Year 2022,
Volume: 14 Issue: 2, 346 - 354, 30.12.2022
Ali Mutlu
,
Kübra Özkan
,
Utku Gürdal
References
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- Abbas, M., Rhoades, B.E., Common fixed point results for noncommuting mappings without continuity in generalized metric spaces, Appl. Math. Comput., 215(1)(2009), 262–269.
- Abbas, M., Nazir, T., Radenovi´c, S., Common fixed points of four maps in partially ordered metric spaces, Appl. Math. Lett., 24(9)(2011), 1520–1526.
- Abdeljawad, T., Karapınar E., Tas¸, K., Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24(11)(2011), 1900–1904.
- Aghajani, A., Abbas, M., Roshan, J., Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64(4)(2014), 941–960.
- Ahmad, J., Al-Rawashdeh, A., Common fixed points of set mappings endowed with directed graphs, Tbil. Math. J., 11(3)(2018), 107–123.
- Balaj, M., Jorquera, E.D., Khamsi, M.A., Common fixed points of set-valued mappings in hyperconvex metric spaces, J. Fixed Point Theory Appl., 20(1)(2018), 1–14.
- Berinde, V., A common fixed point theorem for compatible quasi contractive self mappings in metric spaces, Appl. Math. Comput., 213(2)(2009), 348–354.
- Ciric, L., Abbas, M., Saadati, R., Hussain, N., Common fixed points of almost generalized contractive mappings in ordered metric spaces, Appl. Math. Comput., 217(12)(2011), 5784–5789.
- Das, K.M., Naik, K.V., Common fixed-point theorems for commuting maps on a metric space, Proc. Amer. Math. Soc., 77(3)(1979), 369–373.
- Hussain, N., Roshan, J.R., Parvaneh V., Abbas, M., Common fixed point results for weak contractive mappings in ordered b-dislocated metric spaces with applications, J. Inequalities Appl., 2013(1)(2013), 1–21.
- Imdad, M., Ali, J., Jungck’s common fixed point theorem and EA property, Acta Math. Sin. Engl. Ser., 24(1)(2008), 87–94.
- Jungck, G., Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9(4)(1986), 771–779.
- Kadelburg, Z., Pavlovi´c M., Radenovi´c, S., Common fixed point theorems for ordered contractions and quasi contractions in ordered cone metric spaces, Comput. Math. with Appl., 59(9)(2010), 3148–3159.
- Kang, S.M., Cho, Y.J., Jungck, G., Common fixed points of compatible mappings, Int. J. Math. Math. Sci., 13(1)(1990), 61–66.
- Karapinar, E., Yüksel, U., Some common fixed point theorems in partial metric spaces, J. Appl. Math., 2011(2011), Article ID 263621.
- Kuczumow, T., Reich, S., Shoikhet, D., The existence and non-existence of common fixed points for commuting families of holomorphic mappings, Nonlinear Anal., 43(1)(2001), 45–59.
- Li, J., Fu, M., Liu Z., Kang, S.M., A common fixed point theorem and its application in dynamic programming, Appl. Math. Sci., 2(17)(2008), 829–842.
- Mutlu, A., Gürdal, U., Bipolar metric spaces and some fixed point theorems, J. Nonlinear Sci. Appl., 9(9)(2016), 5362–5373.
- Mutlu, A., Özkan, K., Gürdal, U., Coupled fixed point theorems on bipolar metric spaces, Eur. J. Pure Appl., 10(4)(2017), 655–667.
- Pant, R.P., Common fixed points of noncommuting mappings, J. Math. Anal. Appl., 188(1994), 436–440.
- Pathaka, H.K., Khanb, M.S., Tiwaric ,R., A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. with Appl., 53(2007), 961–971.
- Precup, R., Fixed point theorems for decomposable multi-valued maps and applications, Z. Anal. Anwend., 22(4)(2003), 843-–861.
- Sessa, S., On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd), 32(1982), 149–153.
- Sintunavarat, W., Kumam, P., Generalized common fixed point theorems in complex valued metric spaces and applications, J. Inequalities Appl., 2012(1)(2012), 1–12.
- Tahat, N., Aydi, H., Karapinar, E., Shatanawi, W., Common fixed points for single-valued and multi-valued maps satisfying a generalized contraction in G-metric spaces, Fixed Point Theory Appl., 2012(1)(2012), 1–9.
