Abstract
Fixed point results for generalized weak contractions under w-distance are proved using discontinuous control functions that are more relaxed than functions used in related work for metric spaces. Later, we apply our theory to coupled coincidence point problems and existence of solution of Fredholm type integral equation. We present examples to justify our claims.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Batra, R., Vashistha, S.: Coupled coincidence point theorems for nonlinear contractions under c-distance in cone metric spaces. Ann. Funct. Anal. 4(1), 138–148 (2013)
Batra, R., Vashistha, S.: Coupled coincidence point theorems for nonlinear contractions under \((F, g)\)-invariant set in cone metric spaces. J. Nonlinear Sci. Appl. 6(2), 86–96 (2013)
Batra, R., Vashistha, S.: Some coupled coincidence point results under c-distance in cone metric spaces. Eng. Math. Lett. 2(2), 90–114 (2013)
Batra, R., Vashistha, S.: Fixed point theorem for \(F_w\)-contractions in complete metric spaces. J. Nonlinear Anal. Appl. 2013, 1–6 (2013)
Bhaskar, T.Gnana, Lakshmikantham, V.: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65(7), 1379–1393 (2006)
Cho, Y.J., Saadati, R., Wang, S.: Common fixed point theorems on generalized distance in ordered cone metric spaces. Comput. Math. Appl. 61(4), 1254–1260 (2011)
Choudhury, B.S., Kundu, A.: A coupled coincidence point result in partially ordered metric spaces for compatible mappings. Nonlinear Anal. 73(8), 2524–2531 (2010)
Choudhury, B.S., Kundu, A.: \((\psi,\alpha,\beta )\)-weak contractions in partially ordered metric spaces. Appl. Math. Lett. 25(1), 6–10 (2012)
Choudhury, B.S., Metiya, N., Postolache, M.: A generalized weak contraction principle with applications to coupled coincidence point problems. Fixed Point Theory Appl. 2013, Art. 152 (2013)
Harjani, J., Sadarangani, K.: Fixed point theorems for weakly contractive mappings in partially ordered sets. Nonlinear Anal. 71(7–8), 3403–3410 (2009)
Jungck, G.: Compatible mappings and common fixed points. Int. J. Math. Math. Sci. 9(4), 771–779 (1986)
Jungck, G., Rhoades, B.E.: Fixed points for set valued functions without continuity. Indian J. Pure Appl. Math. 29(3), 227–238 (1998)
Kada, O., Suzuki, T., Takahashi, W.: Nonconvex minimization theorems and fixed point theorems in complete metric spaces. Math. Jpn. 44(2), 381–391 (1996)
Kadelburg, Z., Pavlović, M., Radenović, S.: Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces. Comput. Math. Appl. 59(9), 3148–3159 (2010)
Lakshmikantham, V., Ćirić, L.: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. 70(12), 4341–4349 (2009)
Nieto, J.J., Rodríguez-López, R.: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta Math. Sin. (Engl. Ser.) 23(12), 2205–2212 (2007)
Ran, A.C.M., Reurings, M.C.B.: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Am. Math. Soc. 132(5), 1435–1443 (2004)
Turinici, M.: Abstract comparison principles and multivariable Gronwall–Bellman inequalities. J. Math. Anal. Appl. 117(1), 100–127 (1986)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Tomonari Suzuki.
Rights and permissions
About this article
Cite this article
Batra, R., Vashistha, S. A Generalized Contraction Principle Under w-Distance for a Partially Ordered Metric Space. Bull. Malays. Math. Sci. Soc. 40, 1159–1174 (2017). https://doi.org/10.1007/s40840-016-0347-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40840-016-0347-x