Suzuki - $(\mathcal{Z}_{\psi}(\alpha,\beta))$ - type rational contractions

Year 2022, Volume: 5 Issue: 2, 151 - 160, 30.06.2022

M L Himabindu V

https://doi.org/10.53006/rna.754938

Abstract

In this paper, we obtain a unique common fixed point results by using Suzuki - $(\mathcal{Z}_{\psi}(\alpha,\beta))$ - type rational contractive mappings in metric spaces. Also we give an example which supports our main theorem.

Keywords

$Z$- contraction , Suzuki-$\mathcal{Z}_{\psi}(\alpha,\beta)$-type rational contraction , Metric space

References

• [1] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equation integrals, Fund. Math.,3(1922),133-181.1
• [2] S. Radenovic, Z. Kadelburg, D. Jandrlixex and A. Jandrlixex, Some results on weak contraction maps, Bull. Iran. Math. Soc. 2012, 38, 625-645.
• [3] T.Suzuki, A generalized Banach contraction principle which characterizes metric completeness, Proc. Amer. Math. Soc. 2008. vol. 136, pp. 1861-1869.
• [4] B. Samet, C. Vetro, P. Vetro, Fixed point Theorems for α - ψ- contractive type mappings, Nonlinear Anal. 75, 2154- 2165(2012).
• [5] F. Khojasteh, S. Shukla, S. Radenovic, A new approach to the study of fixed point theory for simulation functions, Filomat 29, 1189?1194 (2015).
• [6] Gh. Heidary J, A. Farajzadeh, M. Azhini and F. Khojasteh, A New Common Fixed Point Theorem for Suzuki Type Contractions via Generalized ψ-simulation Functions, Sahand Communications in Mathematical Analysis (SCMA) Vol. 16 No. 1 (2019), 129-148.
• [7] A.S.S. Alharbi, H.H. Alsulami and E. Karapinar, On the Power of Simulation and Admissible Functions in Metric Fixed Point Theory, Journal of Function Spaces, 2017 (2017), Article ID 2068163, 7 pages.
• [8] B. Alqahtani, A. Fulga, E. Karapinar, Fixed Point Results On ∆-Symmetric Quasi-Metric Space Via Simulation Function With An Application To Ulam Stability, Mathematics 2018, 6(10), 208.
• [9] H. Aydi, A. Felhi, E. Karapinar, F.A. Alojail, Fixed points on quasi-metric spaces via simulation functions and consequences, J. Math. Anal.(ilirias) 9(2018) No:2, Pages 10-24.
• [10] R.P. Agarwal and E. Karapinar, Interpolative Rus-Reich-Ciric Type Contractions Via Simulation Functions, An. St. Univ. Ovidius Constanta, Ser. Mat., Volume XXVII (2019) fascicola 3 Vol. 27(3),2019, 137-152.
• [11] H. Aydi, E.Karapinar and V. Rakocevic, Nonunique Fixed Point Theorems on b-Metric Spaces Via Simulation Functions, Jordan Journal of Mathematics and statistics, Volume: 12 Issue: 3 Pages: 265-288 Published: SEP 2019.
• [12] A.F. Roldán-López-de-Hierro, E. Karapinar, C. Roldán-López-de-Hierro, J. Martínez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math. 275 (2015), 345-355.
• [13] H. Aydi, M. A. Barakat, E. Karapinar, Z.D. Mitrovic, T.Rashid, On L-simulation mappings in partial metric spaces, AIMS Mathematics , 4(4)(2019): 1034-1045. Doi:10.3934/math.2019.4.1034.