Convergence of AA-Iterative Algorithm for Generalized α-Nonexpansive Mappings with an Application

Ismat Beg; Mujahid Abbas; Muhammad Waseem Asghar

doi:10.3390/math10224375

Convergence of AA-Iterative Algorithm for Generalized α-Nonexpansive Mappings with an Application

Ismat Beg
, Mujahid Abbas
, Muhammad Waseem Asghar

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

7 Citations (Scopus)

Abstract

The aim of this paper is to approximate the fixed points of generalized (Formula presented.) -nonexpansive mappings using (Formula presented.) -iterative algorithm. We establish some weak and strong convergence results for generalized (Formula presented.) -nonexpansive mappings in uniformly convex Banach spaces. A numerical example is also given to show that the (Formula presented.) -iterative algorithm converges faster than some others algorithms for generalized (Formula presented.) -nonexpansive mappings. Lastly, using the (Formula presented.) -iterative algorithm, we approximate the weak solution of delay composite functional differential equation of the Volterra–Stieltjes type.

Original language	English
Article number	4375
Journal	Mathematics
Volume	10
Issue number	22
DOIs	https://doi.org/10.3390/math10224375
Publication status	Published - Nov 2022
Externally published	Yes

Keywords

AA-iteration
Banach space
fixed point
generalized α-nonexpansive mapping

ASJC Scopus subject areas

Computer Science (miscellaneous)
General Mathematics
Engineering (miscellaneous)

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10.3390/math10224375

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title = "Convergence of AA-Iterative Algorithm for Generalized α-Nonexpansive Mappings with an Application",

abstract = "The aim of this paper is to approximate the fixed points of generalized (Formula presented.) -nonexpansive mappings using (Formula presented.) -iterative algorithm. We establish some weak and strong convergence results for generalized (Formula presented.) -nonexpansive mappings in uniformly convex Banach spaces. A numerical example is also given to show that the (Formula presented.) -iterative algorithm converges faster than some others algorithms for generalized (Formula presented.) -nonexpansive mappings. Lastly, using the (Formula presented.) -iterative algorithm, we approximate the weak solution of delay composite functional differential equation of the Volterra–Stieltjes type.",

keywords = "AA-iteration, Banach space, fixed point, generalized α-nonexpansive mapping",

author = "Ismat Beg and Mujahid Abbas and Asghar, \{Muhammad Waseem\}",

note = "Publisher Copyright: {\textcopyright} 2022 by the authors.",

year = "2022",

month = nov,

doi = "10.3390/math10224375",

language = "English",

volume = "10",

journal = "Mathematics",

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T1 - Convergence of AA-Iterative Algorithm for Generalized α-Nonexpansive Mappings with an Application

AU - Beg, Ismat

AU - Abbas, Mujahid

AU - Asghar, Muhammad Waseem

PY - 2022/11

Y1 - 2022/11

N2 - The aim of this paper is to approximate the fixed points of generalized (Formula presented.) -nonexpansive mappings using (Formula presented.) -iterative algorithm. We establish some weak and strong convergence results for generalized (Formula presented.) -nonexpansive mappings in uniformly convex Banach spaces. A numerical example is also given to show that the (Formula presented.) -iterative algorithm converges faster than some others algorithms for generalized (Formula presented.) -nonexpansive mappings. Lastly, using the (Formula presented.) -iterative algorithm, we approximate the weak solution of delay composite functional differential equation of the Volterra–Stieltjes type.

AB - The aim of this paper is to approximate the fixed points of generalized (Formula presented.) -nonexpansive mappings using (Formula presented.) -iterative algorithm. We establish some weak and strong convergence results for generalized (Formula presented.) -nonexpansive mappings in uniformly convex Banach spaces. A numerical example is also given to show that the (Formula presented.) -iterative algorithm converges faster than some others algorithms for generalized (Formula presented.) -nonexpansive mappings. Lastly, using the (Formula presented.) -iterative algorithm, we approximate the weak solution of delay composite functional differential equation of the Volterra–Stieltjes type.

KW - AA-iteration

KW - Banach space

KW - fixed point

KW - generalized α-nonexpansive mapping

UR - https://www.scopus.com/pages/publications/85142503651

U2 - 10.3390/math10224375

DO - 10.3390/math10224375

M3 - Article

AN - SCOPUS:85142503651

SN - 2227-7390

VL - 10

JO - Mathematics

JF - Mathematics

IS - 22

M1 - 4375

ER -

Convergence of AA-Iterative Algorithm for Generalized α-Nonexpansive Mappings with an Application

Abstract

Keywords

ASJC Scopus subject areas

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