Keywords:-
Keywords:
Quadratic type generalized Z-contraction pair of self maps; simula- tion function; b-metric space; fixed point; common fixed point.
Article Content:-
Abstract
In this paper, we introduce quadratic type generalized Z-contraction with respect to a simulation function and study the existence of common fixed points of such mappings in complete b- metric spaces. We extend it to a se- quence of self maps. We infer some corollaries from our main result and provide examples to verify our results.
References:-
References
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2. G. V. R. Babu, T. M. Dula and P. S. Kumar, A common fixed point theorem in b-metric spaces via simulation function, Fixed Point Theory, 12(2018), 15.
3. I. A. Bakhtin, The contraction mapping principle in almost metric spaces, (Russian) Func- tional Analysis,Ulyanovsk. Gos. Ped.Inst. Ulyanovsk, 30(1989), 26-37.
4. S. Banach, Sur les operation dans les ensembles abstraits et leur application aux equation integrals ,Fundamentals ,Math.,3(1922), 133-181.1
5. N. Bourbaki, Topologie Generale , Herman : Paris, France, 1974.
6. M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int.
J. Modern Math., 4(2009), 285-301.
7. F. E. Browder, On the convergence of successive approximations for nonlinear functional equations , Nederl. Akad. Wetensch. Ser.A 71 = Indag. Math., 30(1968),27-35.
8. M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur.J. Math, 8(2), (2010), 367-377.
9. S. Czerwik, Contraction mapping in b-metric spaces, Acta Math. Inform. Univ.Ostraviensis,1 (1993), 5-11.
10. H. Huang, G. Deng, S. Radenovic, Fixed point theorems for c-class functions in b-metric spaces and applications, J. Nonlinear Sci. Appl.,10(2017),5853-5868.
11. M. Jovanovic, Z. Kadelburg,S. Radenovic, Common fixed point results in b-metric type spaces, Fixed point Theory Appl., 2010(2010), 15pages.
12. A. Kari, M. Rossafi, E. Marhrani, M. Aamri, fixed point theorem for nonlinear F-contraction via w-distance, Adv. Math. Phys., 2020(2020),10 pages.
13. R. Kannan, Some results on fixed points-II, Amer. Math. Monthly, 76(1969), 405-408.
14. F. Khojasteh, S. Shukla, S. Radenovic, A new approach to the study of fixed point theorems via simulation functions, Filomat,29,(2015)1189-1194.
15. M. Olgun, Bicer and T. Alyildiz, A new aspect to Picard operators with simulation func- tions,Turk.J.Math.,(2016) 40: 832-837.
16. V. Ozturk, S. Radenovic Some remarks on b-(E.A)-property in b-metric spaces, Springer Plus, 5(2016), 10 pages.
17. S. Reich, Some remarks concerning contraction mappings,Canad. Math. Bull.,14(1971), 121-124.
18. J. R. Roshan, V. Parvaneh, Z. Kadelburg, Common Fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces, J.Nonlinear Sci.Appl., 7(2014), 229-245.
19. W. Shatanawi, Fixed and Common fixed point for mappings satisfying some nonlinear contraction in b-metric spaces, J. math. Anal., 7(2016), 1 - 12.
2. G. V. R. Babu, T. M. Dula and P. S. Kumar, A common fixed point theorem in b-metric spaces via simulation function, Fixed Point Theory, 12(2018), 15.
3. I. A. Bakhtin, The contraction mapping principle in almost metric spaces, (Russian) Func- tional Analysis,Ulyanovsk. Gos. Ped.Inst. Ulyanovsk, 30(1989), 26-37.
4. S. Banach, Sur les operation dans les ensembles abstraits et leur application aux equation integrals ,Fundamentals ,Math.,3(1922), 133-181.1
5. N. Bourbaki, Topologie Generale , Herman : Paris, France, 1974.
6. M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int.
J. Modern Math., 4(2009), 285-301.
7. F. E. Browder, On the convergence of successive approximations for nonlinear functional equations , Nederl. Akad. Wetensch. Ser.A 71 = Indag. Math., 30(1968),27-35.
8. M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in b-metric spaces, Cent. Eur.J. Math, 8(2), (2010), 367-377.
9. S. Czerwik, Contraction mapping in b-metric spaces, Acta Math. Inform. Univ.Ostraviensis,1 (1993), 5-11.
10. H. Huang, G. Deng, S. Radenovic, Fixed point theorems for c-class functions in b-metric spaces and applications, J. Nonlinear Sci. Appl.,10(2017),5853-5868.
11. M. Jovanovic, Z. Kadelburg,S. Radenovic, Common fixed point results in b-metric type spaces, Fixed point Theory Appl., 2010(2010), 15pages.
12. A. Kari, M. Rossafi, E. Marhrani, M. Aamri, fixed point theorem for nonlinear F-contraction via w-distance, Adv. Math. Phys., 2020(2020),10 pages.
13. R. Kannan, Some results on fixed points-II, Amer. Math. Monthly, 76(1969), 405-408.
14. F. Khojasteh, S. Shukla, S. Radenovic, A new approach to the study of fixed point theorems via simulation functions, Filomat,29,(2015)1189-1194.
15. M. Olgun, Bicer and T. Alyildiz, A new aspect to Picard operators with simulation func- tions,Turk.J.Math.,(2016) 40: 832-837.
16. V. Ozturk, S. Radenovic Some remarks on b-(E.A)-property in b-metric spaces, Springer Plus, 5(2016), 10 pages.
17. S. Reich, Some remarks concerning contraction mappings,Canad. Math. Bull.,14(1971), 121-124.
18. J. R. Roshan, V. Parvaneh, Z. Kadelburg, Common Fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces, J.Nonlinear Sci.Appl., 7(2014), 229-245.
19. W. Shatanawi, Fixed and Common fixed point for mappings satisfying some nonlinear contraction in b-metric spaces, J. math. Anal., 7(2016), 1 - 12.
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Tiwari, R., Sharma, N., & Patel, A. R. (2025). Quadratic Type Generalozed Z-Contraction with Respect to a Simulation Function and Common Fixed-Point Theorem. International Journal Of Mathematics And Computer Research, 13(10), 5698-5710. https://doi.org/10.47191/ijmcr/v13i10.04