Some New Results for a Class of Multivalued Interpolative Kannan-Type Contractions

被引：4

作者：

Konwar, Nabanita ^{[1
]}

Srivastava, Rekha ^{[2
]}

Debnath, Pradip ^{[3
]}

Srivastava, Hari Mohan ^{[2
,4
,5
,6
]}

机构：

[1] Birjhora Mahavidyalaya, Dept Math, Bongaigaon 783380, Assam, India

[2] Univ Victoria, Dept Math & Stat, Victoria, BC V8W 3R4, Canada

[3] Assam Univ, Dept Appl Sci & Humanities, Silchar 788011, Assam, India

[4] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung 40402, Taiwan

[5] Azerbaijan Univ, Dept Math & Informat, 71 Jeyhun Hajibeyli St, AZ-1007 Baku, Azerbaijan

[6] Int Telemat Univ Uninettuno, Sect Math, I-00186 Rome, Italy

来源：

AXIOMS | 2022年 / 11卷 / 02期

关键词：

fixed point; Kannan-type contraction; interpolative map; multivalued map; contraction map; common fixed point; differential equation; integral equation; metric space; FIXED-POINT THEOREMS; METRIC-SPACES;

D O I：

10.3390/axioms11020076

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce the notion of multivalued interpolative Kannan-type contractions. We also introduce a more general version of this notion by relaxing the degrees of freedom of the powers arising in the contractive condition. Gaba et al. (2021) recently pointed out a significant error in the paper of Gaba and Karapinar (2019), showing that a particular type of generalized interpolative Kannan-type contraction does not posses a fixed point in general in a complete metric space. Thus, the study of generalized Kannan-type mappings remains an interesting and mathematically challenging area of research. The main aim of this article is to address such existing results for multivalued mappings. We also investigate common fixed points for this type of contractions. Our results extend and unify some existing results in the literature.

引用

页数：9

共 25 条

[1] ω-Interpolative Ciric-Reich-Rus-Type Contractions
Aydi, Hassen
Karapinar, Erdal
Lopez de Hierro, Antonio Francisco Roldan
[J]. MATHEMATICS, 2019, 7 (01)
[2] Interpolative Ciric-Reich-Rus Type Contractions via the Branciari Distance
Aydi, Hassen
Chen, Chi-Ming
Karapinar, Erdal
[J]. MATHEMATICS, 2019, 7 (01)
[3] Bojor F, 2012, AN STI U OVID CO-MAT, V20, P31
[4] Boriceanu M., 2010, INTERNAT J MATH STAT, V6, P65
[5] Czerwik S., 1998, ATTI SEM MATH FIS U, V46, P263, DOI DOI 10.4236/APM.2012.21002
[6] Debnath P., 2021, Metric fixed point theory: Applications in science, engineering and behavioural sciences, DOI 10.1007/978-981-16-4896-0
[7] Banach, Kannan, Chatterjea, and Reich-type contractive inequalities for multivalued mappings and their common fixed points
Debnath, Pradip
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2022, 45 (03) : 1587 - 1596
[8] Fixed Points of Some Asymptotically Regular Multivalued Mappings Satisfying a Kannan-Type Condition
Debnath, Pradip
Mitrovic, Zoran D.
Srivastava, Hari Mohan
[J]. AXIOMS, 2021, 10 (01) : 1 - 7
[9] Debnath P, 2020, MAT VESTN, V72, P368
[10] Global Optimization and Common Best Proximity Points for Some Multivalued Contractive Pairs of Mappings
Debnath, Pradip
Srivastava, Hari Mohan
[J]. AXIOMS, 2020, 9 (03)

← 1 2 3 →