Fibonacci-Mann iteration for monotone asymptotically nonexpansive mappings in modular spaces

Buthinah A.Bin Dehaish; Mohamed A. Khamsi

doi:10.3390/sym10100481

Fibonacci-Mann iteration for monotone asymptotically nonexpansive mappings in modular spaces

Buthinah A.Bin Dehaish, Mohamed A. Khamsi^*

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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 x_n+1 = t_nT^ϕ(n)(x_n) + (1 - t_n)x_n, for n ∈ ℕ, when T is a monotone asymptotically nonexpansive self-mapping.

Original language	English
Article number	481
Journal	Symmetry
Volume	10
Issue number	10
DOIs	https://doi.org/10.3390/sym10100481
State	Published - 2018

Bibliographical note

Publisher Copyright:
© 2018 by the authors.

Keywords

Asymptotically nonexpansive mapping
Fibonacci sequence
Fixed point
Mann iteration process
Modular function spaces
Monotone Lipschitzian mapping
Opial condition
Uniformly convexity

ASJC Scopus subject areas

Computer Science (miscellaneous)
Chemistry (miscellaneous)
General Mathematics
Physics and Astronomy (miscellaneous)

Access to Document

10.3390/sym10100481

Cite this

@article{260d66bd8f954e438083b10113177ed8,

title = "Fibonacci-Mann iteration for monotone asymptotically nonexpansive mappings in modular spaces",

abstract = "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 xn+1 = tnTϕ(n)(xn) + (1 - tn)xn, for n ∈ ℕ, when T is a monotone asymptotically nonexpansive self-mapping.",

keywords = "Asymptotically nonexpansive mapping, Fibonacci sequence, Fixed point, Mann iteration process, Modular function spaces, Monotone Lipschitzian mapping, Opial condition, Uniformly convexity",

author = "Dehaish, \{Buthinah A.Bin\} and Khamsi, \{Mohamed A.\}",

note = "Publisher Copyright: {\textcopyright} 2018 by the authors.",

year = "2018",

doi = "10.3390/sym10100481",

language = "English",

volume = "10",

journal = "Symmetry",

issn = "2073-8994",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "10",

}

TY - JOUR

T1 - Fibonacci-Mann iteration for monotone asymptotically nonexpansive mappings in modular spaces

AU - Dehaish, Buthinah A.Bin

AU - Khamsi, Mohamed A.

PY - 2018

Y1 - 2018

N2 - 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 xn+1 = tnTϕ(n)(xn) + (1 - tn)xn, for n ∈ ℕ, when T is a monotone asymptotically nonexpansive self-mapping.

AB - 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 xn+1 = tnTϕ(n)(xn) + (1 - tn)xn, for n ∈ ℕ, when T is a monotone asymptotically nonexpansive self-mapping.

KW - Asymptotically nonexpansive mapping

KW - Fibonacci sequence

KW - Fixed point

KW - Mann iteration process

KW - Modular function spaces

KW - Monotone Lipschitzian mapping

KW - Opial condition

KW - Uniformly convexity

UR - https://www.scopus.com/pages/publications/85055751180

U2 - 10.3390/sym10100481

DO - 10.3390/sym10100481

M3 - Article

AN - SCOPUS:85055751180

SN - 2073-8994

VL - 10

JO - Symmetry

JF - Symmetry

IS - 10

M1 - 481

ER -

Fibonacci-Mann iteration for monotone asymptotically nonexpansive mappings in modular spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this