scholarly journals Approximating fixed points of $\rho$-nonexpansive mappings by RK-iterative process in modular function spaces

2019 ◽  
Vol 3 (1) ◽  
Keyword(s):  
Fixed Points ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Modular Function ◽  
Function Spaces ◽  
Modular Function Spaces

scholarly journals On Monotone Asymptotic Pointwise Nonexpansive Mappings in Modular Function Spaces

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
B. A. Bin Dehaish
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Fixed Points ◽  
Function Space ◽  
Nonexpansive Mappings ◽  
Modular Function ◽  
Function Spaces ◽  
Modular Function Space ◽  
Modular Function Spaces ◽  
Asymptotic Pointwise Nonexpansive Mapping

In this work, we investigate the existence of the fixed points of a monotone asymptotic pointwise nonexpansive mapping defined in a modular function space. Our result extends the fixed point result of Khamsi and Kozlowski.

scholarly journals Fibonacci–Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 481 ◽  
Author(s):  
Buthinah Dehaish ◽  
Mohamed Khamsi
Keyword(s):  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Modular Function ◽  
Function Spaces ◽  
Mann Iteration ◽  
Modular Spaces ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Modular Function Spaces ◽  
Mann Iteration Process

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci–Mann iteration process, introduced recently by Alfuraidan and Khamsi, defined by

scholarly journals Iterative Approximation of Fixed Point of Multivalued ρ-Quasi-Nonexpansive Mappings in Modular Function Spaces with Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Godwin Amechi Okeke ◽  
Sheila Amina Bishop ◽  
Safeer Hussain Khan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Nonexpansive Mappings ◽  
Modular Function ◽  
Point Theory ◽  
Function Spaces ◽  
Initial Value ◽  
Iterative Approximation ◽  
Modular Function Spaces ◽  
Nonlinear Mappings

Recently, Khan and Abbas initiated the study of approximating fixed points of multivalued nonlinear mappings in modular function spaces. It is our purpose in this study to continue this recent trend in the study of fixed point theory of multivalued nonlinear mappings in modular function spaces. We prove some interesting theorems for ρ-quasi-nonexpansive mappings using the Picard-Krasnoselskii hybrid iterative process. We apply our results to solving certain initial value problem.

scholarly journals Fibonacci-Mann Iteration for Monotone Asymptotically Nonexpansive Mappings in Modular Spaces

2018 ◽  
Author(s):  
Buthinah A. Bin Dehaish ◽  
Mohamed A Khamsi
Keyword(s):  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Modular Function ◽  
Function Spaces ◽  
Mann Iteration ◽  
Modular Spaces ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Modular Function Spaces ◽  
Mann Iteration Process

In this work, we extend the fundamental results of Schu to the class of monotone asymptotically nonexpansive mappings in modular function spaces. In particular, we study the behavior of the Fibonacci-Mann iteration process defined by $$x_{n+1} = t_n T^{\phi(n)}(x_n) + (1-t_n)x_n,$$ for $n \in \mathbb{N}$, when $T$ is a monotone asymptotically nonexpansive self-mapping.

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