Fuzzy-Prešić-Ćirić Operators and Applications to Certain Nonlinear Differential Equations

In this paper, we introduce a new class of operators called fuzzy-Prešić-Ćirić operators. For this type of operators, the existence and uniqueness of fixed point in M-complete fuzzy metric spaces endowed with H-type t-norms are established. The results proved here generalize and extend some comparab...

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Published inMathematical Modelling and Analysis Vol. 21; no. 6; pp. 811 - 835
Main Authors Shukla, Satish, Gopal, Dhananjay, Rodríguez-López, Rosana
Format Journal Article
LanguageEnglish
Published Taylor & Francis 01.11.2016
Vilnius Gediminas Technical University
Subjects
Differential equations
fixed point
Fixed point theory
Fuzzy
fuzzy metric space
Fuzzy-Prešic-Ciric operator
Fuzzy-Prešić-Ćirić operator
Maps (Mathematics)
Mathematical models
Mathematical research
Mathematics
Metric space
Metric spaces
Nonlinear differential equations
Nonlinearity
Operators (mathematics)
QA1-939
Theorems
Uniqueness
Fuzzy-Prešic-Ciric operator
fixed point
nonlinear differential equations
fuzzy metric space
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Summary:In this paper, we introduce a new class of operators called fuzzy-Prešić-Ćirić operators. For this type of operators, the existence and uniqueness of fixed point in M-complete fuzzy metric spaces endowed with H-type t-norms are established. The results proved here generalize and extend some comparable results in the existing literature. An example is included which illustrates the main result of this paper. Moreover, some applications of our main theorem to the study of certain types of nonlinear differential equations are provided.
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ISSN:1392-6292
1648-3510
DOI:10.3846/13926292.2016.1247303