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Orthogonal sets: Coincidence and fixed point theorems in incomplete metric spaces | ||
Journal of New Researches in Mathematics | ||
مقاله 11، دوره 6، شماره 27، بهمن و اسفند 2020، صفحه 107-118 اصل مقاله (2.48 M) | ||
نوع مقاله: research paper | ||
نویسندگان | ||
Hamid Baghani 1؛ Maryam Ramezani2؛ Hamid Khodaei3 | ||
1Assistant Professor, Department of Mathematics, Faculty of Mathematics, Statistics of Computer Science, Sistan and Baluchestan University, Zahedan, Iran | ||
2Assistant Professor, Department of Mathematics, Faculty of Basic Sciences, Bojnourd University, Bojnourd, Iran | ||
3Assistant Professor, Department of Mathematics, Faculty of Mathematical Sciences and Statistics, Malayer University, Malayer, Iran | ||
چکیده | ||
In this paper, as motivated by a work of Daffer et al. [6], we state and prove some theorems for set valued mappings and by them we conclude the existence of coincidence points and fixed points of a general class of set valued mappings satisfying a new generalized contractive condition which extends some well-known results in the literature. For this reason, firstly, by using a recent work of Eshaghi et al [11], we define the notion of orthogonal sets and by the notion, we consider our results in strongly orthogonal complete metric spaces (not necessarily complete metric spaces). In addition, this article has a new and different view on the subject and consists of several non-trivial examples which signify the motivation of such investigations. Also, in the end of this paper, by using our examples, we show that our results are real generalization of the previous results in the literature. | ||
کلیدواژهها | ||
Set valued mappings؛ fixed and coincidence points؛ orthogonal sets؛ SO-complete metric spaces | ||
مراجع | ||
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[11] M. Eshaghi Gordji, M. Ramezani, M. De La Sen, Y.J. Cho, (2017). On orthogonal sets and Banach fixed Point theorem, Fixed Point Theory 18, 569-578.
[12] H. Baghani, M. Eshaghi Gordji, M. Ramezani, (2016). Orthogonal sets: The axiom of choice and proof of a fixed pointtheorem, J. Fixed Point Theory Appl. 18, 465-477.
[13] Z. Ahmadi, R. Lashkaripour, H. Baghani, (2018). A fixed point problem with constraint inequalities via a contraction inincomplete metric spaces, Filomat 32, 234-254.
[14] H. Baghani, (2018). Existence and uniqueness of solutions to fractional Langevin equations involving two fractional orders, J. Fixed Point Theory Appl. 20:3.
[15] H. Baghani, M. Ramezani, (2017). A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarilycomplete) metric spaces, Filomat 31, 3875-3884.
[16] O. Baghani, H. Baghani, (2017). A new contraction condition and its application to weakly singular Volterra integral equations of the second kind, J. Fixed Point Theory Appl .19, 2601-2615.
[17] M. Ramezani, H. Baghani, (2017). The Meir-Keeler fixed point theorem in incomplete modular spaces with application, J.Fixed Point Theory Appl. 19, 2369-2382. | ||
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