Coincidence Theorems in New Generalized Metric Spaces Under Locally g-transitive Binary Relation


  • H.N.B. Garhwal University, Srinagar, India


In this paper, we establish coincidence point theorems for contractive mappings, using locally g-transitivity of binary relation in new generalized metric spaces. In the present results, we use some relation theoretic analogues of standard metric notions such as continuity, completeness and regularity. In this way our results extend, modify and generalize some recent fixed point theorems, for instance, Karapinar et al [J. Fixed Point Theory Appl. 18(2016) 645-671], Alam and Imdad [Fixed Point Theory, in press].


Generalized Metric Space, Modular Spaces, R-continuity, Coincidence Point, Locally g-transitive Binary Relation

Subject Discipline

Functional Analysis, Fixed Point Theory

Full Text:


Agarwal, R.P., Karapinar, E., O' Regan, D., Roldan-Lopez-de-Hierro, A.F., Fixed Point Theory in Metric Type Spaces. Springer, Switzerland, 2015.

Ahamad, M.A., Zeyada, F.M., Hasan, G.F., Fixed point theorems in generalized types of dislocated metric spaces and its applications. Thai J. Math. 11, (2013) 67-73.

Akkouchi, M., Common fixed point theorems for two self mappings of a b-metric space under an implicit relation. Hacet. J. Math. Stat. 40(6), (2011) 805-810.

Alam, A., Imdad, M., Relation-theoretic contraction principle. J. Fixed Point Theory Appl. 17(4), (2015) 693-702.

Alam, A., Imdad, M., Nonlinear contractions in metric spaces under locally T-transitive binary relations. Fixed Point Theory (In Press).

Alam, A., Khan, A.R., Imdad, M., Some coincidence theorems for generalized nonlinear contractions in ordered metric spaces with applications. Fixed Point Theory and Appl., 216 (2014).

Alam, A., Imdad, M., Relation-theoretic metrical coincidence theorems. Filomate (In Press ).

Berinde, V., Sequences of operators and fixed points in quasimetric spaces. Stud. Univ. Babe s-Bolyai, Math. 41, (1996) 23-27.

Berzig, M., Coincidence and common fixed point results on metric spaces endowed with an arbitrary binary relation and applications. J. Fixed Point Theory Appl., 12, (2012) 221-238 .

Boriceanu, M., Bota, M., Petrusel, A., Multivalued fractals in b-metric spaces. Cent. Eur. J. Math. 8(2), (2010) 367-377.

Czerwik, S., Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostrav. 1, (1993) 5-11.

Czerwik, S., Dlutek, K., Singh, S.L., Round-off stability of iteration procedures for set-valued operators in b-metric spaces. J. Natur. Phys. Sci. 11, (2001) 87-94.

Dominguez Benavides, T., Khamsi, M.A., Samadi, S., Uniformly Lipschitzian mappings in modular function spaces. Nonlinear Anal. 46(2), (2001) 267-278.

Haghi, R.H., Rezapour, Sh., Shahzad, N., Some fixed point generalizations are not real generalizations. Nonlinear Anal : Theory, Method & Appl. 74(5), (2011) 1799-1803.

Hitzler, P., Generalized metrics and topology in logic programming semantic. Dissertation, Faculty of Science, National University of Ireland, University College, Cork (2001).

Hitzler, P., Seda, A.K., Dislocated topologies. J. Electr. Eng. 51(12), (2000) 3-7.

Jleli, M., Samet, B., A generalized metric space and related fixed point theorems. Fixed Point Theory Appl. (2015), doi:10.1186/s13663-015-0312-7, 14 pages.

Karapinar, E., ORegan, D., Roldan-Lopez-de-Hierro, A.F., Shahzad, N., Fixed point theorems in new generalized metric spaces. J. Fixed Point Theory Appl. 18, (2016) 645-671.

Karapinar, E., Roldan-Lopez-de-Hierro, A.F., A note on (G, F)-Closed set and tripled point of coincidence theorems for generalized compatibility in partially metric spaces. J. Inequal. Appl. 522 (2014).

Karapinar, E., Roldan, A., Shahzad, N., Sintunavarat, W., Discussion of coupled and tripled coincidence point theorems for '-contractive mappings without the mixed g-monotone property. Fixed Point Theory Appl. 92 (2014).

Karapinar, E, Salimi, P., Dislocated metric space to metric spaces with some xed point theorems. Fixed Point Theory Appl. 222 (2013).

Kirk, W., Shahzad, N., b-Metric spaces. In: Fixed Point Theory in Distance Spaces. Springer, Berlin (2014) 113-131.

Khamsi, M.A., Nonlinear semigroups in modular function spaces. Math. Jpn. 37, (1992) 291-299.

Khamsi, M.A., Kozlowski, W.M., Reich, S., Fixed point theory in modular function spaces. Nonlinear Anal. 14, (1990) 935-953.

Kozlowski, W.M., Modular Function Spaces. Monographs and Textbooks in Pure and Applied Mathematics. Dekker, New York, 122 (1988).

Musielak, J., Orlicz, W., On modular spaces. Stud. Math. 18, (1959) 49-65.

Nakano, H., Modular semi-ordered spaces. Tokyo, Japan (1959).

Nieto, J.J., Rodriguez-Lopez, R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22(3), (2005) 223-239.

Popovic, B., Radenovic, S., Shukla, S., Fixed point results to tvs-cone b-metric spaces. Gulf J. Math. 1, (2013) 51-64.

Ran, A.C.M., Reurings, M.C.B., A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Amer. Math. Soc. 132(5), (2004) 1435-1443.

Samet, B., Turinici, M., Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications. Commun. Math. Anal. 13(2), (2012) 82-97.

Turinici, M., Abstract comparison principles and multivariable Gronwall-Bellman inequalities. J. Math. Anal. Appl. 117(1), (1986) 100-127.

Turinici, M., Contractive maps in locally transitive relational metric spaces. The Sci. World J. 169358 (2014).

Turinici, M., Contractive operators in relational metric spaces, Handbook of Functional Equations, Springer Optimization and its Appl., Springer, 95, (2014) 419-458.

Turinici, M., Fixed points for monotone iteratively local contractions. Demonstr. Math. 19(1), (1986) 171-180.


  • There are currently no refbacks.