REFERENCES. differential equations, Nonlinear Anal., 72 (2010), A. Amini-Harandi and M. Fakhar, Fixed point theory in cone metric

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1 REFERENCES 1. A. Amini - Harandi and H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal., 72 (2010), A. Amini-Harandi and M. Fakhar, Fixed point theory in cone metric spaces via scalarization method, Computers and Mathematics with Applications, 59 (2010), A. Azam, M. Arshad and I. Beg, Common fixed points of two maps in cone metric spaces, Rendiconti del Circolo Matematico di Palermo, 57 (2008), A. Cabada and J. J. Nieto, Fixed points and approximate solutions for nonlinear operator equations, J.Comput.Appl.Math., 113 (2000), A. C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), A. George and P. Veeramani, On some results in fuzzy metric space, Fuzzy Sets Syst., 64 (1994), A.Muhammad, A. Akbar and V. Pasquale, Some Common fixed points in cone metric space, Fixed Point Theory and Applications, Volume 2009, (2009), Article ID , 11 pages. 8. B.E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226 (1977),

2 9. B.E. Rhoades, A fixed point theorem for a multi - valued non - self mapping, Comment. Math. Univ. Carolin., 37 (1996), B. Samet and C. Vetro, Coupled fixed point theorems for multi - valued nonlinear contraction mappings in partially ordered metric spaces, Nonlinear Analysis, 74 (2011), B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), B. Singh and M. S. Chauhan, Common fixed points of compatible maps in fuzzy metric spaces, Fuzzy Sets Syst., 115 (2000), B. Singh and S. Jain, Semi compatibility and fixed point theorems in fuzzy metric space using implicit relation, Internat. J. Math. Math. Sci., 16 (2005), B. Singh and S. Jain, Semi compatibility, compatibility and fixed point theorems in fuzzy metric space, J. Chung Cheong Math. Soc., 18 (1), (2005), B. S. Choudhury and N. Metiya, Fixed points of weak contractions in cone metric spaces, Nonlinear analysis, 72 (2010), B. S. Choudhury and N. Metiya, The point of coincidence and common fixed point for a pair of mappings in cone metric spaces, Comput. Math. Appl., 60(6), (2010), D.Ilic and V.Rakocevic, Common fixed points for maps on cone metric spaces, J.Math.Anal.Appl., 341 (2008),

3 18. D. Ilić, V. Pavlović and V. Rakočević, Some new extensions of Banach s contraction principle to partial metric spaces, Appl. Math. Letters, 24(8), (2011), D. Turkoglu, M. Abuloha and T. Abdeljawad, KKM mappings in cone metric spaces and some fixed point theorems, Nonlinear Analysis: Theory, Methods and Applications, 72(1), (2010), E. Karapínar, Fixed point theorems in cone Banach spaces, Fixed Point Theory Appl., Volume 2009, (2009), 9 pages, Article ID E. Karapínar, Couple fixed point theorems for nonlinear contractions in cone metric spaces, Computers and Mathematics with Applications, 59 (2010), E. Karapínar, Some non - unique fixed point theorems of Ciric type on cone metric spaces, Abstr. Appl. Anal., Volume 2010, (2010), 14 pages, Article ID , doi: /2010/ E. Karapínar and D. A. Turkoglu, Best approximations theorem for a couple in cone Banach Space, Fixed Point Theory Appl., Volume 2010, (2010), 9 pages, Article ID E. Karapínar, Couple fixed point on cone metric spaces, Gazi University J. Sci., 24(1), (2011), E. Karapínar, Generalizations of Caristi Kirk s Theorem on Partial metric Spaces, Fixed Point Theory and. Appl., (2011), 2011:4, 7 pages, doi: /