Some Common Fixed Point Theorems in Bipolar Metric Spaces
Year 2022,
Volume: 14 Issue: 2, 346 - 354, 30.12.2022
Ali Mutlu
,
Kübra Özkan
,
Utku Gürdal
Abstract
In this article, we introduce the notion of commutativity for covariant and contravariant mappings in bipolar metric spaces. Afterwards, by using this notion, we prove some common fixed point theorems which show the existence and uniqueness of common fixed point for covariant and contravariant mappings satisfying contractive type conditions.
References
- Abbas, M., Jungck, G., Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341(1)(2008), 416–420.
- Abbas, M., Rhoades, B.E., Common fixed point results for noncommuting mappings without continuity in generalized metric spaces, Appl. Math. Comput., 215(1)(2009), 262–269.
- Abbas, M., Nazir, T., Radenovi´c, S., Common fixed points of four maps in partially ordered metric spaces, Appl. Math. Lett., 24(9)(2011), 1520–1526.
- Abdeljawad, T., Karapınar E., Tas¸, K., Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24(11)(2011), 1900–1904.
- Aghajani, A., Abbas, M., Roshan, J., Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64(4)(2014), 941–960.
- Ahmad, J., Al-Rawashdeh, A., Common fixed points of set mappings endowed with directed graphs, Tbil. Math. J., 11(3)(2018), 107–123.
- Balaj, M., Jorquera, E.D., Khamsi, M.A., Common fixed points of set-valued mappings in hyperconvex metric spaces, J. Fixed Point Theory Appl., 20(1)(2018), 1–14.
- Berinde, V., A common fixed point theorem for compatible quasi contractive self mappings in metric spaces, Appl. Math. Comput., 213(2)(2009), 348–354.
- Ciric, L., Abbas, M., Saadati, R., Hussain, N., Common fixed points of almost generalized contractive mappings in ordered metric spaces, Appl. Math. Comput., 217(12)(2011), 5784–5789.
- Das, K.M., Naik, K.V., Common fixed-point theorems for commuting maps on a metric space, Proc. Amer. Math. Soc., 77(3)(1979), 369–373.
- Hussain, N., Roshan, J.R., Parvaneh V., Abbas, M., Common fixed point results for weak contractive mappings in ordered b-dislocated metric spaces with applications, J. Inequalities Appl., 2013(1)(2013), 1–21.
- Imdad, M., Ali, J., Jungck’s common fixed point theorem and EA property, Acta Math. Sin. Engl. Ser., 24(1)(2008), 87–94.
- Jungck, G., Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9(4)(1986), 771–779.
- Kadelburg, Z., Pavlovi´c M., Radenovi´c, S., Common fixed point theorems for ordered contractions and quasi contractions in ordered cone metric spaces, Comput. Math. with Appl., 59(9)(2010), 3148–3159.
- Kang, S.M., Cho, Y.J., Jungck, G., Common fixed points of compatible mappings, Int. J. Math. Math. Sci., 13(1)(1990), 61–66.
- Karapinar, E., Yüksel, U., Some common fixed point theorems in partial metric spaces, J. Appl. Math., 2011(2011), Article ID 263621.
- Kuczumow, T., Reich, S., Shoikhet, D., The existence and non-existence of common fixed points for commuting families of holomorphic mappings, Nonlinear Anal., 43(1)(2001), 45–59.
- Li, J., Fu, M., Liu Z., Kang, S.M., A common fixed point theorem and its application in dynamic programming, Appl. Math. Sci., 2(17)(2008), 829–842.
- Mutlu, A., Gürdal, U., Bipolar metric spaces and some fixed point theorems, J. Nonlinear Sci. Appl., 9(9)(2016), 5362–5373.
- Mutlu, A., Özkan, K., Gürdal, U., Coupled fixed point theorems on bipolar metric spaces, Eur. J. Pure Appl., 10(4)(2017), 655–667.
- Pant, R.P., Common fixed points of noncommuting mappings, J. Math. Anal. Appl., 188(1994), 436–440.
- Pathaka, H.K., Khanb, M.S., Tiwaric ,R., A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. with Appl., 53(2007), 961–971.
- Precup, R., Fixed point theorems for decomposable multi-valued maps and applications, Z. Anal. Anwend., 22(4)(2003), 843-–861.
- Sessa, S., On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd), 32(1982), 149–153.
- Sintunavarat, W., Kumam, P., Generalized common fixed point theorems in complex valued metric spaces and applications, J. Inequalities Appl., 2012(1)(2012), 1–12.
- Tahat, N., Aydi, H., Karapinar, E., Shatanawi, W., Common fixed points for single-valued and multi-valued maps satisfying a generalized contraction in G-metric spaces, Fixed Point Theory Appl., 2012(1)(2012), 1–9.