Suzuki Type Common Fixed Point Theorem For Four Maps Using α - admissible Functions In Partial Ordered Complex Valued Metric Spaces

K.P. R. Rao; P. Ranga Swamy; Sk. Sadik; E.Taraka Ramudu

K.P. R. Rao Department of Mathematics, Acharya Nagarjuna University, Nagarjuna Nagar -522 510, A.P. India
P. Ranga Swamy Department of Mathematics, St. Ann's college of Engineering and Technology, Chirala-523 187, Andhra Pradesh, India
Sk. Sadik Department of Mathematics, Sir C R R College of Engineering, Eluru, West Godhawari - 534007, Andhra Pradesh, India
E.Taraka Ramudu Department of Science and Humanities, Nova College of Engineering and Technology, Jupudi-521 456, Krishna Dt., Andhra Pradesh, India

Keywords: Complex valued metric, compatible maps, Suzuki type contraction, admissible function.

Abstract

In this paper, we obtain a Suzuki type unique common fixed point theorem for four self maps using α-admissible function in partial ordered complex valued metric spaces. Also we give an example to illustrate our main theorem.

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References

A.Azam,B.Fisher and M.Khan,Common fixed point theorems in complex valued metric spaces,Numer.Funct.Anal.Optim.32(3),(2011),243-253.

B.Samet,C.Vetro , P.Vetro, Fixed point theorems for α − ψ-contractive type mappings,Nonlinear Analysis,75,(2012),2154-2165.

C.Klin-eam and C.Suanoom,Some common fixed point theorems for

generralized contractive type mappings on complex valued metric spaces, Abstr.Appl.Anal.,2013,6 pages,Article ID 604215,

doi.10.1155/2013/604215.

D.Doric,Z.Kadelburg, S.Radenovic,Edelstein-Suzuki type fixed point

results in metric and abstract metric spaces,Nonlinear Analysis,

,(2012),1927-1932.

E.Karapinar,Edelstein type fixed point theorems,Ann.Funct.Anal., 2(1), (2011),51-58.

F. Rouzkard and M. Imdad, Some common fixed point theorems on complex valued metric spaces, Comp. Math.Appls., 64,(2012), 1866-1874.

G.Jungck,Compatible mappings and common fixed points,

Int.J.Math.Math.Sci.,9(4),(1986),771-779.

G.Jungck and B.E.Rhoades,Fixed points for set valued functions without continuity,Indian J.Pure.Appl.Math.,29(3),(1998),227-238.

H. K. Nashine, M. Imdad and M. Hasan,Common fixed point theorems

under rational contractions in complex valued metric spaces,J. Nonlinear

Sci. Appl.,7,(2014), 42-50.

I.Altun , A.Erduran, A Suzuki type fixed point theorem, Internat. Math. Math.Sci.,2011,(2011),9 pages,Article ID 736063.

K.Sitthikul and S.Saejung,Some fixed points in complex valued metric spaces, Fixed point theory Appl.,2012,11 pages,Article ID 189 .

M.Abbas,N.Talat Nazir and S.Radenovic,Common fixed points of four

maps in partially ordered metric spaces,Appl.Math.Lett.,24,(2011),1520-

M.Abbas,B.Fisher and T.Nazir,Well-posedness and peroidic point property of mappings satisfying a rational inequality in an ordrerd complex valuedmetric spaces,Sci. Stud. Res., Ser. Math. Inform. 22(1),(2012),5-24.

M.Abbas,M.Arshad and A.Azam,Fixed points of asympotically regular

mappings in complex valued metric spaces,Georgian Math.J.,20,(2013),

-221(2013):10.1515/gmj-2013-0013.

M.A.Kutbi,A.Azam,J.Ahmad, and C.Di Bari, Some common fixed point results for generalized contraction in complex-valued metric spaces, J.Appl. Math.,2013,10 pages, ArticleID 35297.

M.Kumar,P. Kumar and S. Kumar,Common fixed point theorems in complex valued metric spaces,J. Ana. Num. Theor. 2(2),(2014), 103-109.

N.Singh,D.Singh,A.Badal and V.Joshi,Fixed point theorems in complex valued metric spaces, Journal of the Egyptian Mathematical Society, (2015),1-8 (In Press).

P.Shahi,J.Kumar , S.S.Bhatia,Coincidence and common fixed point results for generalized α − ψ-contractive type mappings withapplications, Bull.Belg.Math.Soc. Simon Stevin,22(2),(2015),299-318.

R.K.Verma and H.K.Pathak,Common fixed point theorems for a pair of mappings in complex -Valued metric spaces,Journal of mathematics and computer Science, 6 (2013), 18-26.

S.Chandok and D.Kumar, Some common fixed point results for rational type contraction mappings in complex valued metric spaces, Journal of Operators, 2013,6 pages, Article ID 813707.

S.L.Singh,H.K.Pathak , S.N.Mishra,On a Suzuki type general fixed

point theorems with applications,Fixed Point Theory Appl.,2010,(2010),15

pages, Article ID 234717.

T.Abdeljawad,Meier-Keeler α-contractive fixed and common fixed point theorems,Fixed point theory Appl.,2013,(2013):19,10 pages,

doi:10.1186/1687-1812-2013-19.

T.Senthil Kumar and R.Jahir Hussain,Common coupled fixed point theorem for contractive type mappings in closed ball of complex valued metric spaces,Adv.Inequal.Appl.2014,1-7,2014:34.

T .Suzuki, A generalized Banach contraction principle which characterizes metric completeness.Proc.Amer.Math.Soc.,136,(2008), 1861-1869.

T.Suzuki,A new type of fixed point theorem in metric spaces, Nonlinear Analysis,71,(2009),5313-5317.

W.Sintunavarat and P.Kumam,Generalized common fixed point theorems in complex valued metric spaces and applications, J.Inequal.appl.,2012, 11 pages,Article ID 84.