Fixed point results for decreasing convex orbital operators in Hilbert spaces

被引：9

作者：

Petrusel, Adrian ^{[1
]}

Petrusel, Gabriela ^{[2
]}

机构：

[1] Babes Bolyai Univ, Dept Math, Cluj Napoca 400084, Romania

[2] Babes Bolyai Univ, Dept Business, Cluj Napoca 400084, Romania

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2021年 / 23卷 / 03期

关键词：

Hilbert space; contraction; graphic contraction; generalized contraction; convex orbital Lipschitz operator; decreasing operator; fixed point; Picard operator; weakly Picard operator; open problem; CONTRACTION-MAPPINGS; THEOREMS; STABILITY;

D O I：

10.1007/s11784-021-00873-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let (X, <.>) be a Hilbert space and T : X -> X be a decreasing operator. Under a metric condition involving the convex combination of x and T(x), we will prove some fixed point theorems which generalize and complement several results in the theory of nonlinear operators. Our results are closely related to the admissible perturbations approach in fixed point theory.

引用

页数：10

共 25 条

[1] Fixed point theorems for convex contraction mappings on cone metric spaces [J].

Alghamdi, Mohammad A. ;

Alnafei, Shahrazad H. ;

Radenovic, Stojan ;

Shahzad, Naseer .

MATHEMATICAL AND COMPUTER MODELLING, 2011, 54 (9-10) :2020-2026

[2]

Berinde V, 2016, SPRINGER OPTIM APPL, V111, P75, DOI 10.1007/978-3-319-31281-1_4

[3]

Berinde V., 2020, ANN ACAD ROM SCI SER, V12, P11, DOI 10.56082/annalsarscimath.2020.1-2.11

[4] Approximating fixed points of enriched contractions in Banach spaces [J].

Berinde, Vasile ;

Pacurar, Madalina .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2020, 22 (02)

[5]

Berinde V, 2013, CARPATHIAN J MATH, V29, P9

[6]

Bisht RK, 2017, J MATH ANAL, V8, P90

[7] GENERALIZATION OF BANACHS CONTRACTION PRINCIPLE [J].

CIRIC, LB .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 45 (02) :267-273

[8]

Istratescu V.I., 1981, Libertas Math, V1, P151

[9]

Kirk W.A., 2001, Handbook of Metric Fixed Point Theory

[10] APPROXIMATE FIXED POINT THEOREMS FOR PARTIAL GENERALIZED CONVEX CONTRACTION MAPPINGS IN α-COMPLETE METRIC SPACES [J].

Latif, Abdul ;

Sintunavarat, Wutiphol ;

Ninsri, Aphinat .

TAIWANESE JOURNAL OF MATHEMATICS, 2015, 19 (01) :315-333

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