Main Article Content
Abstract
In this paper we define convex, strict convex and normal structures for sets in fuzzy cone metric spaces. Also, existence and uniqueness of a fixed point for non-self mappings with nonlinear contractive condition will be proved, using the notion of strictly convex structure. Moreover, we give some examples illustrate our results.
Keywords
Article Details
References
- %==============================================================
- bibitem{AK}
- N.A. Assad, W.A. Kirk, Fixed-point theorems for set-valued mappings of contractive type, Pacic
- J. Math., {bf43}(1972), 553--562.
- %==================================================================================
- bibitem{Banach}
- S. Banach, Sur la op'erations dans les ensembles abstraits et leurs applications aux 'equations
- int'egrales, Fund. Math., {bf3}(1922), 133--181.
- %=======================================================================
- bibitem{BW}
- D.W. Boyd, J.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., {bf20}(1969), 458--464.
- %===================================================================================
- bibitem{C1}
- L.B. 'Ciri'c, Common fixed point theorems for family on non-self mappings in convex metric
- spaces, Nonlinear Anal., {bf71}(2009), 1662--1669.
- %====================================================
- bibitem{C2}
- L.B. 'Ciri'c, Quasi-contraction non-self mappings on Banach spaces, Bull. Acad. Serbe Sci. Arts,
- {bf23}(1998), 25--31.
- %===============================================================================
- bibitem{C3}
- L.B. 'Ciri'c, Contractive type non-self mappings on metric spaces of hyperbolic type, J. Math.
- Anal. Appl., {bf317}(2006), 28--42.
- %========================================================================
- bibitem{GR1}
- L. Gaji'c, V. Rakov cevi'c, Quasicontraction nonself-mappings on convex metric spaces and com-
- mon fixed point theorems, Fixed Point Theory Appl., {bf3}(2005), 365--375.
- %============================================================================
- bibitem{GR2}
- L. Gaji'c, V. Rakov cevi'c, Pair of non-self-mappings and common xed points, Appl. Math. Com-
- put., {bf187}(2007), 999--1006.
- %=============================================================================
- bibitem{GV}
- A. George and P. Veeramani, On some results in fuzzy metric spaces, J. Fuzzy Sets Syst., textbf{64} (1994), 395--399.
- %========================================================================
- bibitem{Hadzic-0}
- O. Hadv zi'c, Common fixed point theorems in probabilistic metric spaces with convex structure,
- Zb. rad. Prirod-Mat.Fak.ser. Mat. textbf{18} (1987),165--178.
- %=============================================================================================
- bibitem{HZ}
- L.G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings. J. Math.
- Anal. App., textbf{332}(2007), 1468--1476.
- %=======================================================================================
- bibitem{Jesic}
- S.N. Jev si'c, Convex structure, normal structure and a fixed point theorem in intuitionistic fuzzy metric space,
- Chaos, Solitions & Fractals, textbf{41} (2008), 292--301.
- %=====================================================================
- bibitem{Jesic-1}
- S.N. Jev si'c, R. M. Nikolic and A. Babav cev, A common fixed point theorem
- in strictly convex Menger PM-spaces, Filomat textbf{28:4} (2016), 735--743.
- %========================================================================
- bibitem{OKT}
- T. "Oner, M. B. Kandemir and B. Tanay, Fuzzy cone metric spaces, J.Nonlinear Sci. Appl. {bf8}(2015), 610--616.
- %==========================================================================
- bibitem{KM}
- O. Kramosil and J.Michalek, Fuzzy metric and Statistical metric spaces, Kybernetika, textbf{11} (1975), 326--334.
- %========================================================================
- bibitem{R}
- B.E. Rhoades, A fixed point theorem for some non-self mappings, Math. Japon., {bf23}(1978),
- --459.
- %==================================================================================
- bibitem{RH}
- Sh. Rezapour, R. Hamlbarani, Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings",
- J. Math. Anal. Appl., textbf{345}, 719--724 (2008).
- %============================================================================
- bibitem{Sch2}
- B. Schweizer and A. Sklar, Probabilistical Metric Spaces, Dover Publications, New York, 2005.
- %========================================================================================
- bibitem{TA}
- D. Turkoglu , M. Abuloha, Cone metric spaces and fixed point theorems in diametrically contractive mappings,
- Acta Math. Sin., textbf{26 }, 489--496(2010).
- %===========================================================================
- bibitem{Takahashi}
- W. Takahashi, A convexity in metric space and nonexpansive mappings, Kodai Math. Sem. Rep., textbf{22}(1970), 142--149.
