Some results by quasi­contractive mappings in f­-orbitally complete metric space

Document Type: Original Article

Authors

1 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

2 Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran.

3 Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran.

Abstract

The purpose of this paper is to obtain the fixed point results by quasi-contractive mappings in f-orbitally
complete metric space. These results are generalizations of Ciric fixed point theorems. Also, we extend the
recent results which are presented in [P. Kumam, N. Van Dung, K. Sitthithakerngkiet, Filomat, 29 (2015),
1549{1556] and [M. Beesyei, Expo. Math., 33 (2015), 517-525].

Keywords


[1] M. Beesyei, Nonlinear quasicontractions in complete metric spaces, Expo. Math., 33 (2015), 517-525.

[2] F. E. Browder, Remarks on fixed point theorems of contractive type, Nonlinear Anal., 3 (1979), 657-661.

[3] L. B. Ciric, A generalization of Banach contraction principle, Proc. Amer. Math. Soc., 45 (1974), 267-273.

[4] M. Hegedus, T. Szilgyi, Equivalent conditions and a new fixed point theorem in the theory of contractive type
mappings, Math. Japon., 25 (1980), 147-157.

[5] P. Kumam, N. Van Dung, K. Sitthithakerngkiet, A Generalization of Ciric Fixed Point Theorems, Filomat, 29
(2015), 1549-1556.

[6] J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc.,
62 (1977), 344-348.

[7] S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math.
(Beograd) (N.S.), 32 (1982), 149-153.

[8] W. Walter, Remarks on a paper by F. Browder about contraction, Nonlinear Anal., 5 (1981), 21-25.