ON NEW MODIFIED GENERALIZED NONEXPANSIVE MAPPINGS WITH AN APPLICATION TO THE TRANSVERSE WAVES IN A HOMOGENEOUS BAR

Mi Zhou; Rizwan Anjum; Muhammad Din; Mujahid Abbas

ON NEW MODIFIED GENERALIZED NONEXPANSIVE MAPPINGS WITH AN APPLICATION TO THE TRANSVERSE WAVES IN A HOMOGENEOUS BAR

Mi Zhou
, Rizwan Anjum
, Muhammad Din
, Mujahid Abbas

Construction Management and Quantity Surveying

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

Abstract

This paper introduces modified versions of generalized nonexpansive and contraction mappings, called pointwise (r, t/)-modified and pointwise r-modified mappings. These modifications ensure the existence of fixed points and convergence of modified Mann and Picard-Mann iterations, expanding the applicability of nonexpansive mapping theory. The results are validated numerically and applied to a boundary value problem for transverse oscillations in a homogeneous bar.

Original language	English
Pages (from-to)	3381-3398
Number of pages	18
Journal	Journal of Nonlinear and Convex Analysis
Volume	26
Issue number	12
Publication status	Published - 2025

Keywords

k-Fold averaged mapping
modified Mann iteration
modified Picard-Mann iteration
pointwise (τ, ν)-modified generalized nonexpansive/contraction mapping
pointwise τ-modified generalized nonexpansivecontraction mapping
τ-modified generalized nonexpansive/contraction mapping

ASJC Scopus subject areas

Analysis
Geometry and Topology
Control and Optimization
Applied Mathematics

Cite this

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title = "ON NEW MODIFIED GENERALIZED NONEXPANSIVE MAPPINGS WITH AN APPLICATION TO THE TRANSVERSE WAVES IN A HOMOGENEOUS BAR",

abstract = "This paper introduces modified versions of generalized nonexpansive and contraction mappings, called pointwise (r, t/)-modified and pointwise r-modified mappings. These modifications ensure the existence of fixed points and convergence of modified Mann and Picard-Mann iterations, expanding the applicability of nonexpansive mapping theory. The results are validated numerically and applied to a boundary value problem for transverse oscillations in a homogeneous bar.",

keywords = "k-Fold averaged mapping, modified Mann iteration, modified Picard-Mann iteration, pointwise (τ, ν)-modified generalized nonexpansive/contraction mapping, pointwise τ-modified generalized nonexpansivecontraction mapping, τ-modified generalized nonexpansive/contraction mapping",

author = "Mi Zhou and Rizwan Anjum and Muhammad Din and Mujahid Abbas",

year = "2025",

language = "English",

volume = "26",

pages = "3381--3398",

journal = "Journal of Nonlinear and Convex Analysis",

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publisher = "Yokohama Publishers",

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T1 - ON NEW MODIFIED GENERALIZED NONEXPANSIVE MAPPINGS WITH AN APPLICATION TO THE TRANSVERSE WAVES IN A HOMOGENEOUS BAR

AU - Zhou, Mi

AU - Anjum, Rizwan

AU - Din, Muhammad

AU - Abbas, Mujahid

PY - 2025

Y1 - 2025

N2 - This paper introduces modified versions of generalized nonexpansive and contraction mappings, called pointwise (r, t/)-modified and pointwise r-modified mappings. These modifications ensure the existence of fixed points and convergence of modified Mann and Picard-Mann iterations, expanding the applicability of nonexpansive mapping theory. The results are validated numerically and applied to a boundary value problem for transverse oscillations in a homogeneous bar.

AB - This paper introduces modified versions of generalized nonexpansive and contraction mappings, called pointwise (r, t/)-modified and pointwise r-modified mappings. These modifications ensure the existence of fixed points and convergence of modified Mann and Picard-Mann iterations, expanding the applicability of nonexpansive mapping theory. The results are validated numerically and applied to a boundary value problem for transverse oscillations in a homogeneous bar.

KW - k-Fold averaged mapping

KW - modified Mann iteration

KW - modified Picard-Mann iteration

KW - pointwise (τ, ν)-modified generalized nonexpansive/contraction mapping

KW - pointwise τ-modified generalized nonexpansivecontraction mapping

KW - τ-modified generalized nonexpansive/contraction mapping

UR - https://www.scopus.com/pages/publications/105028273151

M3 - Article

AN - SCOPUS:105028273151

SN - 1345-4773

VL - 26

SP - 3381

EP - 3398

JO - Journal of Nonlinear and Convex Analysis

JF - Journal of Nonlinear and Convex Analysis

IS - 12

ER -

ON NEW MODIFIED GENERALIZED NONEXPANSIVE MAPPINGS WITH AN APPLICATION TO THE TRANSVERSE WAVES IN A HOMOGENEOUS BAR

Abstract

Keywords

ASJC Scopus subject areas

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