Fixed points of (fi,psi) - almost generalized weakly contractive maps with rational expressions in partially ordered metric spaces
Abstract
In this paper, we introduce a notion of (φ; )-almost generalizedweakly contractive maps involving rational type expressions in partially ordered metric spaces and prove the existence of xed points. These results generalize the results of Chandok, Choudhury and Metiya [16]. Also we provide examples in support of our results.
References
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[3] I. Altun and H. Simsek. Some Fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl., Volume 2010, Article ID 621469, 17 pages
[4] 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.: Theory, Meth. Appl., 72(5)(2010), 2238-2242.
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[6] M. Abbas, T. Nazir and S. Radenovic. Common fixed points of four maps in partially ordered metric spaces. Appl. Math. Letters, 24(9)(2011), 1520-1526.
[7] A. Brondsted. Common fixed points and partial orders, Proc. Amer. Math. Soc., 77(3)(1979), 365-368.
[8] V. Berinde. Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum, 9(1)(2004), 43-53.
[9] V. Berinde. General constructive fixed point theorems for Ciric-type almost contractions in metric spaces, Carpathian J. Math., 24(2)(2008), 10-19.
[10] G. V. R. Babu, M. L. Sandhya and M. V. R. Kameswari. A note on a fixed point theorem of Berinde on weak contractions. Carpathian J. Math., 24(1)(2008), 8-12.
[11] G. V .R. Babu and P. D. Sailaja, A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces, Thai J. Math., 9(1)(2011), 1-10.
[12] Lj. B. Ciric, N. Cakic, M. Rajovic and J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed point Theory Appl., Article ID 131294, (2008),
1-11.
[13] Lj. B. Ciric, M. Abbas, R. Saadati and N. Hussain, Common fixed points of almost generalized contractive mappings in ordered metric spaces, Appl. Math and Computation, 217
(12)(2011), 5784-5789.
[14] B. S. Choudhury and Amaresh Kundu, A kannan-like contraction in partially ordred metric spaces, Demonstratio Mathematics, 2013, 46123.
[15] I. Cabrera, J. Harjani and K. Sadarangani, A fixed point theorem for contractions of rational type in partially ordered metric spaces, Ann. Univ. Ferrara., 59(2)(2013), 251-258.
[16] S. Chandok, B. S. Choudhury and N. Metiya. Fixed point results in ordered metric spaces for rational type expressions with auxiliary functions, J. Egypt. Math. Soc., 23(1)(2015),
95-101.
[17] B. K. Dass and S. Gupta. An extension of Banach contraction principle through rational expressions, Indian J. pure appl. Math., 6(1975), 1455-1458.
[18] P. N. Dutta and B. S. Choudhury. A generalisation of contraction principle in metric spaces, Fixed Point Theory and Applications, Article ID 406368, (2008), 8 pages.
[19] D. Doric. Common fixed point for generalized ( ; φ)- weak contraction, Appl. Math. Lett., 22(12)(2009), 1896-1900.
[20] J. Harjani and K. Sadarangani. Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72(3-4)(2010), 1188-
1197.
[21] J. Harjani, B. Lopez, K. Sadarangani. Fixed point theorems for weakly C -contractive mappings in ordered metric spaces. Comput. Math. Appl., 61(4)(2011), 790-796 .
[22] M. S. Khan, M. Swaleh and S. Sessa. Fixed point theorems by altering distance between points. Bull. Aust. Math. Soc., 30(1)(1984), 1-9.
[23] J. J. Nieto and R.Rodriguez-Lopez. Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order, 22(3)(2005), 223-239.
[24] J. J. Nieto and R. Rodriguez-Lopez. Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica,
23(12)(2007), 2205-2212 .
[25] H. K. Nashine and B. Samet. Fixed point results for mappings satisfying ( ; ϕ) -weakly contractive condition in partially ordered metric spaces, Nonlinear Anal., 74(6)(2011),
2201-2209.
[26] H. K. Nashine, B. Samet and J. K. Kim. Fixed point results for contractions involving generalized altering distances in ordered metric spaces, Fixed point Theory Appl., 2011,
2011: 5.
[27] H. K. Nashine and I. Altun. A common xed point theorem on ordered metric spaces, Bull. Iranian Math. Soc., 38(4)(2012), 925-934.
[28] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47(4)(2001), 2683-2693.
[29] 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(5)(2004), 1435-1443.
[30] D. O'Regan and A. Petrutel. Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341(2)(2008), 1241-1252.
and appl., Vol. 98 (1997) of the series Operator Theory: Advances and Applications, (pp. 7-22). Birkhuser Basel 1997.
