The nonlinear principles and fixed-point theorems for non-self F contraction and non-expansive set-valued mappings by applying Caristi fixed-point theorem in locally complete convex spaces

George Xianzhi Yuan; Yuanlei Luo; Yeol Je Cho

doi:10.1515/9783112215760-007

The nonlinear principles and fixed-point theorems for non-self F contraction and non-expansive set-valued mappings by applying Caristi fixed-point theorem in locally complete convex spaces

George Xianzhi Yuan
, Yuanlei Luo
, Yeol Je Cho

College of Business

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 12 - Chapter in an edited book (Author) › peer-review

Abstract

The goal of this paper is to establish fixed-point theorems for non-self F contraction and non-self non-expansive set-valued mappings by applying Caristi fixed point as a tool in locally complete spaces. In particular, we first derive a few of key principles widely used in nonlinear analysis and optimization by using Caristi fixed-point theorem as a tool in both complete metric spaces and locally complete convex spaces, respectively. Secondly, as applications of Caristi fixed-point theorem being a starting point, we establish fixed-point theorems for non-self F contraction and non-self non-expansive set-valued mappings. These results improve or unify corresponding results in the literature. © 2026 Walter de Gruyter GmbH, Berlin/Boston, Genthiner Straße 13, 10785 Berlin

Original language	English
Title of host publication	Fixed Point Theory and Functional Analysis
Subtitle of host publication	Metric Spaces, Banach Spaces, Hilbert Spaces
Editors	Pradip Debnath, Hari Mohan Srivastava, Yeol Je Cho
Publisher	Walter de Gruyter GmbH
Chapter	7
Pages	149-178
Number of pages	30
ISBN (Electronic)	9783112215760
ISBN (Print)	9783119145039
DOIs	https://doi.org/10.1515/9783112215760-007
Publication status	Published - 21 Nov 2025

Research Keywords

Banach disc (disk)
boundary condition (α)
Cantor intersection theorem
Caristi fixed-point theorem
complete metric space
demiclosed
Ekeland variational principle
F contraction set-valued mapping
fixed point
locally complete convex space
non-expansive set-valued mapping
non-self mapping
Nonlinear analysis
Oettli–Théra theorem
P-Opial condition
Takahashi nonconvex minimization theorem
weakly inward mapping

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Yuan, G. X., Luo, Y., & Cho, Y. J. (2025). The nonlinear principles and fixed-point theorems for non-self F contraction and non-expansive set-valued mappings by applying Caristi fixed-point theorem in locally complete convex spaces. In P. Debnath, H. M. Srivastava, & Y. J. Cho (Eds.), Fixed Point Theory and Functional Analysis: Metric Spaces, Banach Spaces, Hilbert Spaces (pp. 149-178). Walter de Gruyter GmbH. https://doi.org/10.1515/9783112215760-007

Yuan, George Xianzhi ; Luo, Yuanlei ; Cho, Yeol Je. / The nonlinear principles and fixed-point theorems for non-self F contraction and non-expansive set-valued mappings by applying Caristi fixed-point theorem in locally complete convex spaces. Fixed Point Theory and Functional Analysis: Metric Spaces, Banach Spaces, Hilbert Spaces. editor / Pradip Debnath ; Hari Mohan Srivastava ; Yeol Je Cho. Walter de Gruyter GmbH, 2025. pp. 149-178

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abstract = "The goal of this paper is to establish fixed-point theorems for non-self F contraction and non-self non-expansive set-valued mappings by applying Caristi fixed point as a tool in locally complete spaces. In particular, we first derive a few of key principles widely used in nonlinear analysis and optimization by using Caristi fixed-point theorem as a tool in both complete metric spaces and locally complete convex spaces, respectively. Secondly, as applications of Caristi fixed-point theorem being a starting point, we establish fixed-point theorems for non-self F contraction and non-self non-expansive set-valued mappings. These results improve or unify corresponding results in the literature. {\textcopyright} 2026 Walter de Gruyter GmbH, Berlin/Boston, Genthiner Stra{\ss}e 13, 10785 Berlin",

keywords = "Banach disc (disk), boundary condition (α), Cantor intersection theorem, Caristi fixed-point theorem, complete metric space, demiclosed, Ekeland variational principle, F contraction set-valued mapping, fixed point, locally complete convex space, non-expansive set-valued mapping, non-self mapping, Nonlinear analysis, Oettli–Th{\'e}ra theorem, P-Opial condition, Takahashi nonconvex minimization theorem, weakly inward mapping",

author = "Yuan, \{George Xianzhi\} and Yuanlei Luo and Cho, \{Yeol Je\}",

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Yuan, GX, Luo, Y & Cho, YJ 2025, The nonlinear principles and fixed-point theorems for non-self F contraction and non-expansive set-valued mappings by applying Caristi fixed-point theorem in locally complete convex spaces. in P Debnath, HM Srivastava & YJ Cho (eds), Fixed Point Theory and Functional Analysis: Metric Spaces, Banach Spaces, Hilbert Spaces. Walter de Gruyter GmbH, pp. 149-178. https://doi.org/10.1515/9783112215760-007

