Fixed point theorems for a new generalization of contractive maps in incomplete metric spaces and its application in boundary value problems

• Autorzy: Ahmadi, Zahra , Lashkaripour, Rahmatollah , Baghani, Hamid
• Języki publikacji: EN

Abstrakty

EN

In this paper, we obtain some fixed point theorems for multivalued mappings in incomplete metric spaces. Moreover, as motivated by the recent work of Olgun, Minak and Altun [M. Olgun, G. Minak and I. Altun, A new approach to Mizoguchi-Takahashi type fixed point theorems, J. Nonlinear Convex Anal. 17 (2016), no. 3, 579-587],we improve these theorems with a new generalization contraction condition for multivalued mappings in incomplete metric spaces. This result is a significant generalization of somewell-known results in the literature. Also,we provide some examples to show that our main theorems are a generalization of previous results. Finally, we give an application to a boundary value differential equation.

Słowa kluczowe

EN

Hausdorff-Pompeiu metric; multivalued contraction; Nadler’s fixed point theorem; SO-complete metric space; differential equation

• Czasopismo: Journal of Applied Analysis
• Rocznik: 2021
• Tom: Vol. 27, nr 2
• Strony: 199--207
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Ahmadi, Zahra

• Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran,

autor

Lashkaripour, Rahmatollah

• Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran,

autor

Baghani, Hamid

• Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran,

Bibliografia

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• [3] H. Baghani, R. P. Agarwal and E. Karapınar, On coincidence point and fixed point theorems for a general class of multivalued mappings in incomplete metric spaces with an application, Filomat 33 (2019), no. 14, 4493-4508.
• [4] H. Baghani, M. Eshaghi Gordji and M. Ramezani, Orthogonal sets: The axiom of choice and proof of a fixed point theorem, J. Fixed Point Theory Appl. 18 (2016), no. 3, 465-477.
• [5] H. Baghani and M. Ramezani, A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces, Filomat 31 (2017), no. 12, 3875-3884.
• [6] H. Baghani and M. Ramezani, Coincidence and fixed points for multivalued mappings in incomplete metric spaces with applications, Filomat 33 (2019), no. 1, 13-26.
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• [13] G. Mınak and I. Altun, Some new generalizations of Mizoguchi-Takahashi type fixed point theorem, J. Inequal. Appl. 2013 (2013), Paper No. 493.
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• [15] S. B. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475-488.
• [16] M. Olgun, G. Minak and I. Altun, A new approach to Mizoguchi-Takahashi type fixed point theorems, J. Nonlinear Convex Anal. 17 (2016), no. 3, 579-587.
• [17] M. Ramezani and H. Baghani, The Meir-Keeler fixed point theorem in incomplete modular spaces with application, J. Fixed Point Theory Appl. 19 (2017), no. 4, 2369-2382.
• [18] S. Reich, Some problems and results in fixed point theory, in: Topological Methods in Nonlinear Functional Analysis (Toronto 1982), Contemp. Math. 21, American Mathematical Society, Providence (1983), 179-187.
• [19] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012 (2012), Article ID 94.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)

Identyfikatory

DOI

10.1515/jaa-2021-2046