Fixed point results via generalized rational and convex type contractions in modular metric spaces

• Autorzy: Salam A. , Sarwar M. , Kumari P. S.

Identyfikatory

DOI

10.21008/j.0044-4413.2020.0005

• Języki publikacji: EN

Abstrakty

EN

In the current manuscript, some fixed point results for generalized rational and convex type contractions in the context of modular metric spaces are established. The derived results generalizes some well known results from the existing literature.

Słowa kluczowe

EN

rational type contraction; generalize convex contraction in modular metric space

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2020
• Tom: nr 63
• Strony: 63--86
• Opis fizyczny: Bibliogr. 29 poz.

Twórcy

autor

Salam A.

• Department of Mathematics University of Malakand Chakdara Dir(L), Pakistan

autor

Sarwar M.

• Department of Mathematics University of Malakand Chakdara Dir(L), Pakistan

autor

Kumari P. S.

• Department of Mathematics University of Malakand Chakdara Dir(L), Pakistan

Bibliografia

• [1] Dass B.K., Gupta S., An extention of Banach’s contraction principle through rational expression, Indian J. Pure Appl.Math., 6(1975), 1455-1458.
• [2] Chistyakov V., Modular metric spaces, I: Basic concepts, Nonlinear Anal, 72(2010), 1-14.
• [3] Chistyakov V., Modular metric spaces, II: Application to superposition operators, Nonlinear Anal., 72(2010), 15-30.
• [4] Chaipunya P., Mongkolkeha C., Sintunavarat W., Kumam P., Fixed point theorems for multivalued mappings in modular metric spaces, Abstract and Appl. Anal, Article ID 503504, (2012), 14 pages.
• [5] Cho Y., Saadati R., Sadeghi G., Quasi-contraction mapping in modular metric spaces, J. Appl. Math., Article ID 907951, (2012), 5 pages.
• [6] Fisher B., Common fixed point for four mappings, Bull. Inst, of Math. Academia Sinicia, 11(1983), 103-113.
• [7] Chistyakov V., A fixed point theorem for contractions in modular metric spaces, Perprint submited to arXiv., ...(2011), ....
• [8] Jungck G., Rhoades B.E., Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math., 29(1998), 227-238.
• [9] Jungck G., Common fixed points for noncontinuous nonself maps on nonmetric spaces, J. Math. Sci., 4(1996), 19-215.
• [10] Jungck G., Compatible mappings and common fixed points, Int. J. Math. Sci., 9(1986), 771-779.
• [11] Mongkolkeha C., Sintunavarat W., Kumam P., Fixed poit theorems for contraction mappings in modular metric spaces, Fixed Point Theory and Appl., 93(2011), ...
• [12] Rahimpoor H., Ebadian A., Eshaghi Gordji M., Zohri A., Some fixed point theorems on modular metric spaces, Acta Universitatis Apulensis, 37(2014), 161-170.
• [13] Rahimpoor H., Ebadian A., Eshaghi Gordji M., Zohri A., Fixed point theory for generalized quasi-contraction maps in modular metric spaces, J. of Math. Computer Science, 10(2014), 54-60.
• [14] Sessa S., On a weak commutativity condition of mappings of fixed point considerations, Publ. Inst. Math., 321982), 149-153.
• [15] Rus I.A., Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, (2001).
• [16] Rus I.A., Petrusel A., Petrusel G., Fixed Point Theory, Cluj University Press, Cluj-Napoca, (2008).
• [17] Rahimpoor H. et al, Common fixed point theorems in modular metric spaces, Int. J. of Pure and Appl. Math., 99(2015) 373-383.
• [18] Sarwar et al, Some fixed point results in dislocated quasi metric (dq-metric) spaces, J. Inequalities and Appl., (2014), 11 pages.
• [19] Istratescu V.I., Some fixed point theorem for convex contraction mappings and convex non expansive mappings, Libertas Math., 1(1981), 151-163.
• [20] Alghamdi M.A., Alnafei S.H., Radenovic S., Shahzsd N., Fixed point theorem for convex contraction mappings on cone metric spaces, Math. Com-put. Modelling, 54(2011), 2020-2026.
• [21] Ghorbanian V., Rezapour N., Shahza N., Some ordered fixed point results and the property, Comput. Math. Appl., 63(2012), 1361-1368.
• [22] Latif A., Sintunavarat W., Ninsri A., Approximate fixed point theorems for partial generalized convex contraction mappings in a-complete metric spaces, Taiwanese J. Math., 19(2015), 315-333.
• [23] Miandaragh M.A., Postolache M., Rezapour S., Approximate fixed points of generalized convex contractions, Fixed Point Theory Appl., (2013), 5 pages.
• [24] Miculescu R., Mihail A., A generalization of Istratescu’s fixed point theorem for convex contraction, ArXiv., 1(2015), 17 pages.
• [25] Ramezani R., Orthognal metric space and convex contractions, Int. J. Nonlinear Anal. Appl., 6(2015), 127-132.
• [26] Sastry K.P.R., Rao C.S., Chandra Sekhar A., Balaiah M., A fixed point theorem for cone convex contractions of order m ≥ 2, Int. J. Math. Sci. Eng. Appl., 6(2012), 263-271.
• [27] Khan M.S., Singh Y.M., Maniu G., Postolache M., On generalized convex contractions of type-2 in 6-metric and 2-metric spaces, J. Nonlinear Sci. Appl., 10(2017), 2902-2913.
• [28] Padcharoen A., Gopal D., Chaipunya P., Kumam P., Fixed point and periodic point results for a — typeF-contractions in modular metric spaces, ..., (2016) 2016:39. DOI:10.1186/sl3663-016-0525-4.
• [29] Padcharoen A., Kumam P., Jaygopal D., Coincidence and periodic point results in a modular metricspace endowed with a graph and applications, Creat. Math. Inform., 26(1)(2017), 95-104.

Uwagi

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