Fixed Points of Set-Valued F-Contractions and its Application to Non-Linear Integral Equations

被引：8

作者：

Shukla, Satish ^{[1
]}

Gopal, Dhananjay ^{[2
]}

Martinez-Moreno, Juan ^{[3
]}

机构：

[1] Shri Vaishnav Inst Technol & Sci, Dept Appl Math, Gram Baroli, India

[2] SV Natl Inst Technol, Dept Appl Math & Humanities, Surat, India

[3] Univ Jaen, Dept Matemat, Jaen, Spain

来源：

FILOMAT | 2017年 / 31卷 / 11期

关键词：

Fixed points; F-contractions; non-linear integral equations; PARTIALLY ORDERED SETS; THEOREMS;

D O I：

10.2298/FIL1711377S

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We observe that the assumption of set-valued F-contractions (Sgroi and Vetro [13]) is actually very strong for the existence of fixed point and can be weakened. In this connection, we introduce the notion of set-valued alpha-F-contractions and prove a corresponding fixed point theorem in complete metric spaces. Consequently, we derive several fixed point theorems in metric spaces. Some examples are given to illustrate the new theory. Then we apply our results to establishing the existence and uniqueness of solutions for a certain type of non-linear integral equations.

引用

页码：3377 / 3390

页数：14

共 42 条

[1] Fixed points of some set-valued F-contractions
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[3] Existence of fixed points of generalized set-valued F-contractions of b-metric spaces br
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[4] Set-valued contractions and fixed points
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[9] Fixed Points of Set-valued F-contraction Operators in Quasi-ordered Metric Spaces with an Application to Integral Equations
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[10] Fixed points of set-valued contractions in partial metric spaces endowed with a graph
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