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Mayumi Hojo, Weak convergence theorems for infinite families of extended generalized hybrid mappings in Banach spaces

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DOI: 10.23952/jnva.3.2019.2.05
Volume 3, Issue 2, 1 August 2019, Pages 159-170

 

Abstract. Let E be a real Banach space and let C be a nonempty subset of E. A mapping T:C\rightarrow E is said to be extended generalized hybrid if there are \alpha, \beta, \gamma, \delta\in \mathbb{R} such that \alpha+\beta+\gamma+\delta \geq 0, \alpha+\beta >0 and \alpha \|Tx-Ty\|^2 + \beta \|x-Ty\|^2 + \gamma \|Tx-y\|^2 + \delta \|x-y\|^2 \leq 0 for all x,y \in C. In this paper, we prove a weak convergence theorem of Mann’s type iteration for infinite families of extended generalized hybrid mappings in a Banach space satisfying the Opial’s condition.

 

How to Cite this Article:
Mayumi Hojo, Weak convergence theorems for infinite families of extended generalized hybrid mappings in Banach spaces, J. Nonlinear Var. Anal. 3 (2019), 159-170.