is to characterize conditions for the convergence of the implicit Mann iterative scheme due to Xu and Ori (An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001), (767-773) to the unique fixed point of φ-hemicontractive mappings defined on a nonempty convex subset of an arbitrary Banach space.

Keywords

Implicit Iterative Scheme, φ-Hemicontractive Mappings, Banach Spaces.
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  • Implicit Mann Iteration Scheme for Hemicontractive Mappings

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Authors

Arif Rafiq
Hajvery University, 43-52 Industrial Area, Gulberg-III, Lahore, Pakistan
Mohammad Imdad
Department of Mathematics, Aligarh Muslim University, Aligarh - 202 002, India

Abstract


The purpose of this paper is to characterize conditions for the convergence of the implicit Mann iterative scheme due to Xu and Ori (An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001), (767-773) to the unique fixed point of φ-hemicontractive mappings defined on a nonempty convex subset of an arbitrary Banach space.

Keywords


Implicit Iterative Scheme, φ-Hemicontractive Mappings, Banach Spaces.