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2012•Taiwanese Journal of MathematicsOpen access

STRONG CONVERGENCE THEOREMS BY MONOTONE HYBRID METHOD FOR A FAMILY OF GENERALIZED NONEXPANSIVE MAPPINGS IN BANACH SPACES

Chakkrid Klin-eam, Suthep Suantai, Wataru Takahashi

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Abstract

In this paper, we study monotone hybrid method for finding a commonfixed point of a family of generalized nonexpansive mappings and then prove astrong convergence theorem for a family of generalized nonexpansive mappings inBanach spaces. Using this theorem, we obtain some new results for a generalizednonexpansive mapping and two generalized nonexpansive mappings in Banachspaces. Moreover, we apply our main result to obtain a strong convergence theoremfor a family of nonexpansive mappings in a Hilbert space.

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In this paper, we study monotone hybrid method for finding a commonfixed point of a family of generalized nonexpansive mappings and then prove astrong convergence theorem for a family of generalized nonexpansive mappings inBanach spaces. Using this theorem, we obtain some new results for a generalizednonexpansive mapping and two generalized nonexpansive mappings in Banachspaces. Moreover, we apply our main result to obtain a strong convergence theoremfor a family of nonexpansive mappings in a Hilbert space.

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Available abstract

In this paper, we study monotone hybrid method for finding a commonfixed point of a family of generalized nonexpansive mappings and then prove astrong convergence theorem for a family of generalized nonexpansive mappings inBanach spaces. Using this theorem, we obtain some new results for a generalizednonexpansive mapping and two generalized nonexpansive mappings in Banachspaces. Moreover, we apply our main result to obtain a strong convergence theoremfor a family of nonexpansive mappings in a Hilbert space.

Key concepts: Mathematics, Banach space, Monotone polygon, Hilbert space, Convergence (economics), Pure mathematics, Fixed point, Scheme (mathematics)

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STRONG CONVERGENCE THEOREMS BY MONOTONE HYBRID METHOD FOR A FAMILY OF GENERALIZED NONEXPANSIVE MAPPINGS IN BANACH SPACES — Research Paper | ScholarLens