- %===================================================================================
- bibitem{Zadeh}
- L.A. Zadeh, Fuzzy Sets, Inform Contr. textbf{8} (1965), 338--353.
- %==========================================================================================================
References
%==============================================================
bibitem{AK}
N.A. Assad, W.A. Kirk, Fixed-point theorems for set-valued mappings of contractive type, Pacic
J. Math., {bf43}(1972), 553--562.
%==================================================================================
bibitem{Banach}
S. Banach, Sur la op'erations dans les ensembles abstraits et leurs applications aux 'equations
int'egrales, Fund. Math., {bf3}(1922), 133--181.
%=======================================================================
bibitem{BW}
D.W. Boyd, J.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., {bf20}(1969), 458--464.
%===================================================================================
bibitem{C1}
L.B. 'Ciri'c, Common fixed point theorems for family on non-self mappings in convex metric
spaces, Nonlinear Anal., {bf71}(2009), 1662--1669.
%====================================================
bibitem{C2}
L.B. 'Ciri'c, Quasi-contraction non-self mappings on Banach spaces, Bull. Acad. Serbe Sci. Arts,
{bf23}(1998), 25--31.
%===============================================================================
bibitem{C3}
L.B. 'Ciri'c, Contractive type non-self mappings on metric spaces of hyperbolic type, J. Math.
Anal. Appl., {bf317}(2006), 28--42.
%========================================================================
bibitem{GR1}
L. Gaji'c, V. Rakov cevi'c, Quasicontraction nonself-mappings on convex metric spaces and com-
mon fixed point theorems, Fixed Point Theory Appl., {bf3}(2005), 365--375.
%============================================================================
bibitem{GR2}
L. Gaji'c, V. Rakov cevi'c, Pair of non-self-mappings and common xed points, Appl. Math. Com-
put., {bf187}(2007), 999--1006.
%=============================================================================
bibitem{GV}
A. George and P. Veeramani, On some results in fuzzy metric spaces, J. Fuzzy Sets Syst., textbf{64} (1994), 395--399.
%========================================================================
bibitem{Hadzic-0}
O. Hadv zi'c, Common fixed point theorems in probabilistic metric spaces with convex structure,
Zb. rad. Prirod-Mat.Fak.ser. Mat. textbf{18} (1987),165--178.
%=============================================================================================
bibitem{HZ}
L.G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings. J. Math.
Anal. App., textbf{332}(2007), 1468--1476.
%=======================================================================================
bibitem{Jesic}
S.N. Jev si'c, Convex structure, normal structure and a fixed point theorem in intuitionistic fuzzy metric space,
Chaos, Solitions & Fractals, textbf{41} (2008), 292--301.
%=====================================================================
bibitem{Jesic-1}
S.N. Jev si'c, R. M. Nikolic and A. Babav cev, A common fixed point theorem
in strictly convex Menger PM-spaces, Filomat textbf{28:4} (2016), 735--743.
%========================================================================
bibitem{OKT}
T. "Oner, M. B. Kandemir and B. Tanay, Fuzzy cone metric spaces, J.Nonlinear Sci. Appl. {bf8}(2015), 610--616.
%==========================================================================
bibitem{KM}
O. Kramosil and J.Michalek, Fuzzy metric and Statistical metric spaces, Kybernetika, textbf{11} (1975), 326--334.
%========================================================================
bibitem{R}
B.E. Rhoades, A fixed point theorem for some non-self mappings, Math. Japon., {bf23}(1978),
--459.
%==================================================================================
bibitem{RH}
Sh. Rezapour, R. Hamlbarani, Some notes on the paper "Cone metric spaces and fixed point theorems of contractive mappings",
J. Math. Anal. Appl., textbf{345}, 719--724 (2008).
%============================================================================
bibitem{Sch2}
B. Schweizer and A. Sklar, Probabilistical Metric Spaces, Dover Publications, New York, 2005.
%========================================================================================
bibitem{TA}
D. Turkoglu , M. Abuloha, Cone metric spaces and fixed point theorems in diametrically contractive mappings,
Acta Math. Sin., textbf{26 }, 489--496(2010).
%===========================================================================
bibitem{Takahashi}
W. Takahashi, A convexity in metric space and nonexpansive mappings, Kodai Math. Sem. Rep., textbf{22}(1970), 142--149.
%===================================================================================
bibitem{Zadeh}
L.A. Zadeh, Fuzzy Sets, Inform Contr. textbf{8} (1965), 338--353.
%==========================================================================================================