On Discontinuity Problem at Fixed Point

被引：48

作者：

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

Ozgur, Nihal Yilmaz ^{[2
]}

Tas, Nihal ^{[2
]}

机构：

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

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

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2020年 / 43卷 / 01期

关键词：

Fixed point; (epsilon - delta) Condition; k-continuity; Fixed circle; NEURAL-NETWORKS; THEOREM;

D O I：

10.1007/s40840-018-0698-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain some fixed point theorems under contractive conditions which admit discontinuity at the fixed point. Our results subsume all the known results of similar type, provide new answers to the question of continuity of contractive mappings at their fixed points, and also extend some recent results. Furthermore, we consider the fixed-circle problem on metric spaces. We obtain new fixed-circle results as the generalizations of some known fixed-circle theorems. Some applications of obtained results to discontinuous activation functions are also given.

引用

页码：499 / 517

页数：19

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