International Journal of Nonlinear Analysis and Applications
Some common fixed point theorems for strict contractions
Document Type : Research Paper
Author
College of Science and Humanities at Howtat Sudair, Majmaah University, Saudi Arabia
Abstract
The extension of Aamri and El Moutawakil's property [1] to set-valued mappings arena is given. Also, some common fixed point theorems for strict contractions are established. these theorems extend results in [1,8].
Keywords
[1] M. Aamri and D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002) 181–188.
[2] M.A. Ahmed, Common fixed point theorems for set-valued and single-valued mappings, Demonstratio Math. 36(2 (2003) 471–481.
[3] M.A. Ahmed, Common fixed point theorems for weakly compatible mappings, Rocky Mountain J. Math. 33(4) (2003) 1189–1203.
[4] M.A. Ahmed, Common fixed point theorems under contractive conditions of Skof type, PU. M. A. 15(1) (2004) 17–27.
[5] M.A. Ahmed and B.E. Rhoades, Some common fixed point theorems for compatible mappings, Indian J. Pure Appl. Math. 32(8) (2001) 1247–1254.
[6] T.-H. Chang, Fixed point theorems for contractive type set-valued mappings, Math. Japonica 38(4) (1993), 675-790.
[7] Lj.B. Ciric and J.S. Ume, Some common fixed point theorems for weakly compatible mappings, J. Math. Anal. Appl. 314 (2006) 488–499.
[8] A. Constantin, A unified approach for some fixed point theorems, Indian J. Math. 36(2) (1994) 91–101.
[9] B. Fisher, Common fixed points of mapppings and set-valued mappings, Rostick. Math. Kollaq. 18 (1981) 69–77.
[10] G. Jungck, compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986) 771–779.[11] G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 16(3) (1998) 227–238.
[12] A.R. Khan, A.A. Domlo and N. Hussain, Coincidences of Lipchitz-type hybrid maps and invariant approximation, Numer. Funct. Anal. Optim. 28(9-10) (2007) 1165–1177.
[13] H.K. Pathak and B. Fisher, Common fixed point theorems with applications in dynamic programming, Glas. Math. 31(51) (1996) 321–328.
[14] H.K. Pathak, S.N. Mishra and A.K. Kalinde, Some Gregus type common fixed point theorems with applications, Demonstratio Math. 36(2) (2003) 413–426.
[15] B.E. Rhoades, Common fixed points of compatible set-valued mappings, Publ. Math. Debrecen 48(3-4) (1996) 237–240.
[16] M. Zima, A general fixed point theorem and its applications to integral-functional equations, Bull. Austral. Math.
Soc. 46 (1992) 179–186.
[2] M.A. Ahmed, Common fixed point theorems for set-valued and single-valued mappings, Demonstratio Math. 36(2 (2003) 471–481.
[3] M.A. Ahmed, Common fixed point theorems for weakly compatible mappings, Rocky Mountain J. Math. 33(4) (2003) 1189–1203.
[4] M.A. Ahmed, Common fixed point theorems under contractive conditions of Skof type, PU. M. A. 15(1) (2004) 17–27.
[5] M.A. Ahmed and B.E. Rhoades, Some common fixed point theorems for compatible mappings, Indian J. Pure Appl. Math. 32(8) (2001) 1247–1254.
[6] T.-H. Chang, Fixed point theorems for contractive type set-valued mappings, Math. Japonica 38(4) (1993), 675-790.
[7] Lj.B. Ciric and J.S. Ume, Some common fixed point theorems for weakly compatible mappings, J. Math. Anal. Appl. 314 (2006) 488–499.
[8] A. Constantin, A unified approach for some fixed point theorems, Indian J. Math. 36(2) (1994) 91–101.
[9] B. Fisher, Common fixed points of mapppings and set-valued mappings, Rostick. Math. Kollaq. 18 (1981) 69–77.
[10] G. Jungck, compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9 (1986) 771–779.[11] G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 16(3) (1998) 227–238.
[12] A.R. Khan, A.A. Domlo and N. Hussain, Coincidences of Lipchitz-type hybrid maps and invariant approximation, Numer. Funct. Anal. Optim. 28(9-10) (2007) 1165–1177.
[13] H.K. Pathak and B. Fisher, Common fixed point theorems with applications in dynamic programming, Glas. Math. 31(51) (1996) 321–328.
[14] H.K. Pathak, S.N. Mishra and A.K. Kalinde, Some Gregus type common fixed point theorems with applications, Demonstratio Math. 36(2) (2003) 413–426.
[15] B.E. Rhoades, Common fixed points of compatible set-valued mappings, Publ. Math. Debrecen 48(3-4) (1996) 237–240.
[16] M. Zima, A general fixed point theorem and its applications to integral-functional equations, Bull. Austral. Math.
Soc. 46 (1992) 179–186.
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Volume 13, Issue 1
March 2022Pages 1445-1450
- Receive Date: 17 March 2019
- Accept Date: 11 September 2019