RELATION-THEORETIC METRICAL FIXED POINT THEOREMS UNDER NONLINEAR CONTRACTIONS

被引:10
作者
Ahmadullah, Md [1 ]
Imdad, Mohammad [1 ]
Gubran, Rqeeb [1 ]
机构
[1] Aligarh Muslim Univ, Dept Math, Aligarh 202002, UP, India
来源
FIXED POINT THEORY | 2019年 / 20卷 / 01期
关键词
Complete metric spaces; binary relations; contraction mappings; fixed point; PARTIALLY ORDERED SETS; SPACES;
D O I
10.24193/fpt-ro.2019.1.01
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We establish fixed point theorems for nonlinear contractions on a metric space (not essentially complete) endowed with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those contained in Samet and Turinici [Commun. Math. Anal. 13, 82-97 (2012)] and Alam and Imdad [J. Fixed Point Theory Appl. 17(4), 693-702 (2015)]. Interestingly a corollary to one of our main results proved under symmetric closure of any binary relation remains a sharpened version of a theorem due to Samet and Turinici. Finally, we use examples to highlight the realized improvements in the results proved in this paper.
引用
收藏
页码:3 / 17
页数:15
相关论文
共 23 条
[1]  
Ahmadullah M., 2016, FIXED POINT THEORY A, P1
[2]   NONLINEAR CONTRACTIONS IN METRIC SPACES UNDER LOCALLY T-TRANSITIVE BINARY RELATIONS [J].
Alam, Aftab ;
Imdad, Mohammad .
FIXED POINT THEORY, 2018, 19 (01) :13-23
[3]   Relation-Theoretic Metrical Coincidence Theorems [J].
Alam, Aftab ;
Imdad, Mohammad .
FILOMAT, 2017, 31 (14) :4421-4439
[4]   Relation-theoretic contraction principle [J].
Alam, Aftab ;
Imdad, Mohammad .
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2015, 17 (04) :693-702
[5]   INTEGRAL TEST FOR SERIES AND GENERALIZED CONTRACTIONS [J].
ALTMAN, M .
AMERICAN MATHEMATICAL MONTHLY, 1975, 82 (08) :827-829
[6]  
[Anonymous], 2006, STUDIES LOGIC FDN MA
[7]  
Banach S., 1922, Fund. Maths., V3, P133, DOI [DOI 10.4064/FM-3-1-133-181, 10.4064/fm-3-1-133-181]
[8]   The Ran-Reurings fixed point theorem without partial order: A simple proof [J].
Ben-El-Mechaiekh, Hichem .
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2014, 16 (1-2) :373-383
[9]  
CHATTERJEA SK, 1972, DOKL BOLG AKAD NAUK, V25, P727
[10]   GENERALIZATION OF BANACHS CONTRACTION PRINCIPLE [J].
CIRIC, LB .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 45 (02) :267-273