A General Fixed Point Theorem for Pairs of Mappings in Orbitally 0-Complete Partial Metric Spaces
Abstract
The purpose of this paper is to prove a general xed point theoremfor two pairs of mappings satisfying implicit relations in orbitally 0 - complete partial metric space, which include also a result of Hardy - Rogers type.
References
[1] T. Abdeljawad, E. Karapinar and K. Tas. Existence and uniqueness of a common fixed point on a partial metric space. Appl. Math. Lett., 24(11)(2011), 1900-1904.
[2] J. Achari. Circ's non - unique fixed point. Mat. Vesnik, 13(28)(1976), 255-257.
[3] A. E. B. Ahmad, Z. M. Fadail, V. C. Rajic and S. Radenovic: Nonlinear contractions in 0 - complete partial metric spaces, Abstr. Appl. Anal., Vol. 2012(2012), Article ID 451239.
[4] I. Altun and H. Simsek. Some fixed point theorems on dualistic metric spaces. J. Adv. Math. Stud., 1(2008), 1-8.
[5] I. Altun, F. Sola and H. Simsek. Generalized contractions on partial metric spaces. Topology Appl., 157(18)(2010), 778-2785.
[6] H. Aydi, M. Jellali and E. Karapinar. Common fixed points for generalized - implicit contractions in partial metric spaces: consequences and application. Revista de la Real Academia
de Ciencias Exactas, Fsicas y Naturales. Serie A. Matemticas, 109(2)(2015), 367-384.
[7] L. Ciric. On some maps with nonunique fixed points. Publ. Inst. Math. New Ser., 17(31)(1974), 52-58.
[8] L. Ciric and N. Jotic. A further extension of maps with nonunique fixed points. Mat. Vesnik, 50(1-2)(1998), 1-4.
[9] S. Gulyaz and E. Karapinar. Coupled fixed point results in partial ordered metric spaces through implicit functions. Hacet. J. Math. Stat., 42(4)(2013), 347-357.
[10] S. Gulyaz, E. Karapinar and S. Yuce. A coupled coincidence point theorem in partially ordered metric spaces with an implicit relation. Fixed Point Theory Appl., 2013, 2013:38.
[11] Z. Kadelburg, H. K. Nashine and S. Radenovic. Fixed point results under various contractive conditions in partial metric spaces. Revista de la Real Academia de Ciencias Exactas, Fsicas
y Naturales. Serie A. Matemticas, 107(2)(2013), 241-256.
[12] E. Karapinar and I. M. Erhan. Fixed point theorems for operators on partial metric spaces. Appl. Math. Lett., 24(11)(2011), 1894-1899.
[13] S. G. Matthews. Partial metric topology. In S. Andima et.al. (Eds.) Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., 728(1994), 183-197.
[14] H. K. Nashine, W. Sintunavarat, Z. Kadelburg and P. Kumam. Fixed point theorems in orbitally 0 - complete partial metric spaces via rational contractive conditions. Afr. Math.
DOI 10110007/s13370-014-2097.
[15] H. K. Pathak. Some nonunique fixed point theorems for a new class of mappings, Ranchi Univ. Math. J., 17(1986), 65-70.
[16] H. K. Pathak. On some nonunique fixed point theorems for the maps of Dhage type. Pure Appl. Math. Sci., 27(1988), 41-47.
[17] V. Popa. Fixed point theorems for implicit contractive mappings, Stud. Cercet. Stiint., Ser. Mat., Univ. Bacau, 7(1997), 129-133.
[18] V. Popa. Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstr. Math., 32(1)(1999), 159-163.
[19] S. Romaguera. A Kirk type characterization of completeness for partial metric spaces. Fixed Point Theory Appl., 2010(2010), Article ID 493298.
[20] S. Romaguera. Matkowski's type theorems for generalized contractions on (ordered) partial metric spaces. Appl. Gen. Topol., 12(2)(2011), 213-220.
[21] D. Turkoglu, O. Ozer and B. Fisher. Fixed point theorems for T - orbitally complete metric spaces. Stud. Cercet. Stiint., Ser. Mat., Univ. Bacau, 9(1999), 211-218.
