New results on discontinuity at fixed point

被引：13

作者：

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

Ozgur, Nihal ^{[2
]}

Tas, Nihal ^{[2
]}

Pant, Abhijit ^{[1
]}

Joshi, Mahesh C. ^{[3
]}

机构：

[1] Kumaun Univ, Dept Math, Naini Tal, India

[2] Balikesir Univ, Dept Math, TR-10145 Balikesir, Turkey

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

来源：

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS | 2020年 / 22卷 / 02期

关键词：

Fixed point; fixed circle; fixed disc; discontinuity; simulation function; NEURAL-NETWORKS; CONTRACTION; THEOREMS;

D O I：

10.1007/s11784-020-0765-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain a Meir-Keeler type fixed-point theorem which gives a new solution to the Rhoades' problem on the existence of contractive mappings that admit discontinuity at the fixed point. Meir-Keeler type solutions of the Rhoades' problem have not been reported in literature before this. Presenting a new approach, we give another solution to this problem using the set of simulation functions. To emphasize the importance of our theoretical results, we obtain two applications of the main results with some illustrative examples.

引用

页数：14

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