PROINOV CONTRACTIONS AND DISCONTINUITY AT FIXED POINT

被引：4

作者：

Bisht, Ravindra K. ^{[1
]}

Pant, R. P. ^{[2
]}

Rakocevic, Vladimir ^{[3
]}

机构：

[1] Natl Def Acad, Dept Math, Pune, Maharashtra, India

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

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

来源：

MISKOLC MATHEMATICAL NOTES | 2019年 / 20卷 / 01期

关键词：

fixed point; (epsilon - delta) contractions; power contraction; orbital continuity; MEIR; THEOREMS;

D O I：

10.18514/MMN.2019.2277

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we show that the contractive definition considered by Proinov [Fixed point theorems in metric spaces, Nonlinear Analysis 64 (2006) 546 - 557] is strong enough to generate a fixed point but does not force the mapping to be continuous at the fixed point. Thus we provide several answers to the open question posed by B.E. Rhoades in Contractive definitions and continuity, Contemporary Mathematics 72(1988), 233-245.

引用

页码：131 / 137

页数：7

共 24 条

[1]

Abtahi M, 2017, RACSAM REV R ACAD A, V111, P57, DOI 10.1007/s13398-016-0275-5

[2] GENERALIZED MEIR-KEELER TYPE CONTRACTIONS AND DISCONTINUITY AT FIXED POINT [J].

Bisht, Ravindra K. ;

Rakocevic, Vladimir .

FIXED POINT THEORY, 2018, 19 (01) :57-64

[3] A remark on discontinuity at fixed point [J].

Bisht, Ravindra K. ;

Pant, R. P. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2017, 445 (02) :1239-1242

[4] ON NONLINEAR CONTRACTIONS [J].

BOYD, DW ;

WONG, JSW .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 20 (02) :458-&

[5] SOLUTION BY ITERATION OF NONLINEAR FUNCTIONAL EQUATIONS IN BANACH SPACES [J].

BROWDER, FE ;

PETRYSHYN, WV .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1966, 72 (03) :571-+

[6]

Chung K. J., 1978, MATH JPN, V23, P381

[7]

Ciri L.B., 1971, PUBL I MATH-BEOGRAD, V12, P19

[8] EQUIVALENT CONDITIONS AND THE MEIR-KEELER TYPE THEOREMS [J].

JACHYMSKI, J .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 194 (01) :293-303

[9] ON GENERALIZATIONS OF THE MEIR-KEELER TYPE CONTRACTION MAPS - CORRECTIONS [J].

JUNGCK, G ;

MOON, KB ;

PARK, SH ;

RHOADES, BE .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 180 (01) :221-222

[10] SOME RESULTS ON FIXED POINTS .2. [J].

KANNAN, R .

AMERICAN MATHEMATICAL MONTHLY, 1969, 76 (04) :405-&

← 1 2 3 →