Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

Servet Kutukcu;Adnan Tuna;Atakan T. Yakut

doi:10.1007/s10483-007-0610-z

Applied Mathematics and Mechanics >

2007 , Vol. 28 >Issue 6: 799 - 809

DOI: https://doi.org/10.1007/s10483-007-0610-z

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Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations

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1. Department of Mathematics, Faculty of Science and Arts, Ondokuz Mayis University, Kurupelit, 55139 Samsun, Turkey;
2. Department of Mathematics, Faculty of Science and Arts, Gazi University, Teknikokullar, 06500 Ankara, Turkey;
3. Department of Mathematics, Faculty of Science and Arts, Nigde University, Nigde, Turkey

Received date: 2006-07-10

Revised date: 2007-01-31

Online published: 2007-06-18

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Abstract

Using the idea of Atanassov, we define the notion of intuitionistic Menger spaces as a netural generalizations of Menger spaces due to Menger. We also obtain a new generalized contraction mapping and utilize this contraction mapping to prove the existance theorems of solutions to differential equations in intuitionistic Menger spaces.

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Servet Kutukcu;Adnan Tuna;Atakan T. Yakut . Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations[J]. Applied Mathematics and Mechanics, 2007 , 28(6) : 799 -809 . DOI: 10.1007/s10483-007-0610-z

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