Citation: Md Hasanuzzaman, Mohammad Imdad. Relation theoretic metrical fixed point results for Suzuki type $\mathcal{Z_\mathcal{R}}$-contraction with an application[J]. AIMS Mathematics, 2020, 5(3): 2071-2087. doi: 10.3934/math.2020137
[1] | S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1992), 133-181. |
[2] | M. Edelstein, On fixed and periodic points under contractive mappings, J. Lond. Math. Soc., 1 (1962), 74-79. |
[3] | J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc., 62 (1977), 344-348. doi: 10.1090/S0002-9939-1977-0436113-5 |
[4] | D. W. Boyd, J. S. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20 (1969), 458-464. doi: 10.1090/S0002-9939-1969-0239559-9 |
[5] | J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), 1359-1373. |
[6] | B. E. Rhoades, A comparison of various definitions of contractive mappings, T. Am. Math. Soc., 226 (1977), 257-290. doi: 10.1090/S0002-9947-1977-0433430-4 |
[7] | D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory A., 2012 (2012), 94. |
[8] | A. Alam, M. Imdad, Relation-theoretic contraction principle, J. Fixed Point Theory A., 17 (2015), 693-702. doi: 10.1007/s11784-015-0247-y |
[9] | L. Ćirić, Some recent results in fixed point theory, University of Belgrade, Beograd, Serbia, 2003. |
[10] | A. Razani, Results in fixed point theory, Andisheh Zarrin, Ghazvin, Iran, 2010. |
[11] | A. Razani, R. Moradi, Fixed point theory in modular space, Saieh Ghostar publisher, Qazvin, 2006. |
[12] | A. Razani, A fixed point theorem in the menger probabilistic metric space, New Zealand J. Math., 35 (2006), 109-114. |
[13] | A. Razani, Existence of fixed point for the nonexpansive mapping of intuitionistic fuzzy metric spaces, Chaos Soliton. Fract., 30 (2006), 367-373. doi: 10.1016/j.chaos.2005.10.010 |
[14] | A. Razani, An existence theorem for ordinary differential equation in menger probabilistic metric space, Miskolc Math. Notes, 15 (2014), 711-716. doi: 10.18514/MMN.2014.640 |
[15] | A. Razani, A contraction theorem in fuzzy metric spaces, Fixed Point Theory Appl., 2005 (2005), 257-265. |
[16] | F. Khojasteh, A. Razani, S. Moradi, A fixed point of generalized TF-contraction mappings in cone metric spaces, Fixed Point Theory A., 2011 (2011), 14. |
[17] | M. Turinici, Fixed points for monotone iteratively local contractions, Demonstr. Math., 19 (1986), 171-180. |
[18] | A. C. Ran, M. C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 2004 (2004), 1435-1443. |
[19] | B. Samet, M. Turinici, Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications, Commun. Math. Anal., 13 (2012), 82-97. |
[20] | A. Alam, M. Imdad, Relation-theoretic metrical coincidence theorems, Filomat, 31 (2017), 4421-4439. doi: 10.2298/FIL1714421A |
[21] | F. Khojasteh, S. Shukla, S. Radenović, A new approach to the study of fixed point theory for simulation functions, Filomat, 29 (2015), 1189-1194. doi: 10.2298/FIL1506189K |
[22] | K. Sawangsup, W. Sintunavarat, On modified Z-contractions and an iterative scheme for solving nonlinear matrix equations, J. Fixed Point Theory A., 20 (2018), 80. |
[23] | T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313-5317. doi: 10.1016/j.na.2009.04.017 |
[24] | P. Kumam, D. Gopal, L. Budhiyi, A new fixed point theorem under Suzuki type Z-contraction mappings, J. Math. Anal., 8 (2017), 113-119. |
[25] | E. Karapınara, Fixed points results via simulation functions, Filomat, 30 (2016), 2343-2350. doi: 10.2298/FIL1608343K |
[26] | H. H. Alsulami, E. Karapınar, F. Khojasteh, et al. A proposal to the study of contractions in quasimetric spaces, Discrete Dyn. Nat. Soc., 2014 (2014), 269286. |
[27] | A. F. Roldán López-de Hierro, E. Karapınar, C. Roldán López-de Hierro, et al. Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math., 275 (2015), 345-355. doi: 10.1016/j.cam.2014.07.011 |
[28] | A. Hussain, T. Kanwal, Z. Mitrović, et al. Optimal solutions and applications to nonlinear matrix and integral equations via simulation function, Filomat, 32 (2018), 6087-6106. doi: 10.2298/FIL1817087H |
[29] | A. Chanda, L. K. Dey, S. Radenović, Simulation functions: A survey of recent results, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A. Mat., 113 (2019), 2923-2957. |
[30] | S. Radenovic, F. Vetro, J. Vujaković, An alternative and easy approach to fixed point results via simulation functions, Demonstr. Math., 50 (2017), 223-230. doi: 10.1515/dema-2017-0022 |
[31] | X. L. Liu, A. H. Ansari, S. Chandok, et al. On some results in metric spaces using auxiliary simulation functions via new functions, J. Comput. Anal. Appl., 24 (2018), 1103-1114. |
[32] | S. Radenovic, S. Chandok, Simulation type functions and coincidence points, Filomat, 32 (2018), 141-147. doi: 10.2298/FIL1801141R |
[33] | E. Karapınar, F. Khojasteh, An approach to best proximity points results via simulation functions, J. Fixed Point Theory A., 19 (2017), 1983-1995. doi: 10.1007/s11784-016-0380-2 |
[34] | A. Alam, M. Imdad, Nonlinear contractions in metric spaces under locally T-transitive binary relations, Fixed Point Theor-Ro, 19 (2018), 13-24. doi: 10.24193/fpt-ro.2018.1.02 |
[35] | B. Kolman, R. C. Busby, S. Ross, Discrete mathematical structures, 3 Eds., PHI Pvt. Ltd., New Delhi, 2000. |
[36] | A. Razani, Weak and strong detonation profiles for a qualitative model, J. Math. Anal. Appl., 276 (2002), 868-881. doi: 10.1016/S0022-247X(02)00459-6 |
[37] | A. Razani, Subsonic detonation waves in porous media, Phys. Scripta, 94 (2019), 085209. |
[38] | A. Razani, Fixed points for total asymptotically nonexpansive mappings in a new version of bead space, Int. J. Ind. Math., 6 (2014), 329-332. |
[39] | M. Berzig, B. Samet, Solving systems of nonlinear matrix equations involving Lipshitzian mappings, Fixed Point Theory A., 2011 (2011), 89. |
[40] | M. Berzig, Solving a class of matrix equations via the Bhaskar-Lakshmikantham coupled fixed point theorem, Appl. Math. Lett., 25 (2012), 1638-1643. doi: 10.1016/j.aml.2012.01.028 |
[41] | J. Long, X. Hu, L. Zhang, On the hermitian positive definite solution of the nonlinear matrix equation X + A*X-1 A+ B*X-1 B=I, Bull. Braz. Math. Soc., 39 (2008), 371-386. doi: 10.1007/s00574-008-0011-7 |