MEIR-KEELER TYPE AND CARISTI TYPE FIXED POINT THEOREMS

被引：2

作者：

Pant, Abhijit ^{[1
]}

Pant, R. P. ^{[1
]}

Rakocevic, Vladimir ^{[2
]}

机构：

[1] Kumaun Univ, Dept Math, DSB Campus, Naini Tal 263002, India

[2] Fac Sci & Math, Visegradska 33, Nish 18000, Serbia

来源：

APPLICABLE ANALYSIS AND DISCRETE MATHEMATICS | 2019年 / 13卷 / 03期

关键词：

Caristi type maps; contractive mappings; fixed point; k-continuity; NEURAL-NETWORKS;

D O I：

10.2298/AADM181224037P

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Agarwal et al [1] have proved some interesting local and global fixed point theorems for Meir-Keeler [7] type and Caristi [2] type maps. We obtain analogues of the main results of Agarwal et al [1] under weaker conditions so as to include continuous as well as discontinuous maps. Our results provide new answers to Rhoades' problem ([15], p. 242) on existence of contractive definitions which admit discontinuity at the fixed point. Several examples are given to illustrate our results.

引用

页码：849 / 858

页数：10

共 16 条

[1] Fixed point theory for generalized contractive maps of Meir-Keeler type [J].

Agarwal, RP ;

O'Regan, D ;

Shahzad, N .

MATHEMATISCHE NACHRICHTEN, 2004, 276 :3-22

[2] FIXED-POINT THEOREMS FOR MAPPINGS SATISFYING INWARDNESS CONDITIONS [J].

CARISTI, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 215 (JAN) :241-251

[3]

Ciric L.B., 1971, Math. Balk, V1, P52

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

CIRIC, LB .

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

[5] Mittag-Leffler synchronization of delayed fractional-order bidirectional associative memory neural networks with discontinuous activations: state feedback control and impulsive control schemes [J].

Ding, Xiaoshuai ;

Cao, Jinde ;

Zhao, Xuan ;

Alsaadi, Fuad E. .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2017, 473 (2204)

[6] Global convergence of neural networks with discontinuous neuron activations [J].

Forti, M ;

Nistri, P .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2003, 50 (11) :1421-1435

[7] A THEOREM ON CONTRACTION MAPPINGS [J].

MEIR, A ;

KEELER, E .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1969, 28 (02) :326-&

[8]

NIE X., IEEE T CYBERNATICS

[9]

Nie XB, 2014, 2014 4TH AUSTRALIAN CONTROL CONFERENCE (AUCC), P245, DOI 10.1109/AUCC.2014.7358690

[10] Multistability of neural networks with discontinuous non-monotonic piecewise linear activation functions and time-varying delays [J].

Nie, Xiaobing ;

Zheng, Wei Xing .

NEURAL NETWORKS, 2015, 65 :65-79

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