4 26. E. Karapínar, Weak φ - contraction on partial contraction and existence of fixed points in partially ordered sets, Mathematica Aeterna, 1(4), (2011), E. Karapínar and I. M. Erhan, Fixed point theorems for operators on partial metric spaces, Applied Mathematics Letters, 24 (11), (2011), G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9 (1986), G. Jungck and B. E. Rhoades, Fixed point for set valued functions without continuity, Indian. J. Pure Appl. Math., 29 (3), (1998), G.Jungck, S. Radenovic, S. Radojevic and V. Rakocevic, Common fixed point theorems for weakly compatible pairs on Cone Metric Spaces, Fixed Point Theory and Applications, Volume 2009, (2009), 13 pages, Article ID , doi : //2009/ H. Aydi, Fixed point results for weakly contractive mappings in ordered partial metric spaces, Journal of Advanced Mathematical and Studies, 4(2), (2011), H. Aydi, Some coupled fixed point results on partial metric spaces, International Journal of Mathematics and Mathematical Sciences, Volume 2011, (2011), 11 pages, Article ID , doi: /2011/ H. Aydi, B. Samet and C. Vetro, Coupled fixed point results in cone metric spaces for W - compatible mappings, Fixed Point Theory and Applications, (2011), 2011:27 (8 August 2011). 214

5 34. H. Aydi, M. Abbas and M. Postolache, Coupled coincidence points for hybrid pair of mappings via mixed monotone property, J. Adv. Math. Stud., 5(1), (2012), No. 1, H.G. Li, s - coincidence and s - common fixed point theorems for two pairs of set - valued non - compatible mappings in metric space, J. Nonlinear Sci. Appl., 3 (2010), H. K. Nashine, B. Samet, Fixed point results for mappings satisfying (ψ, φ) - weakly contractive condition in partially ordered metric spaces, Nonlinear Anal., 74 (2011), H. K. Nashine, B. Samet, C. Vetro, Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces, Math. Comput. Model., 54 (2011), H. K. Nashine, I. Altun, Fixed point theorems for generalized weakly contractive condition in ordered metric spaces, Fixed Point Theory and Appl., Volume 2011 (2011), Article ID , 20 pages. 39. H.P.A. Künzi, H. Pajoohesh, and M.P. Schellekens, Partial quasi - metrics, Theoret. Comput. Sci., 365 (3), (2006), I. Altun, A common fixed point theorem for multi - valued Círíc type mappings with new type compatibility, An. St. Univ. Ovidius Constanta., 17(2), (2009), I. Altun and A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory and Applications, Volume 2011, (2011), 10 pages, Article ID , doi: / 2011/

6 42. I. Altun, B. Damjanovic and D. Djoric, Fixed point and common fixed point theorems on ordered cone metric spaces, Applied Mathematics Letters, 23(3), (2010), I. Altun, F. Sola and H. Simsek, Generalized contractions on partial metric spaces, Topology and its Applications., 157(6), (2010), I. Altun, K. Sadarangani, Corrigendum to Generalized contractions on partial metric spaces [Topology Appl., 157, (2010), ], Topology Appl., 158 (6), (2011), I. Arandjelovic, Z. Kadelburg and S. Radenovic, Boyd - Wong type common fixed point results in cone metric spaces, Applied Mathematics and Computation, 217 (2011), I. Beg and A. R. Butt, Coupled common fixed points of set valued mappings in partially ordered metric spaces, J. Nonlinear Sci. Appl., 3(2010), I. Beg and A. R. Butt, Fixed point for set - valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal. 71 (2009), I. Beg, M. Abbas and T. Nazir, Generalized cone metric spaces, J. Nonlinear Sci. Appl., 3 (1), (2010), I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11 (1975),

7 50. I.Sahin and M.Telci, Fixed points of contractive mappings on complete cone metric spaces, Hacet.J.Math.stat., 38(1), (2009), J. Caballero, J. Harjani and K. Sadarangani, Contractive - like mapping principles in ordered metric spaces and application to ordinary differential equations, Fixed Point Theory and Appl., Volume 2010 (2010), Article ID , 14 pages. 52. J. Harjani, B. López and K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal., 74 (2011), J. Harjani and K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal., 71 (2009), J. Harjani and K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72 (2010), J. J. Nieto and R. Rodriguez - Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), J. Rodríguez López and S. Romaguera, The Hausdorff fuzzy metric on compact sets, Fuzzy Sets Syst., 147 (2004), L. A. Zadeh, Fuzzy sets, Inform and Control, 8 (1965),

