Volume 35, Issue 3
Common Fixed Points for Two Mappings with Implicit-Linear Contractions on Partially Ordered 2-Metric Spaces

Commun. Math. Res., 35 (2019), pp. 225-234.

Published online: 2019-12

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• Abstract

In this paper, we introduce a new class ${\cal U}$ of 3-dimensional real functions, use ${\cal U}$ and a 2-dimensional real function $\phi$ to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results well generalize and improve the corresponding conclusions in references.

• Keywords

2-metric space, class $\cal U$ of functions, implicit-linear contraction, common fixed point

47H05, 47H10, 54E40

sxpyj@ybu.edu.cn (Yongjie Piao)

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@Article{CMR-35-225, author = {Yongjie and Piao and sxpyj@ybu.edu.cn and 5984 and Department of Mathematics, College of Science, Yanbian University, Yanji, Jilin, 133002 and Yongjie Piao}, title = {Common Fixed Points for Two Mappings with Implicit-Linear Contractions on Partially Ordered 2-Metric Spaces}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {35}, number = {3}, pages = {225--234}, abstract = {

In this paper, we introduce a new class ${\cal U}$ of 3-dimensional real functions, use ${\cal U}$ and a 2-dimensional real function $\phi$ to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results well generalize and improve the corresponding conclusions in references.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2019.03.04}, url = {http://global-sci.org/intro/article_detail/cmr/13528.html} }
TY - JOUR T1 - Common Fixed Points for Two Mappings with Implicit-Linear Contractions on Partially Ordered 2-Metric Spaces AU - Piao , Yongjie JO - Communications in Mathematical Research VL - 3 SP - 225 EP - 234 PY - 2019 DA - 2019/12 SN - 35 DO - http://doi.org/10.13447/j.1674-5647.2019.03.04 UR - https://global-sci.org/intro/article_detail/cmr/13528.html KW - 2-metric space, class $\cal U$ of functions, implicit-linear contraction, common fixed point AB -

In this paper, we introduce a new class ${\cal U}$ of 3-dimensional real functions, use ${\cal U}$ and a 2-dimensional real function $\phi$ to construct a new implicit-linear contractive condition and obtain some existence theorems of common fixed points for two mappings on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point. The obtained results well generalize and improve the corresponding conclusions in references.

Yong-jie Piao. (2019). Common Fixed Points for Two Mappings with Implicit-Linear Contractions on Partially Ordered 2-Metric Spaces. Communications in Mathematical Research . 35 (3). 225-234. doi:10.13447/j.1674-5647.2019.03.04
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