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Abstract
In this paper we study and prove the existence of some common fixed point theorems for two pairs of compatible, weakly compatible and occasionally weakly compatible mappings of integral type in modular metric spaces. Our results extend and generalize the results of Azadifar et al. [2], Rashwan and Hammad [28], Rahimpoor et.al. [27], and Pariya Aklesh et. al. [25], Abdou, A. and Khamsi,[1], Chirasak [5], Nawab [24], Hanna, et al [10].
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References
Abdou,A., and Khamsi, M. A., On the fixed points of non-expansive mappings in modular metric spaces, Fixed Point Theory and Appl., 229 (2013), 1-13.
Azadifar, B, et al.: Integral type contractions in modular metric spaces, J. Inequal. Appl., 483(2013).
Banach,S., Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fundamenta Mathematicae, 3 (1922), 133-181.
Branciari, A., A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Sci. 29 (2002), 531-536.
Chirasak M., Sintunavarat W. and Kumam, P., Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory and Applications, 2011, 2011:93.
Chirasak M., Sintunavarat W. and Kumam, P., Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory and Applications, 2012, 2012:103.
Chistyakov,V., A fixed point theorem for contractions in modular metric spaces, arXiv:1112.5561v1 [math. FA], Dec.2011.
Chistyakov, V., Modular metric spaces, I: basic concepts, Nonlinear Analysis 72, (2010), 1-14.
Chistyakov, V., Modular metric spaces, II: Applications to superposition operators, Nonlinear Analysis 72, (2010), 15-30.
Hanaa K., Wasfi S. and abdalla T., Common fixed point theorems via integral type contraction in modular metric spaces, U.P.B. Sci. Bull., Series A, 83(3) (2021), 125-136.
Jungck, G., Compatible mappings and common fixed points, International Journal of Mathematics and Mathematical Sciences, 9 (4) (1986), 771-779.
Jungck, G., Common fixed points for non-continuous non-self maps on nonmetric spaces, Far East Journal of Mathematical Sciences, Vol.4(2) (1996), 199-215.
Jungck, G. and Rhoades, B.E., Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory, 7(ll), (2006), 287-296.
Kilinc, E. and Alaca, C., A fixed point theorem in modular metric space, Adv. Fixed Point Theory, 4 (2014), 199-206.
Koshi, S. and Shimogaki, T., On F-norms of quasi-modular spaces, J FacSci Hokkaido Univ Ser l,15(3-4), (1961), 202-218.
Mazur,S. and Orlicz, W., On some classes of linear spaces, Studia Math., 17, (1958), 97-119.
Mongkolkeha, C., Sintunavarat, W. and Kumam, P., Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory and Applications,2011, 2011:93, 12.
Mongkolkeha, C., Sintunavarat,W. and Kumam, P., Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory and Applications,2012, 2012:103.
Musielak,J. and Orlicz,W., On modular spaces, Studia Mathematica, Vol. 18 (1959), 49-65.
Musielak,J. Orlicz spaces and modular Spaces, Vol.1034 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1983.
Nakano,H., Modular semi-ordered linear spaces, Vol. 1 of Tokyo Mathematical Book Series, Maruzen, Tokyo, Japan, 1950.
Nakano,H., Topology of linear Topological spaces, Vol. 3 of Tokyo Mathematical Book Series, Maruzen,Tokyo, Japan, 1951.
Nawab H., Kutbi Marwan A., Nazra Sultana and Iram Iqba, Weak contractive integral inequalities and fixed points in modular metric spaces, Journal of Inequalities and Applications, (2016), 2016:89.
Olatinwo,M.O., Some fixed point theorems for weak contraction condition of integral type, Acta Universitatis Apulensis, 24, (2010), 331-338.
Pariya, Aklesh, Pathak P., Badshah, V.H. and Gupta N., Fixed point theorems for various types of compatible mappings of integral type in modular metric spaces, Journal of Mathematics and Informatics, Vol.8(2017), 7-18.
Rahimpoor, H., Ebadian, A., EshaghiGordji, M. and Zohri, A., Some fixed point theorems on modular metric spaces, Acta Universitatis Apulensis, 37 (2014), 161-170.
Rahimpoor, H.,Ebadian, A.,Gordji, M.E. and Zohri, A., Common fixed point theorems in modular metric spaces, Int. J. of Pure and Appl. Math., 99 (2015), 373-383.
Rashwan, R.A. and Hamad, H.A., Common fixed point theorems for weak contraction mapping of integral type in modular spaces, Universal Journal of Computational Mathematics, 2(4)(2014), 69-86.
Sessa, S., On a weak commutativity condition of mappings in fixed point considerations, Publicationd de I’Institut Math’ematique, Vol.32(46) (1982), 149-153.
Singh, S.P. and Meade, B.A., On common fixed point theorem, Bull. Aust. Mat. Soc.,16(1977),49-53.
Yamamuro, S., On conjugate spaces of Nakano spaces, Trans Amer Math Soc., 90,(1959), 291-311.