2015•Mathematical sciencesOpen access

Some fixed point theorems for contractive maps in N-cone metric spaces

Jerolina Fernandez, Geeta Modi, Neeraj Malviya

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Abstract

In present paper, we prove unique fixed point theorems for contractive maps in N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document} -cone metric spaces. Our results extend and generalize some well-known results of (Banach, Fund Math 3:133–181 1992 ; Chatterjee, Rend Acad Bulgare Sci 25:727–730 1972 ; Kannan, Bull Calcutta Math Soc 60:71–76 1968 ; Rezapour and Hamlbarani, J Math Anal Appl 345:719–724 2008 ) in the setting of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document} -cone metric spaces.

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In present paper, we prove unique fixed point theorems for contractive maps in N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document} -cone metric spaces. Our results extend and generalize some well-known results of (Banach, Fund Math 3:133–181 1992 ; Chatterjee, Rend Acad Bulgare Sci 25:727–730 1972 ; Kannan, Bull Calcutta Math Soc 60:71–76 1968 ; Rezapour and Hamlbarani, J Math Anal Appl 345:719–724 2008 ) in the setting of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document} -cone metric spaces.

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Available abstract

In present paper, we prove unique fixed point theorems for contractive maps in N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document} -cone metric spaces. Our results extend and generalize some well-known results of (Banach, Fund Math 3:133–181 1992 ; Chatterjee, Rend Acad Bulgare Sci 25:727–730 1972 ; Kannan, Bull Calcutta Math Soc 60:71–76 1968 ; Rezapour and Hamlbarani, J Math Anal Appl 345:719–724 2008 ) in the setting of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document} -cone metric spaces.

Key concepts: Mathematics, Metric space, Cone (formal languages), Chatterjee, Banach space, Fixed-point theorem, Fixed point, Pure mathematics

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