Common fixed point theorems satisfying implicit relation conditions in quasi metric spaces and their applications ∗
DOI:
https://doi.org/10.48165/Keywords:
Common fixed point, Quasi valued metric spaces, Implicit relation, Inte gral type contractionAbstract
The aim of this paper is to establish and prove several results on common fixed point theorems for self operator satisfying implicit relation conditions in quasi met ric space.
References
Waszkiewicz, P. (2003). The local triangle axioms in topology and domain theory, Applied General Topology, 4(1), 47–70.
Aubin, J.P. (1977). Applied Abstract Analysis, Wiley, New York.
Petryshyn, W.V. and Williamson, T.E. Jr. (1973). Strong and weak convergence of the se- quence of successive approximations for quasi-nonexpansive mappings, J. Math. Anal. Appl., 43(2), 459– 497.
Kirk, W.A. (2000). Nonexpansive mappings and asymptotic regularity, Nonlinear Anal., Theory, Methods, Appl., 40, 323–332.
Zeyada, F.M., Hassan, G.H. and Ahmed, M.A. (2006). A generalization of a fixed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces, Arab. J. Sci. Eng. Sect. A Sci., 31, No. 1A, 111–114.
Popa, V. (1997). Fixed point theorems for implicit contractive mappings, Stud. Cerc. St. Ser. Mat. Univ. Bacsau, 7, 127–133.
Rus, I.A. (2001). Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca. [8] Berinde, V. (2003). On the approximation of fixed points of weak contractive mappings, Carpathian J. Math., 19(1), 7–22.
Berinde, V. (2008). General constructive fixed point theorems for Ciric-type almost contractions in metric spaces, Carpathian J. Math., 24(2), 10–19.
Berinde, V. (2010). Common fixed points of noncommuting almost contractions in cone metric spaces, Math. Commun., 15(1), 229–241.
Branciari, A. (2002). A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29(9), 531–536.
Djoudi, A. and Aliouche, A. (2007). Common fixed point theorems of Gregus type for weakly com patible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl., 329(1), 31–45.
Rhoades, B.E. (2003). Two fixed point theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 63, 4007–4013.
Sessa, S. (1986). On a weak commutativity condition in a fixed point consideration, Publ. Inst. Math., 32(46), 149–153.
Jungck, G. (1986). Compatible mappings and common fixed points, Int. J. Math. Math. Sci., 9, 771–779.
Popa, Valeriu (1999). Some fixed point theorems for compatible mappings satisfying an implicit re lation, Demonstratio Mathematica, Warsaw Technical University Institute of Mathematics, 32(1), 157–163.