Notes on multidimensional fixed-point theorems

• Autorzy: Akhadkulov H. , Noorani S. M. , Saaban A. B. , Alipiah F. M. , Alsamir H.

Identyfikatory

DOI

10.1515/dema-2017-0033

• Języki publikacji: EN

Abstrakty

EN

In this paper we prove the existence and uniqueness of coincident (fixed) points for nonlinear mappings of any number of arguments under a (ψ ,θ, φ)-weak contraction condition without O-compatibility. The obtained results extend, improve and generalize some well-known results in the literature to be discussed below. Moreover, we present an example to show the efficiency of our results.

Słowa kluczowe

EN

fixed-point; contractive mapping; partially ordered set; mixed monotone property

PL

punkt stały; kontrakcja; odwzorowanie zwężające; zbiór częściowo uporządkowany; właściwość monotoniczna

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2017
• Tom: Vol. 50, nr 1
• Strony: 360--374
• Opis fizyczny: Bibliogr. 20 poz.

Twórcy

autor

Akhadkulov H.

• School of Quantitative Sciences, University Utara Malaysia, CAS 06010, UUM Sintok, Kedah Darul Aman, Malaysia

autor

Noorani S. M.

• School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

autor

Saaban A. B.

• School of Quantitative Sciences, University Utara Malaysia, CAS 06010, UUM Sintok, Kedah Darul Aman, Malaysia

autor

Alipiah F. M.

• School of Quantitative Sciences, University Utara Malaysia, CAS 06010, UUM Sintok, Kedah Darul Aman, Malaysia

autor

Alsamir H.

• School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

Bibliografia

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• [2] Alsamir H., Noorani M. S., Shatanawi W., On new fixed point theorems for three types of (α, β) - (ψ, θ, φ)-multivalued contractive mappings in metric spaces, Cogent Math., 2016, 3, 1-13
• [3] Kuman P., Sarwar M., Zada M. B., Fixed point results satisfying rational type contractive conditions in complex valid metric spaces, Ann. Math. Sil., 2016, 30, 89-110
• [4] Sintunavarat W., Kuman P., Gregus type fixed points for a tangential multi-valued mappings satisfying contractive conditions of integral type, J. Inequal. Appl., 2011, https://doi.org/10.1186/1029-242X-2011-3
• [5] Guo D. J., Lakshmikantham V., Coupled xed points of nonlinear operators with applications, Nonlinear Anal., 1987, 11(5), 623-632
• [6] Berinde V., Borcut M., Tripled fixed point theorems for contractive type mappings in partially ordered matric space, Nonlinear Anal., 2011, 74, 4889-4897
• [7] Borcut M., Berinde V., Tripled coincidence theorems for contractive type mappings in partially ordered matric space, Appl. Math. Comput., 2012, 218, 5929-5936
• [8] Karapinar E., Quadruple fixed point theorems for weak φ-contractions, ISRN Mathematical Analysis, 2011, http://dx.doi.org/10.5402/2011/989423
• [9] Roldán A., Martínez-Moreno J., Roldán C., Multidimensional fixed point theorems in partially ordered complete metric spaces, J. Math. Anal. Appl., 2012, 396(2), 536-545
• [10] Roldán A., Martínez-Moreno J., Roldán C., Cho Y. J., Multidimensional fixed point theorems under (ψ, φ)-contractive conditions in partially ordered complete metric spaces, J. Comput. Appl. Math., 2015, 273, 76-87
• [11] Samet B., Karapinar E., Aydi H., Rajic C., Discussion on some coupled fixed point theorems, Fixed Point Theory and Appl., 2013, https://doi.org/10.1186/1687-1812-2013-50
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• [13] Roldán A., Martínez-Moreno J., Roldán C., Karapinar E., Some remarks on multidimensional fixed point theorems, Fixed Point Theory., 2014, 15(2), 545-558
• [14] Shaddad F., Noorani M. S., Alsulami S. M., Akhadkulov H., Coupled point results in partially ordered metric spaces without compatibility, Fixed Point Theory and Appl., 2014, https://doi.org/10.1186/1687-1812-2014-204
• [15] Gnana Bhaskar T., Lakshmikantham V., Fixed point theorems in partially ordered metric space and applications, Nonlinear Anal., 2006, 65(7), 1379-1393
• [16] Berzig M., Samet B., An extension of coupled fixed point’s concept in higher dimension and applications, Comput. Math. Appl., 2012, 63, 1319-1334
• [17] Karapinar E., Berinde V., Quadruple fixed point theorems for nonlinear contractions in partially ordered metric space, Banach J. Math. Anal., 2012, 6(1), 74-89
• [18] Paknazar M., Gordji M. E., De La Sen M., Vaezpour S. M., N-fixed point theorems for nonlinear contractions in partially ordered metric space Fixed Point Theory and Appl., 2013, https://doi.org/10.1186/1687-1812-2013-111
• [19] Saleh A., Alsulami H., Karapinar E., Roldán A., Discussion on "Multidimensional Coincidence Points" via Recent Publications, Abstr. Appl. Anal., 2014, http://dx.doi.org/10.1155/2014/287492
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Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).