Fixed Point Theorems via WF-Contractions
Download PDF
Authors: R. GUBRAN, W. M. ALFAQIH AND M. IMDAD
DOI: 10.46793/KgJMat2103.353G
Abstract:
In this paper, we introduce a new class of contractions which remains a mixed type of weak and F-contractions but not any of them.
Keywords:
Fixed point, WF-contractions, F-contractions, weak contractions.
References:
[1] Y. I. Alber and S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces, in: New Results in Operator Theory and Its Applications, Springer, Verlag, Basel, 1997, 7–22.
[2] J. Ali and M. Imdad, An implicit function implies several contraction conditions, Sarajevo J. Math. 4 (2008), 269–285.
[3] I. Altun and D. Turkoglu, Some fixed point theorems for weakly compatible mappings satisfying an implicit relation, Taiwanese J. Math. 13 (2009), 1291–1304.
[4] H. Argoubi, B. Samet and C. Vetro, Nonlinear contractions involving simulation functions in a metric space with a partial order, J. Nonlinear Sci. Appl. 8 (2015), 1082–1094.
[5] A. Augustynowicz, Existence and uniqueness of solutions for partial differential-functional equations of the first order with deviating argument of the derivative of unknown function, Serdica Math. J. 23 (1997), 203–210.
[6] M. Cvetkovic, E. Karapinar and V. Rakocevic, Fixed point results for admissible z-contractions, Fixed Point Theory 19 (2018), 515–526.
[7] P. Dutta and B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl. (2008), Article ID 406368, 8 pages.
[8] R. Gubran, W. M. Alfaqih and M. Imdad, Common fixed point results for alpha-admissible mappings via simulation function, J. Anal. 25 (2017), 281–290.
[9] M. Imdad and J. Ali, A general fixed point theorem in fuzzy metric spaces via an implicit function, J. Appl. Math. Inform. 26 (2008), 591–603.
[10] M. Imdad, R. Gubran and M. Ahmadullah, Using an implicit function to prove common fixed point theorems, J. Adv. Math. Stud. 11(3) (2018), 481–495.
[11] E. Karapınar, Fixed points results via simulation functions, Filomat 30 (2016), 2343–2350.
[12] F. Khojasteh, S. Shukla and S. Radenović, A new approach to the study of fixed point theory for simulation functions, Filomat 29 (2015), 1189–1194.
[13] A. Kostić, V. Rakočević and S. Radenović, Best proximity points involving simulation functions with w0-distance, Rev. R. Acad. Cienc. Exactas Fís. Nat. (2018), 1–13.
[14] D. O’Regan and A. Petruşel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl. 341 (2008), 1241–1252.
[15] V. Popa, Fixed point theorems for implicit contractive mappings, Stud. Cerc. St. Ser. Mat. Univ. Bacau 7 (1997), 127–133.
[16] V. Popa, A general fixed point theorem for weakly compatible mappings in compact metric spaces, Turkish J. Math. 25 (2001), 465–474.
[17] B. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal. 47 (2001), 2683–2693.
[18] A.-F. Roldán-López-de Hierro, E. Karapınar, C. Roldán-López-de Hierro and J. Martínez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math 275 (2015), 345–355.
[19] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. (2012), Article ID 94, 6 pages.