NONLINEAR COUPLED COINCIDENCE AND COUPLED FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS IN PARTIALLY ORDERED PROBABILISTIC METRIC SPACES

Document Type : Original Article

Authors

1 223, block no.33 ,peer khana road near tewari kothi

2 Department of Mathematics and Informatics, Larbi Ben M'hidi University, Oum El Bouaghi, Algeria.

3 Department of Mathematics and Informatic, The Larbi Ben M'hidi Univer- sity, Oum El Bouaghi, Algeria.

4 Department of Mathematics, The Larbi Ben M'hidi University, Oum El Bouaghi, Algeria.

5 Department of Mathematics and Informatics. The Larbi Ben M'hidi Univer- sity, Oum El Bouaghi.

Abstract

In this paper, we introduce the notion of weaker compatibility
of mappings in partially ordered probabilistic metric spaces and use this no-
tion to establish a coupled coincidence point results. Very recently Dragan
Doric [Nonlinear coupled coincidence and coupled xed point theorems for not
necessary commutative contractive mappings in partially ordered probabilistic
spaces] proved coupled coincidence point theorems for compatible mappings
in partially ordered probabilistic metric spaces. In this paper we proved re-
sults of Dragam under a di erent set of conditions. Precisely, we establish
our results by assuming that two mappings in partially ordered probabilistic
metric spaces are weakly compatible. Our results improve and extend a cou-
pled xed point theorem due to Bhaskar and Lakshmikantham [T-G.Bhaskar ,
V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces
and applications, Nolinear Anal, 65(2006) 1379-1393]. An example is given to
support our result.In this paper, we introduce the notion of weaker compatibility
of mappings in partially ordered probabilistic metric spaces and use this no-
tion to establish a coupled coincidence point results. Very recently Dragan
Doric [Nonlinear coupled coincidence and coupled xed point theorems for not
necessary commutative contractive mappings in partially ordered probabilistic
spaces] proved coupled coincidence point theorems for compatible mappings
in partially ordered probabilistic metric spaces. In this paper we proved re-
sults of Dragam under a different set of conditions. Our results improve and extend a cou-
pled xed point theorem due to Bhaskar and Lakshmikantham. An example is given to
support our result.

Keywords

Communications in Nonlinear Analysis
Volume 10, Issue 1
July 2022
Pages 1-20

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