[2] R. P. Agarwal, M. A. El-Gebeily and D. ORegan. Generalized contractions in partially ordered metric spaces, Appl. Anal., 87(1)(2008), 109-116.
[3] I. Altun and H. Simsek. Some Fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl., Volume 2010, Article ID 621469, 17 pages
[4] 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.: Theory, Meth. Appl., 72(5)(2010), 2238-2242.
[5] M. Abbas, G. V. R. Babu and G. N. Alemayehu. On common fixed points of weakly compatible mappings satisfying generalized condition (B), Filomat, 25(2)(2011), 9-19.
[6] M. Abbas, T. Nazir and S. Radenovic. Common fixed points of four maps in partially ordered metric spaces. Appl. Math. Letters, 24(9)(2011), 1520-1526.
[7] A. Brondsted. Common fixed points and partial orders, Proc. Amer. Math. Soc., 77(3)(1979), 365-368.
[8] V. Berinde. Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum, 9(1)(2004), 43-53.
[9] V. Berinde. General constructive fixed point theorems for Ciric-type almost contractions in metric spaces, Carpathian J. Math., 24(2)(2008), 10-19.
[10] G. V. R. Babu, M. L. Sandhya and M. V. R. Kameswari. A note on a fixed point theorem of Berinde on weak contractions. Carpathian J. Math., 24(1)(2008), 8-12.
[11] G. V .R. Babu and P. D. Sailaja, A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces, Thai J. Math., 9(1)(2011), 1-10.
[12] Lj. B. Ciric, N. Cakic, M. Rajovic and J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed point Theory Appl., Article ID 131294, (2008),
1-11.
[13] Lj. B. Ciric, M. Abbas, R. Saadati and N. Hussain, Common fixed points of almost generalized contractive mappings in ordered metric spaces, Appl. Math and Computation, 217
(12)(2011), 5784-5789.
[14] B. S. Choudhury and Amaresh Kundu, A kannan-like contraction in partially ordred metric spaces, Demonstratio Mathematics, 2013, 46123.
[15] I. Cabrera, J. Harjani and K. Sadarangani, A fixed point theorem for contractions of rational type in partially ordered metric spaces, Ann. Univ. Ferrara., 59(2)(2013), 251-258.
[16] S. Chandok, B. S. Choudhury and N. Metiya. Fixed point results in ordered metric spaces for rational type expressions with auxiliary functions, J. Egypt. Math. Soc., 23(1)(2015),
95-101.
[17] B. K. Dass and S. Gupta. An extension of Banach contraction principle through rational expressions, Indian J. pure appl. Math., 6(1975), 1455-1458.
[18] P. N. Dutta and B. S. Choudhury. A generalisation of contraction principle in metric spaces, Fixed Point Theory and Applications, Article ID 406368, (2008), 8 pages.
[19] D. Doric. Common fixed point for generalized ( ; φ)- weak contraction, Appl. Math. Lett., 22(12)(2009), 1896-1900.
[20] J. Harjani and K. Sadarangani. Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72(3-4)(2010), 1188-
1197.
[21] J. Harjani, B. Lopez, K. Sadarangani. Fixed point theorems for weakly C -contractive mappings in ordered metric spaces. Comput. Math. Appl., 61(4)(2011), 790-796 .
[22] M. S. Khan, M. Swaleh and S. Sessa. Fixed point theorems by altering distance between points. Bull. Aust. Math. Soc., 30(1)(1984), 1-9.
[23] J. J. Nieto and R.Rodriguez-Lopez. Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order, 22(3)(2005), 223-239.
[24] J. J. Nieto and R. Rodriguez-Lopez. Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica,
23(12)(2007), 2205-2212 .
[25] H. K. Nashine and B. Samet. Fixed point results for mappings satisfying ( ; ϕ) -weakly contractive condition in partially ordered metric spaces, Nonlinear Anal., 74(6)(2011),
2201-2209.
[26] H. K. Nashine, B. Samet and J. K. Kim. Fixed point results for contractions involving generalized altering distances in ordered metric spaces, Fixed point Theory Appl., 2011,
2011: 5.
[27] H. K. Nashine and I. Altun. A common xed point theorem on ordered metric spaces, Bull. Iranian Math. Soc., 38(4)(2012), 925-934.
[28] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47(4)(2001), 2683-2693.
[29] 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(5)(2004), 1435-1443.
[30] D. O'Regan and A. Petrutel. Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341(2)(2008), 1241-1252.
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2017-02-10
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