$C$-class Functions and Common Fixed Point Theorems Satisfying $varphi $-weakly Contractive Conditions
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, w...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
University of Maragheh
2019-02-01
|
| Series: | Sahand Communications in Mathematical Analysis |
| Subjects: | |
| Online Access: | http://scma.maragheh.ac.ir/article_31846_d6c970ed6b5f3e0d466239bb147f4213.pdf |
| _version_ | 1818034557117530112 |
|---|---|
| author | Arslan Hojat Ansari Tatjana Dosenovic Stojan Radenovic Jeong Sheok Ume |
| author_facet | Arslan Hojat Ansari Tatjana Dosenovic Stojan Radenovic Jeong Sheok Ume |
| author_sort | Arslan Hojat Ansari |
| collection | DOAJ |
| description | 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<br />in literature.We finally propose three open problems. |
| first_indexed | 2024-12-10T06:41:03Z |
| format | Article |
| id | doaj.art-2fa66135867e492fbdc4ec8c6a61b51f |
| institution | Directory Open Access Journal |
| issn | 2322-5807 2423-3900 |
| language | English |
| last_indexed | 2024-12-10T06:41:03Z |
| publishDate | 2019-02-01 |
| publisher | University of Maragheh |
| record_format | Article |
| series | Sahand Communications in Mathematical Analysis |
| spelling | doaj.art-2fa66135867e492fbdc4ec8c6a61b51f2022-12-22T01:58:46ZengUniversity of MaraghehSahand Communications in Mathematical Analysis2322-58072423-39002019-02-01131173010.22130/scma.2018.59792.21131846$C$-class Functions and Common Fixed Point Theorems Satisfying $varphi $-weakly Contractive ConditionsArslan Hojat Ansari0Tatjana Dosenovic1Stojan Radenovic2Jeong Sheok Ume3Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.Faculty of Technology, Bulevar cara Lazara 1, University of Novi Sad, Serbia.Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia.Department of Mathematics, Changwon National University, Changwon, 641-773, Korea.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<br />in literature.We finally propose three open problems.http://scma.maragheh.ac.ir/article_31846_d6c970ed6b5f3e0d466239bb147f4213.pdfCommon fixed point$varphi $-weakly contractive conditionsComplete metric spaceWeakly compatible mappings$C$-class function |
| spellingShingle | Arslan Hojat Ansari Tatjana Dosenovic Stojan Radenovic Jeong Sheok Ume $C$-class Functions and Common Fixed Point Theorems Satisfying $varphi $-weakly Contractive Conditions Sahand Communications in Mathematical Analysis Common fixed point $varphi $-weakly contractive conditions Complete metric space Weakly compatible mappings $C$-class function |
| title | $C$-class Functions and Common Fixed Point Theorems Satisfying $varphi $-weakly Contractive Conditions |
| title_full | $C$-class Functions and Common Fixed Point Theorems Satisfying $varphi $-weakly Contractive Conditions |
| title_fullStr | $C$-class Functions and Common Fixed Point Theorems Satisfying $varphi $-weakly Contractive Conditions |
| title_full_unstemmed | $C$-class Functions and Common Fixed Point Theorems Satisfying $varphi $-weakly Contractive Conditions |
| title_short | $C$-class Functions and Common Fixed Point Theorems Satisfying $varphi $-weakly Contractive Conditions |
| title_sort | c class functions and common fixed point theorems satisfying varphi weakly contractive conditions |
| topic | Common fixed point $varphi $-weakly contractive conditions Complete metric space Weakly compatible mappings $C$-class function |
| url | http://scma.maragheh.ac.ir/article_31846_d6c970ed6b5f3e0d466239bb147f4213.pdf |
| work_keys_str_mv | AT arslanhojatansari cclassfunctionsandcommonfixedpointtheoremssatisfyingvarphiweaklycontractiveconditions AT tatjanadosenovic cclassfunctionsandcommonfixedpointtheoremssatisfyingvarphiweaklycontractiveconditions AT stojanradenovic cclassfunctionsandcommonfixedpointtheoremssatisfyingvarphiweaklycontractiveconditions AT jeongsheokume cclassfunctionsandcommonfixedpointtheoremssatisfyingvarphiweaklycontractiveconditions |