A common fixed point theorem for multi-valued θ_{δ} contractions via subsequential continuity

Year 2020, Volume: 69 Issue: 2, 1473 - 1483, 31.12.2020

Ali Ahmed Saadia Mahideb Said Beloul

https://doi.org/10.31801/cfsuasmas.748142

Abstract

The main objective of this paper is to present a common fixed
point theorem for two pairs of single and set valued mappings via subsequential
continuity and \delta- compatibility. To illustrate the validity of our results, an
example is provided and we give also an application for a system of integral
inclusions of Volterra type.

Keywords

\theta contraction, subsequentially continuous, \delta compatible, integral inclusion

Thanks

We would like to thanks the editor and any one who will review this manuscript.

References

• Acar, O., A Fixed Point Theorem for multivalued almost F_{δ}-contraction, Results Math., 72(3) (2017), 1545-1553.
• Beloul, S., Common fixed point theorems for weakly subsequentially continuous generalized contractions with applications, Appl. Maths. E-Notes, 15 (2015), 173-186.
• Beloul, S., Chauhan, S., Gregus type fixed points for weakly subsequentially continuous mappings satisfying strict contractive condition of integral type, Le Mathematiche, 71(2) (2017), 3-15.
• Beloul, S., Common Fixed Point Theorem for strongly tangential and weakly Compatible mappings satisfying implicit relations, Thai. J. Math., 15(2) (2017), 349-358.
• Beloul, S., Tomar, A., A coincidence and common fixed point theorem for subsequentially continuous hybrid pairs of maps satisfying an implicit relation, Math. Moravica, 21(2) (2017), 15-25.
• Beloul, S., Kaddouri, H., Fixed Point Theorems For Subsequentially Multi-Valued F_{δ}-Contractions In Metric Spaces, Facta Univ Nis Ser. Math. Inform., 35(2) (2020), 379-392.
• Bouhadjera, H., Godet Thobie, C., Common fixed point theorems for pairs of subcompatible maps, .(2009), arXiv:0906.3159v1 [math.FA].
• Ćirić, L. B., Generalization of Banach's Contraction Principle, Proc. Amer. Math. Soc., 45 (1974), 267-273.
• Durmaz, G., Some theorems for a new type of multivalued contractive maps on metric space, Turkish J. Math., 41, (2017), 1092-1100.
• Fisher, B., Fixed points for set-valued mappings on metric spaces, Bull. Malays. Math. Sci. Soc., 2(4) (1981), 95-99.
• Isik. H, Ionescu, C., New type of multivalued contractions with related results and applications, U.P.B. Sci. Bull., Series A, 80(2) (2018), 13-22.
• Jleli. M, Samet, B., A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014:38, (2014), 8 pp.
• Jungck, G., Commuting mappings and fixed points, Amer. Math. Monthly, 83(4) (1976), 261-263.
• Jungck, G., Compatible mappings and common fixed points, Int.J.Math.and Math. Sci., 9(4) (1986), 771-779.
• Jungck, G., Rhoades, B.E.,Fixed point theorems for occasionally weakly compatible mappings, Fixed Point Theory, 9 (2008), 383-384.
• Kaneko, H., Sessa, S., Fixed point theorems for compatible multi-valued and single-valued mappings, Internat. J. Math. Math. Sci., 12(2) (1989), 257-262.
• Liu, C., Li-Shan, Common fixed points of a pair of single valued mappings and a pair of set valued mappings, Qufu Shifan Daxue Xuebao Ziran Kexue Ban, 18 (1992), 6-10.
• Nadler, S. B., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488.
• Pant, R. P., A common fixed point theorem under a new condition, Indian J. Pure Appl. Math. 30(2) (1999), 147-152.
• Sessa, S., On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. Beograd, 32(46) (1982), 149-153.
• Singh, S. L., Mishra, S. N., Coincidence and fixed points of reciprocally continuous and compatible hybrid maps, Internat. J. Math. Math. Sci., 10 (2002), 627-635.