[22] C. Vetro and F. Vetro. Common fixed points of mappings satisfying implicit relations in partial metric spaces. J. Nonlinear Sci. Appl., 6(2013), 156-161.
[2] J. Achari. Circ's non - unique fixed point. Mat. Vesnik, 13(28)(1976), 255-257.
[3] A. E. B. Ahmad, Z. M. Fadail, V. C. Rajic and S. Radenovic: Nonlinear contractions in 0 - complete partial metric spaces, Abstr. Appl. Anal., Vol. 2012(2012), Article ID 451239.
[4] I. Altun and H. Simsek. Some fixed point theorems on dualistic metric spaces. J. Adv. Math. Stud., 1(2008), 1-8.
[5] I. Altun, F. Sola and H. Simsek. Generalized contractions on partial metric spaces. Topology Appl., 157(18)(2010), 778-2785.
[6] H. Aydi, M. Jellali and E. Karapinar. Common fixed points for generalized - implicit contractions in partial metric spaces: consequences and application. Revista de la Real Academia
de Ciencias Exactas, Fsicas y Naturales. Serie A. Matemticas, 109(2)(2015), 367-384.
[7] L. Ciric. On some maps with nonunique fixed points. Publ. Inst. Math. New Ser., 17(31)(1974), 52-58.
[8] L. Ciric and N. Jotic. A further extension of maps with nonunique fixed points. Mat. Vesnik, 50(1-2)(1998), 1-4.
[9] S. Gulyaz and E. Karapinar. Coupled fixed point results in partial ordered metric spaces through implicit functions. Hacet. J. Math. Stat., 42(4)(2013), 347-357.
[10] S. Gulyaz, E. Karapinar and S. Yuce. A coupled coincidence point theorem in partially ordered metric spaces with an implicit relation. Fixed Point Theory Appl., 2013, 2013:38.
[11] Z. Kadelburg, H. K. Nashine and S. Radenovic. Fixed point results under various contractive conditions in partial metric spaces. Revista de la Real Academia de Ciencias Exactas, Fsicas
y Naturales. Serie A. Matemticas, 107(2)(2013), 241-256.
[12] E. Karapinar and I. M. Erhan. Fixed point theorems for operators on partial metric spaces. Appl. Math. Lett., 24(11)(2011), 1894-1899.
[13] S. G. Matthews. Partial metric topology. In S. Andima et.al. (Eds.) Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., 728(1994), 183-197.
[14] H. K. Nashine, W. Sintunavarat, Z. Kadelburg and P. Kumam. Fixed point theorems in orbitally 0 - complete partial metric spaces via rational contractive conditions. Afr. Math.
DOI 10110007/s13370-014-2097.
[15] H. K. Pathak. Some nonunique fixed point theorems for a new class of mappings, Ranchi Univ. Math. J., 17(1986), 65-70.
[16] H. K. Pathak. On some nonunique fixed point theorems for the maps of Dhage type. Pure Appl. Math. Sci., 27(1988), 41-47.
[17] V. Popa. Fixed point theorems for implicit contractive mappings, Stud. Cercet. Stiint., Ser. Mat., Univ. Bacau, 7(1997), 129-133.
[18] V. Popa. Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonstr. Math., 32(1)(1999), 159-163.
[19] S. Romaguera. A Kirk type characterization of completeness for partial metric spaces. Fixed Point Theory Appl., 2010(2010), Article ID 493298.
[20] S. Romaguera. Matkowski's type theorems for generalized contractions on (ordered) partial metric spaces. Appl. Gen. Topol., 12(2)(2011), 213-220.
[21] D. Turkoglu, O. Ozer and B. Fisher. Fixed point theorems for T - orbitally complete metric spaces. Stud. Cercet. Stiint., Ser. Mat., Univ. Bacau, 9(1999), 211-218.
[22] C. Vetro and F. Vetro. Common fixed points of mappings satisfying implicit relations in partial metric spaces. J. Nonlinear Sci. Appl., 6(2013), 156-161.
Downloads
Published
2016-12-31
Issue
Section
Чланци