Applying Theorems on b-Metric Spaces to Differential and Integral Equations Through Connected-Image Contractions

被引：0
作者：
Chaichana, Khuanchanok [1 ,2 ,3 ]
Poochinapan, Kanyuta [1 ,2 ,3 ]
Suebcharoen, Teeranush [1 ,2 ,3 ]
Charoensawan, Phakdi [1 ,2 ,3 ]
机构：
[1] Chiang Mai Univ, Adv Res Ctr Computat Simulat, Chiang Mai 50200, Thailand
[2] Chiang Mai Univ, Fac Sci, Dept Math, Chiang Mai 50200, Thailand
[3] Ctr Excellence Math MHESI, Bangkok 10400, Thailand
来源：
MATHEMATICS | 2024年 / 12卷 / 24期
关键词：
connected-image contraction; fixed-point theorem; b-metric space; differential equation; integral equation;
D O I：
10.3390/math12243955
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper introduces a new concept of a connected-image set for a mapping, which extends the notion of edge-preserving properties with respect to mapping. We also present novel definitions of connected-image contractions, with a focus on fixed-point theorems involving auxiliary functions in b-metric spaces. The relationships between these mathematical concepts are explored, along with their applications to solving differential and integral equations. In particular, we discuss existence results for solving integral equations and second-order ordinary differential equations with inhomogeneous Dirichlet boundary conditions, as well as theorems related to contractions of the integral type.
引用
收藏
页数：21
相关论文
共 12 条
  • [1] Partial differential equation models in macroeconomics
    Achdou, Yves
    Buera, Francisco J.
    Lasry, Jean-Michel
    Lions, Pierre-Louis
    Moll, Benjamin
    [J]. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2014, 372 (2028):
  • [2] The integral equation model and surface roughness signatures in soil moisture and tillage type determination
    Colpitts, BG
    [J]. IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, 1998, 36 (03): : 833 - 837
  • [3] Czerwik S., 1993, Acta Mathematica et Informatica Universitatis Ostraviensis, V1, P5
  • [4] Czerwik S., 1998, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia, V46, P263
  • [5] Fixed Point Theorems for Geraghty Contraction Type Mappings in b-Metric Spaces and Applications
    Faraji, Hamid
    Savic, Dragana
    Radenovic, Stojan
    [J]. AXIOMS, 2019, 8 (01)
  • [6] Integral equation of optimal replacement: Analysis and algorithms
    Hritonenko, Natali
    Yatsenko, Yuri
    [J]. APPLIED MATHEMATICAL MODELLING, 2009, 33 (06) : 2737 - 2747
  • [7] Jachymski J, 2008, P AM MATH SOC, V136, P1359
  • [8] Applying new fixed point theorems on fractional and ordinary differential equations
    Karapinar, Erdal
    Abdeljawad, Thabet
    Jarad, Fahd
    [J]. ADVANCES IN DIFFERENCE EQUATIONS, 2019, 2019 (01)
  • [9] REDDY JM, 1989, J AGR ENG RES, V42, P251, DOI 10.1016/0021-8634(89)90028-0
  • [10] Fixed point theorems via auxiliary functions with applications to two-term fractional differential equations with nonlocal boundary conditions
    Suebcharoen, Teeranush
    Atiponrat, Watchareepan
    Chaichana, Khuanchanok
    [J]. AIMS MATHEMATICS, 2023, 8 (03): : 7394 - 7418
12