Document Type : Research Paper
Authors
- Vatan Karakaya ^{} ^{1}
- Necip Şimşek ^{2}
- Derya Sekman ^{3}
^{1} Department of Mathematical Engineering, Yildiz Technical University, Davutpasa Campus, Esenler, 34210 Istanbul, Turkey.
^{2} Department of Mathematics, Istanbul Commerce University, Sutluce Campus, Beyoglu, 34445 Istanbul, Turkey.
^{3} Department of Mathematics, Ahi Evran University, Bagbasi Campus, 40100 Kirsehir, Turkey.
Abstract
The purpose of this work is to investigate the existence of fixed points of some mappings in fixed point theory by combining some important concepts which are F-weak contractions, multivalued mappings, integral transformations and α-admissible mappings. In fixed point theory, it is important to find fixed points of some classess under F- or F-weak contractions. Also multivalued mappings is the other important classes. Along with that, α-admissible mapping is a different approach in the fixed point theory. According to this method, a single or multivalued mapping does not have a fixed point in general. But, under some restriction on the mapping, a fixed point can be obtained. In this article, we combine four significant notions and also establish fixed point theorem for this mappings in complete metric spaces. Moreover, we give an example to show the interesting of our results according to earlier results in literature.
Keywords
[2] I. Altun and G. Minak, Fixed point results for $alpha-admissible$ multivalued F-contractions, Miskolc Mathematical Notes, 17 (2016), pp. 187-199.
[3] I. Altun, G. Minak, and H. Dag, Multivalued F-contractions on complete metric space, J. Nonlinear Convex Anal., 16 (2015), pp. 659-666.
[4] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math., 3 (1922), pp. 133-181.
[5] B.S. Choudhury and C. Bandyopadhyay, A new multivalued contraction and stability of its fixed point sets, Journal of the Egyptian Mathematical Society, 2015 (2015), pp. 321-325.
[6] E. Hacioglu and V. Karakaya, Existence and convergence for a new multivalued hybrid mapping in CAT($kappa $) spaces, Carpathian J. Math., 33 (2017), pp. 319-326.
[7] E. Karapi nar, P. Shahi, and K. Tas, Generalized $ alpha-psi $ contractive type mappings of integral type and related fixed point theorems, Journal of Inequality and Applications, 2014 (2014), pp. 1-18.
[8] S.B. Nadler, Multivalued contraction mappings, Path. J. Math., 30 (1969), pp. 475-488.
[9] D.B. Ojha and M.K. Mishra, Some results on common fixed point of multivalued generalized $varphi$-weak contractive mappings in integral type inequality, Research Journal of Applied Sciences, Engineering and Technology, 2 (2010), pp. 387-395.
[10] H. Piri and S. Rahrovi, Generalized multivalued F-weak contraction on complete metric spaces, Sahand Commun. Math. Anal., 2 (2015), pp. 1-11.
[11] B. Samet, C. Vetro, and P. Vetro, Fixed point theorems for $alpha -psi $ contractive type mappings, Nonlinear Anal., 75 (2012), pp. 2154-2165.
[12] D. Sekman, N.E.H. Bouzara, and V. Karakaya, n-tuplet fixed points of multivalued mappings via measure of noncompactness, Communications in Optimization Theory, 2017 (2017), pp. 1-13.
[13] D. Sekman and V. Karakaya, On the F-contraction properties of multivalued integral type transformations, Methods Funct. Anal. Topology 25 (2019), no. 3, pp. 282-288.
[14] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Appl., 2012 (2012), pp. 1-6.