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

R. Rao, K.P.

Ramudu, E.Taraka

Sadik, Sk.

Swamy, P. Ranga

English

Scitech Research Journals

                                                                      Journal of Progressive Research in Mathematics(JPRM)                                                                                                                                                               ISSN: 2395-0218   Volume 7, Issue 1 available at www.scitecresearch.com/journals/index.php/jprm                                                   928|  SCITECH                                                                           Volume 7, Issue 1  RESEARCH ORGANISATION                Published online: March 29, 2016| Journal of Progressive Research in Mathematics www.scitecresearch.com/journals     Suzuki Type Common Fixed Point Theorem For Four Maps  Using   - admissible Functions In Partial Ordered  Complex Valued Metric Spaces K.P.R.Rao 1 , P.Ranga Swamy 2 , Sk.Sadik 3  and E.Taraka Ramudu 4    1Department of Mathematics,  Acharya Nagarjuna University, Nagarjuna Nagar -522 510, A.P., India.       2Department of Mathematics, St.Ann’s college of Engineering and Technology, Chirala-523 187,Andhra Pradesh, India. 3Department of Mathematics,  Sir C R R College of Engineering, Eluru ,  West Godhawari - 534007, Andhra Pradesh, India.  4Department of Science and Humanities,  Nova College of Engineering and Technology,  Jupudi-521 456, Krishna Dt., Andhra Pradesh, India.  Abstract. In this paper, we obtain a Suzuki type unique common fixed point theorem for four self maps using  -admissible function in partial ordered complex valued metric spaces. Also we give an example to illustrate our main theorem. Keywords: Complex valued metric; compatible maps; Suzuki type contraction; admissible function.   Mathematics Subject Classification: 47H10,54E50,54H25.   1  Introduction and Preliminaries       It is a well-known fact that the mathematical results regarding fixed points of contraction type mappings are very useful for determining the existence and uniqeness of solutions to various mathematical models.      Azam et al.[1] introduced the notion of a complex valued metric space which is a generalization of the classical metric space and obtained sufficent conditions for the existence of common fixed points of a pair of mappings satisfying a rational contractive condition.Though complex valued metric spaces form a special class of cone metric space, yet this idea is intended to define rational expressions which are not meaningful in cone metric spaces and thus many results of analysis cannot be generalized to cone metric spaces. However, in complex valued metric spaces, one can study improvements of a host of results of analysis involving divisions.Later several authors proved fixed and common fixed point theorems in complex valued metric spaces ,for example, refer [3, 6, 9, 11, 13, 14, 16, 17, 19, 20, 23, 26].   In this paper,we prove a unique common fixed point theorem for two pairs of mappings satisfying a contractive condition of rational type in the frame work of complex valued metric spaces using  -admissible function. The proved result generalizes and extends some of the results in the literature.    To begin with, we recall some basic definitions, notations and results.                                                                       Journal of Progressive Research in Mathematics(JPRM)                                                                                                                                                               ISSN: 2395-0218   Volume 7, Issue 1 available at www.scitecresearch.com/journals/index.php/jprm                                                   929|                                                                         Journal of Progressive Research in Mathematics(JPRM)                                                                                                                                                               ISSN: 2395-0218   Volume 7, Issue 1 available at www.scitecresearch.com/journals/index.php/jprm                                                   930|                                                                       Journal of Progressive Research in Mathematics(JPRM)                                                                                                                                                               ISSN: 2395-0218   Volume 7, Issue 1 available at www.scitecresearch.com/journals/index.php/jprm                                                   931|                                                                       Journal of Progressive Research in Mathematics(JPRM)                                                                                                                                                               ISSN: 2395-0218   Volume 7, Issue 1 available at www.scitecresearch.com/journals/index.php/jprm                                                   932|                                                                        Journal of Progressive Research in Mathematics(JPRM)                                                                                                                                                               ISSN: 2395-0218   Volume 7, Issue 1 available at www.scitecresearch.com/journals/index.php/jprm                                                   933|                                                                       Journal of Progressive Research in Mathematics(JPRM)                                                                                                                                                               ISSN: 2395-0218   Volume 7, Issue 1 available at www.scitecresearch.com/journals/index.php/jprm                                                   934|                                                                       Journal of Progressive Research in Mathematics(JPRM)                                                                                                                                                               ISSN: 2395-0218   Volume 7, Issue 1 available at www.scitecresearch.com/journals/index.php/jprm                                                   935|                                                                       Journal of Progressive Research in Mathematics(JPRM)                                                                                                                                                               ISSN: 2395-0218   Volume 7, Issue 1 available at www.scitecresearch.com/journals/index.php/jprm                                                   936|                                                                       Journal of Progressive Research in Mathematics(JPRM)                                                                                                                                                               ISSN: 2395-0218   Volume 7, Issue 1 available at www.scitecresearch.com/journals/index.php/jprm                                                   937|                                                                        Journal of Progressive Research in Mathematics(JPRM)                                                                                                                                                               ISSN: 2395-0218   Volume 7, Issue 1 available at www.scitecresearch.com/journals/index.php/jprm                                                   938| References  [1] 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. 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Journal of Progressive Research in Mathematics(JPRM)                                                                                                                                                               ISSN: 2395-0218   Volume 7, Issue 1 available at www.scitecresearch.com/journals/index.php/jprm                                                   939| [18] P.Shahi,J.Kumar , S.S.Bhatia,Coincidence and common fixed point results for generalized   -contractive type mappings with applications, Bull. Belg.Math. Soc.Simon Stevin,22(2),(2015),299-318. [19] 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. [20] 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. 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Suzuki Type Common Fixed Point Theorem For Four Maps Using α - admissible Functions In Partial Ordered Complex Valued Metric Spaces

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

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