Document Type : Research Paper

Authors

Mathmatics Group‎, ‎Faculty of Basic Sciences‎, ‎Emam Ali University‎, ‎Tehran‎, ‎Iran

Abstract

‎The aim of this work is to introduce the concepts of $(v‎, ‎u‎, ‎\phi)$-contraction and $(q‎, ‎p‎, ‎\phi)$-contraction‎, ‎and to obtain new results in fixed point theory for four mappings in $b$-metric spaces‎. ‎Finally‎, ‎we have developed an example and an application for a system of integral equations that protects the main theorems‎.

Keywords

Main Subjects

[1] H. Aydi, M-F. Bota, E. Karapinar, S. Moradi, A common fixed point for weak-ϕ-contractions on b-metric spaces, Fixed Point Theory. 13 (2012), 337-346.
[2] I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Ulianowsk Gos. Ped. Inst. 30 (1989), 26-37.
[3] M.-F. Bota, C. Chifu, E. Karapinar, Fixed point theorems for generalized (α − ψ)-Ciric-type contractive multivalued operators in b-metric spaces, Abstr. Appl. Anal. (2014), 2014:246806.
[4] M-F. Bota, E. Karapinar, A note on “Some results on multi-valued weakly Jungck mappings in b-metric space”, Cent. Eur. J. Math. 11 (2013), 1711-1712.
[5] M-F. Bota, E. Karapinar, O. Mlesnite, Ulam-Hyers stability results for fixed point problems via α − ψ-contractive mapping in b-metric space, Abstr. Appl. Anal. (2013), 2013:825293.
[6] T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379-1393.
[7] S. Czerwik, Contraction mappings in b-metric spaces, Acta. Math. Inform. Univ. Ostrav. 1 (1993), 5-11.
[8] E. L. Ghasab, H. Majani, E. Karapinar, G. Soleimani Rad, New fixed point results in F-quasi-metric spaces and an application, Adv. Math. Phys. (2020), 2020:9452350.
[9] E. L. Ghasab, H. Majani, G. Soleimani Rad, Integral type contraction and coupled fixed point theorems in ordered G-metric spaces, J. Linear. Topol. Algebra. 9 (2) (2020), 113-120.
[10] G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986), 771-779.
[11] M.A. Kutbi, E. Karapinar, J. Ahmed, A. Azam, Some fixed point results for multi-valued mappings in b-metric spaces, J. Inequal. Appl. 2014, 2014:126.
[12] V. Lakshmikanthama, L.´Ciri´ c, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009), 4341-4349.
[13] H. Majani, R. Zaer Soleimani, J. Izadi, Coupled fixed point results for T-contractions on F-metric spaces and an application, J. Linear. Topol. Algebra. 10 (1) (2021), 1-10.
[14] J. Rezaei Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, W. Shatanawi, Common fixed points of almost generalized (Ψ,Φ)s-contractive mappings in ordered b-metric spaces, Fixed Point Theory Appl. 2013, 2013:159.
[15] W. Shatanawi, A. Pitea, R. Lazovic, Contraction conditions using comparison functions on b-metric spaces, Fixed Point Theory Appl. 2014, 2014:135.
[16] G. Soleimani Rad, H. Aydi, P. Kumam, H. Rahimi, Common tripled fixed point results in cone metric type spaces, Rend. Circ. Mat. Palermo. 63 (2014), 287-300.
[17] G. Soleimani Rad, S. Shukla, H. Rahimi, Some relations between n-tuple fixed point and fixed point results, RACSAM. 109 (2015), 471-481.