A fixed point theorem for contractive mappings with nonlinear combinations of rational expressions in b-metric spaces

• Autorzy: Barrera W. E. , Morales J. R. , Rojas E. M.

Identyfikatory

DOI

10.1515/fascmath-2017-0003

• Języki publikacji: EN

Abstrakty

EN

In this paper we discuss the existence and uniqueness of fixed points for mappings satisfying several (nonlinear-combinations) contractive inequalities of rational type controlled by altering distance functions. Our results extend several fixed point results in the literature.

Słowa kluczowe

EN

fixed point; rational type; generalized weak contraction; b-metric space

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2017
• Tom: Nr 58
• Strony: 29--46
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Barrera W. E.

• Departamento de Física y Matemáticas, NURR, ULA, Trujillo, Venezuela

autor

Morales J. R.

• Departamento de Matemáticas, Universidad de Los Andes Mérida, Venezuela

autor

Rojas E. M.

• Departamento de Matemáticas, Universidad Nacional de Colombia, Bogotá, Colombia

Bibliografia

• [1] Abbas M., Khan M.A., Common fixed point theorem of two mappings satisfying a generalized weak contractive condition, International Journal of Mathematics and Mathematical Sciences, vol. 2009, Article ID 131068, 9 pages, 2009.
• [2] An T.V., Tuyen L.Q., Dung V., Stone-type theorem on b-metric spaces and applications, Topology and its Applications, 185-186(2015), 50-64.
• [3] An T.V., Dung N.V., Kadelburg Z., Various generalizations of metric spaces and fixed point theorems, Rev. Real Acad. Ciencias Ex. Fis. y Nat. Serie A., 109(1)(2015), 175-198.
• [4] Aoki T., Locally bounded topological spaces, Proc. Jpn. Acad. Tokyo, 18(1942), 588-594.
• [5] Arshad M., Karapinar E., Ahmad J., Some unique fixed point theorems for rational contractions in partially ordered metric spaces, Journal of Inequalities and Applications 2013, 248(2013).
• [6] Branciari A., A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29(9)(2002), 531-536.
• [7] Chandoka S., Choudhuryb B.S., Metiyac N., Fixed point results in ordered metric spaces for rational type expressions with auxiliary functions, Journal of the Egyptian Mathematical Society, 23(1)(2015), 95-101.
• [8] Cruz-Uribe D.V., Fiorenza A., Variable Lebesgue spaces, Foundations and harmonic analysis, Appl. Num. Harm. Anal., Birkhäuser, Basel, 2013, 317 pp.
• [9] Dass B.K., Gupta S., An extension of Banach contraction principle through rational expression, Indian J. Pure appl. Math., 6(1975), 1455-1458.
• [10] Harjani J., López B., Sadarangani K., ´ A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space, Abstract and Applied Analysis, Volume 2010 (2010), Article ID 190701, 8 pages.
• [11] Hussain N., Parvaneh V., Samet B., Vetro C., Some fixed point theorems for generalized contractive mappings in complete metric spaces, Fixed Point Theory and Applications 2015, 185(2015).
• [12] Jaggi D.S., Some unique fixed point theorems, Indian J. Pure Appl. Math., 8(2)(1977), 223-230.
• [13] Jaggi D.S., Das B.K., An extension of Banach’s fixed point theorem through rational expression, Bull. Cal. Math. Soc., 72(1980), 261-264.
• [14] Khamsi M.A., Hussain N., KKM mappings in metric type spaces, Nonlinear Anal., 7(9)(2010), 3123-3129.
• [15] Luong N.V., Thuan N.X., Fixed point theorem for generalized weak contractions satisfying rational expressions in ordered metric spaces, Fixed Point Theory Appl., 2011, Art. ID 46, (2011).
• [16] Nashine H.K., Sintunavarat W., Kadelburg Z., Kumam P., Fixed point theorems in orbitally 0-complete partial metric spaces via rational contractive conditions, Afrika Matematika, 26(5)(2015), 1121-1136.
• [17] Macías R.A., Segovia C., Lipschitz functions on spaces of homogeneous type, Adv. Math., 33(1979), 257-270.
• [18] Mitrea D., Mitrea I., Mitrea M., Monniaux S., Groupoid Metrization Theory with Applications to Analysis on Quasi-Metric Spaces and Functional Analysis, Appl. Num. Harm. Anal., Birkhäuser Basel, 2013, 486 pp.
• [19] Morales J.R., Rojas E.M., Contractive mappings of rational type controlled by minimal requirements functions, Afr. Mat., 27(2016), 65-77.
• [20] Rafeiro H., Rojas E., Espacios de Lebesgue con Exponente Variable: Un espacio de Banach de funciones medibles (Spanish), IVIC-Instituto Venezolano de Investigaciones Científicas, 2014, pp. XI+136.
• [21] Roshan J.R., Parnaveh V., Kadelburg Z., Common fixed point theorems for weakly Isotone increasing mappings in ordered b-metric spaces, J. Nonlinear Sci and Appl., 7(2014), 229-245.
• [22] Rolewicz S., On a certain class of linear metric spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 5(1957), 471-473.

Uwagi

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