Sahand Communications in Mathematical Analysis

$C$-class Functions and Common Fixed Point Theorems Satisfying $\varphi $-weakly Contractive Conditions

Document Type : Research Paper

Authors

Arslan Hojat Ansari 1
Tatjana Dosenovic 2
Stojan Radenovic 3
Jeong Sheok Ume 4

1 Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.

2 Faculty of Technology, Bulevar cara Lazara 1, University of Novi Sad, Serbia.

3 Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia.

4 Department of Mathematics, Changwon National University, Changwon, 641-773, Korea.

https://doi.org/10.22130/scma.2018.59792.211
Abstract
In this paper, we discuss and extend some recent common fixed point results established by using $\varphi-$weakly contractive mappings. A very important step in the development of the fixed point theory was given by A.H. Ansari by the introduction of a $C-$class function. Using $C-$class functions, we generalize some known fixed point results. This type of functions is a very important class of functions which contains almost all known type contraction starting from 1922. year, respectively from famous Banach contraction principle. Three common fixed point theorems for four mappings are presented. The obtained results generalizes several existing ones
in literature.We finally propose three open  problems.

Keywords

Common fixed point
$\varphi $-weakly contractive conditions
Complete metric space
Weakly compatible mappings
C-class function

Subjects

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Sahand Communications in Mathematical Analysis
Volume 13, Issue 1
Winter 2019
Pages 17-30

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