A study on a new and fast fixed point iteration process in Banach spaces

This paper presents a fixed point iteration method for approximating the solution of a fractional order model of novel coronavirus (COVID-2019) under Caputo--Fabrizio derivative in Banach spaces. Our result is new and complements some existing results in the literature.

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Some fixed point results for a new three steps iteration process in Banach spaces

Fixed Point Theory ◽

10.24193/fpt-ro.2017.2.50 ◽

2017 ◽

Vol 18 (2) ◽

pp. 625-640 ◽

Cited By ~ 1

Author(s):

V. Karakaya ◽

◽

Y. Atalan ◽

K. Dogan ◽

N. El Houda Bouzara ◽

...

Keyword(s):

Fixed Point ◽

Banach Spaces ◽

Iteration Process

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A random fixed point iteration for three random operators on uniformly convex Banach spaces

Analysis in Theory and Applications ◽

10.1007/bf02835233 ◽

2003 ◽

Vol 19 (2) ◽

pp. 99-107 ◽

Cited By ~ 1

Author(s):

Binayak S. Choudhury

Keyword(s):

Fixed Point ◽

Banach Spaces ◽

Random Operators ◽

Uniformly Convex ◽

Random Fixed Point ◽

Fixed Point Iteration ◽

Uniformly Convex Banach Spaces

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Fixed-point iteration processes for non-Lipschitzian mappings of asymptotically quasi-nonexpansive type

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171203302182 ◽

2003 ◽

Vol 2003 (33) ◽

pp. 2075-2081 ◽

Cited By ~ 3

Author(s):

Daya Ram Sahu ◽

Jong Soo Jung

Keyword(s):

Fixed Point ◽

Banach Spaces ◽

Fixed Point Iteration ◽

Ishikawa Iteration ◽

Lipschitzian Mappings ◽

Iteration Processes

We study convergences of Mann and Ishikawa iteration processes for mappings of asymptotically quasi-nonexpansive type in Banach spaces.

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Implicit Mann Type Iteration Method Involving Strictly Hemicontractive Mappings in Banach Spaces

Journal of Applied Mathematics ◽

10.1155/2012/294718 ◽

2012 ◽

Vol 2012 ◽

pp. 1-11

Author(s):

Arif Rafiq ◽

Shin Min Kang

Keyword(s):

Fixed Point ◽

Banach Spaces ◽

Iteration Method ◽

Iteration Process ◽

Mann Iteration ◽

Hemicontractive Mappings ◽

Mann Iteration Process

We proved that the modified implicit Mann iteration process can be applied to approximate the fixed point of strictly hemicontractive mappings in smooth Banach spaces.

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Three-Step Fixed Point Iteration for Generalized Multivalued Mapping in Banach Spaces

Journal of Applied Mathematics ◽

10.1155/2012/235120 ◽

2012 ◽

Vol 2012 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Zhanfei Zuo

Keyword(s):

Fixed Point ◽

Nonexpansive Mapping ◽

Banach Spaces ◽

Multivalued Mapping ◽

Fixed Point Iteration ◽

Iterative Processes ◽

Multivalued Nonexpansive Mapping

The convergence of three-step fixed point iterative processes for generalized multivalued nonexpansive mapping was considered in this paper. Under some different conditions, the sequences of three-step fixed point iterates strongly or weakly converge to a fixed point of the generalized multivalued nonexpansive mapping. Our results extend and improve some recent results.

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A New Modified Fixed-Point Iteration Process

Mathematics ◽

10.3390/math9233109 ◽

2021 ◽

Vol 9 (23) ◽

pp. 3109

Author(s):

Chanchal Garodia ◽

Afrah A. N. Abdou ◽

Izhar Uddin

Keyword(s):

Banach Space ◽

Fixed Point ◽

Weak Convergence ◽

Nonexpansive Mappings ◽

Iteration Process ◽

Convex Banach Space ◽

Uniformly Convex ◽

Strong And Weak Convergence ◽

Convergence Results ◽

Fixed Point Iteration Process

In this paper, we present a new modified iteration process in the setting of uniformly convex Banach space. The newly obtained iteration process can be used to approximate a common fixed point of three nonexpansive mappings. We have obtained strong and weak convergence results for three nonexpansive mappings. Additionally, we have provided an example to support the theoretical proof. In the process, several relevant results are improved and generalized.

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