The nonlinear principles and fixed-point theorems for non-self F contraction and non-expansive set-valued mappings by applying Caristi fixed-point theorem in locally complete convex spaces. / Yuan, George Xianzhi; Luo, Yuanlei; Cho, Yeol Je.
Fixed Point Theory and Functional Analysis: Metric Spaces, Banach Spaces, Hilbert Spaces. ed. / Pradip Debnath; Hari Mohan Srivastava; Yeol Je Cho. Walter de Gruyter GmbH, 2025. p. 149-178.

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 12 - Chapter in an edited book (Author) › peer-review

TY - CHAP

T1 - The nonlinear principles and fixed-point theorems for non-self F contraction and non-expansive set-valued mappings by applying Caristi fixed-point theorem in locally complete convex spaces

AU - Yuan, George Xianzhi

AU - Luo, Yuanlei

AU - Cho, Yeol Je

PY - 2025/11/21

Y1 - 2025/11/21

N2 - The goal of this paper is to establish fixed-point theorems for non-self F contraction and non-self non-expansive set-valued mappings by applying Caristi fixed point as a tool in locally complete spaces. In particular, we first derive a few of key principles widely used in nonlinear analysis and optimization by using Caristi fixed-point theorem as a tool in both complete metric spaces and locally complete convex spaces, respectively. Secondly, as applications of Caristi fixed-point theorem being a starting point, we establish fixed-point theorems for non-self F contraction and non-self non-expansive set-valued mappings. These results improve or unify corresponding results in the literature. © 2026 Walter de Gruyter GmbH, Berlin/Boston, Genthiner Straße 13, 10785 Berlin

AB - The goal of this paper is to establish fixed-point theorems for non-self F contraction and non-self non-expansive set-valued mappings by applying Caristi fixed point as a tool in locally complete spaces. In particular, we first derive a few of key principles widely used in nonlinear analysis and optimization by using Caristi fixed-point theorem as a tool in both complete metric spaces and locally complete convex spaces, respectively. Secondly, as applications of Caristi fixed-point theorem being a starting point, we establish fixed-point theorems for non-self F contraction and non-self non-expansive set-valued mappings. These results improve or unify corresponding results in the literature. © 2026 Walter de Gruyter GmbH, Berlin/Boston, Genthiner Straße 13, 10785 Berlin

KW - Banach disc (disk)

KW - boundary condition (α)

KW - Cantor intersection theorem

KW - Caristi fixed-point theorem

KW - complete metric space

KW - demiclosed

KW - Ekeland variational principle

KW - F contraction set-valued mapping

KW - fixed point

KW - locally complete convex space

KW - non-expansive set-valued mapping

KW - non-self mapping

KW - Nonlinear analysis

KW - Oettli–Théra theorem

KW - P-Opial condition

KW - Takahashi nonconvex minimization theorem

KW - weakly inward mapping

UR - https://www.scopus.com/pages/publications/105030013111

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U2 - 10.1515/9783112215760-007

DO - 10.1515/9783112215760-007

M3 - RGC 12 - Chapter in an edited book (Author)

SN - 9783119145039

SP - 149

EP - 178

BT - Fixed Point Theory and Functional Analysis

A2 - Debnath, Pradip

A2 - Srivastava, Hari Mohan

A2 - Cho, Yeol Je

PB - Walter de Gruyter GmbH

ER -

Yuan GX, Luo Y, Cho YJ. The nonlinear principles and fixed-point theorems for non-self F contraction and non-expansive set-valued mappings by applying Caristi fixed-point theorem in locally complete convex spaces. In Debnath P, Srivastava HM, Cho YJ, editors, Fixed Point Theory and Functional Analysis: Metric Spaces, Banach Spaces, Hilbert Spaces. Walter de Gruyter GmbH. 2025. p. 149-178 Epub 2025 Nov 21. doi: 10.1515/9783112215760-007

The nonlinear principles and fixed-point theorems for non-self F contraction and non-expansive set-valued mappings by applying Caristi fixed-point theorem in locally complete convex spaces

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Research Keywords

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