8 58. Lj.B. Ćirić, Fixed point theorems for multi - valued contractions in complete metric spaces, J. Math. Anal. Appl., 348 (2008), Lj.B. Ćirić,Multi - valued nonlinear contraction mappings, Nonlinear Anal., 71 (2009), Lj. B. Ćirić, B.Samet, H.Aydi and C.Vetro, Common fixed points of generalized contractions on partial metric spaces and an application, Applied Mathematics and Computation, 218 (2011), Lj.B. Ćirić and J.S. Ume, Common fixed point theorems for multi - valued non - self mappings, Publ. Math. Debrecen, 60 (2002), Lj. B. Círić, N. Cakic, M. Rajovic and J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory and Appl., Volume 2010 (2010), Article ID , 11 pages. 63. L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of Contractive mappings, J. Math.Anal.Appl.,332(2), (2007), M.Abbas and B.E.Rhoades, Fixed and periodic point results in cone metric spaces, Appl.Math.Letters., 22(4), (2009), M.Abbas, B.E.Rhoades and T.Nazir, Common fixed points for four mappings in cone metric spaces, Appl.Math.Comput., 216 (2010), M.Abbas and G.Jungck, Common fixed point results for non commuting mappings without continuity in cone metric spaces, Journal of Mathematical Analysis and Applications, 341(1), (2008),

9 67. M.Abbas, M.Alikhan and S.Radenović, Common coupled fixed point theorems in cone metric spaces for w - compatible mappings, Applied Mathematics and Computation, 217(1), (2010), Pages M. Abbas, T. Nazir and S. Radenović, Common fixed points of four maps in partially ordered metric spaces, Appl. Math. Lett., 24 (2011), M. Frechet, Surquelques points du calcul fonctionnel, Rendic. Circ. Mat. Palermo., 22(1906), M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Syst., 27 (1988), M. O. Olatinwo, Coupled fixed point theorems in cone metric spaces, Ann Univ Ferrara, 57 (2011), M. Pacurar, I.A. Rus, Fixed point theory for cyclic φ - contractions, Nonlinear Anal., 72 (3-4), (2010), M.P.Schellekens, A characterization of partial metrizebility: domains are quantifiable, Theoretical Computer Sciences, 305(1-3), (2003), M.Schellekens, The Smyth completion: A common foundation for denotational semantics and complexity analysis, Electronic Notes in Theoretical Computer Science., 1 (1995), N. Hussain and A. Alotaibi, Coupled coincidences for multi - valued contractions in partially ordered metric spaces, Fixed Point Theory and Applications, 2011, 2011 :

10 76. N. Mizoguchi and W. Takahashi, Fixed point theorems for multi - valued mappings on complete metric spaces, J. Math. Anal. Appl., 141 (1989), N. V. Luong and N. X. Thuan, Coupled fixed points in partially order metric spaces and application, Nonlinear Analysis, 74 (2011), O. Hadzic and E. Pap, A fixed point theorem for multi valued mappings in probabilistic metric spaces and an application in fuzzy metric spaces, Fuzzy Sets Syst., 127 (2002), O. Valero, On Banach fixed point theorems for partial metric spaces, Applied General Topology, 6 (2), (2005), P. Vetro, Common fixed points in cone metric spaces, Rendiconti del Circolo Mathematico di Palermo, series II, 56 (2007), P.Waszkiewicz, Quantitative continuous domains, Applied Categorical Structures, 11(1), (2003), P.Waszkiewicz, Partial metrizebility of continuous posets, Mathematical Structures in Computer Sciences, 16(2), (2006), R. Chugh and S. Kumar, Common fixed point theorems in fuzzy metric spaces, Bull. Cal. Math. Soc., 94 (1) (2002), R. Heckmann, Approximation of metric spaces by partial metric spaces, Appl. Categ. Structures, 7(1-2), (1999), R. Kopperman, S.G. Matthews and H. Pajoohesh, What do partial metrics represent?, Spatial representation: discrete vs. continuous 220

