Fixed points of convex and generalized convex contractions

被引：21

作者：

Bisht, Ravindra K. ^{[1
]}

Rakocevic, Vladimir ^{[2
]}

机构：

[1] Natl Def Acad, Fac Computat Sci, Dept Math, Pune 411023, Maharashtra, India

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

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2020年 / 69卷 / 01期

关键词：

Fixed point; Convex contractions; k-Continuity; NEURAL-NETWORKS; MAPPINGS; DISCONTINUITY; THEOREMS;

D O I：

10.1007/s12215-018-0386-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Istratescu (Lib Math 1:151-163, 1981) introduced the notion of convex contraction. He proved that each convex contraction has a unique fixed point on a complete metric space. In this paper we study fixed points of convex contraction and generalized convex contractions. We show that the assumption of continuity condition in [11] can be replaced by a relatively weaker condition of k-continuity under various settings. On this way a new and distinct solution to the open problem of Rhoades (Contemp Math 72:233-245, 1988) is found. Several examples are given to illustrate our results.

引用

页码：21 / 28

页数：8

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