11 computational models, Dagstuhl Seminar Proceedings, No , Internationales Begegnungs - und Forschungszentrum fr Informatik (IBFI), Schloss Dagstuhl, Germany, (2005), MR 2005j: R. P. Agarwal, M. A. El - Gebeily and D. O Regan, Generalized contractions in partially ordered metric spaces, Applicable Analysis, 87 (2008), R. Saadati, A. Razani, and H. Adibi, A common fixed point theorem in L - fuzzy metric spaces, Chaos, Solitons, Fractals, 33(2), (2006), R. Vasuki, Common fixed points for R - weakly commuting maps in fuzzy metric spaces, Indian J. Pure Appl. Math., 30 (1999), S.Banach, Surles operations dans les ensembles abstraits et leur applications aux equations, integrals, Fund. Math., 3(1922), S. B. Jr. Nadler, Multi - valued contraction mappings, Pacific J. Math., XXX (1969), S.G. Matthews, Partial metric topology, Research Report 212, Dept. of Computer Science, University of Warwick, S.G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, in: Ann. New York Acad. Sci., 728 (1994), Sh. Rezapour, A review on topological properties of Cone metric spaces, in Analysis, Topology and Applications (ATA 08), Vrnjacka Banja, Serbia, May - June

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13 102. S. Radenovic and Z. Kadelburg, Generalized weak contractions in partially ordered metric spaces, Comput. Math. with Appl., 60 (2010), S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory., Vol.2010, (2010), Article ID , 6 pages, doi: / 2010/ S. Romaguera, Fixed point theorems for generalized contractions on partial metric spaces, Topology and its Applications, 159 (2012), S. Romaguera and M. Schellekens, Weightable quasi - metric semigroup and semilattices, Electronic Notes of Theoretical computer science, 40 (2001), S.Romaguera and M.Schellekens, Partial metric monoids and semi valuation spaces, Topology and Applications, 153(5-6), (2005), S.Romaguera and O.Valero, A quantitative computational model for complete partial metric spaces via formal balls, Mathematical Structures in Computer Sciences, 19(3), (2009), S. Sharma, Common fixed point theorems in fuzzy metric spaces, Fuzzy Sets Syst., 127 (2002), T. Abdeljawad and E. Karapínar, Quasi - cone metric spaces and generalizations of Caristi Kirk s theorem, Fixed Point Theory Appl., Volume 2009 (2009), Article ID , 9 pages. 223

14 110. T. Abdeljawad and E. Karapínar, A common fixed point theorem of a Gregus type on convex cone metric spaces, J. Comput. Anal. Appl., 13(4), (2011), T. Abdeljawad, E. Karapínar and K.Tas, Common fixed point theorems in cone Banach spaces, Hacet.J.Math.Stat., 40(2), (2011), T. Abdeljawad, E. Karapínar, K. Tas, Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24 (11), (2011), T.G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis, 65 (2006), V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Analysis, 74(15), (2011), V. Lakshmikantham and Lj. B. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis, 70, (2009), Wei - Shih Du, Some generalizations of Mizoguchi - Takahashi s fixed point theorem, Int. J. Contemp. Math. Sci., 3 (2008) Wei - Shih Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Analysis, TMA, 72 (2010),

15 118. W. Shatanawi, Partially ordered cone metric spaces and coupled fixed point results, Comput. Math. Appl., 60 (2010) W. Shatanawi, B. Samet and Mujahid Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Mathematical and Computer Modeling, 55 (2012), Y.J.Cho, Fixed points in fuzzy metric spaces, J. Fuzzy Math., 5 (1997), Y. J. Cho, H. K. Pathak, S. M. Kang and J. S. Jung, Common fixed points of compatible maps of type (β) on fuzzy metric spaces, Fuzzy Sets Syst., 93 (1998), Z. Kadelburg, M. Pavlović and S. Radenović, Common fixed point theorems for ordered contractions and quasi - contractions in ordered cone metric spaces, Applied Mathematics with Applications, 59 (2010), Z. Kadelburg, S. Radenovic and V. Rakocevic, Remarks on quasi - contraction on a cone metric space, Applied Mathematics Letters, 22 (2009), Z.Mustafa and B.Sims, A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis, 7(2), (2006),

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