Fixed points of generalized (α,ψ,φ)-rational contractive mappings in -complete metric spaces

• Autorzy: Babu G. V. R. , Tolera M. D.

Identyfikatory

DOI

10.1515/fascmath-2017-0014

• Języki publikacji: EN

Abstrakty

EN

In this paper, we introduce generalized (α, ψ, φ)-rational contractive mappings in α-complete metric spaces and prove some new fixed point results for this class of mappings. We provide examples in support of our results. Our results generalize the fixed point results of Singh, Kamal, Sen and Chugh [22] and Piri and Kumam [18].

Słowa kluczowe

EN

complete metric space; admissible mapping; generalized rational contractive mappings; fixed point

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2017
• Tom: Nr 59
• Strony: 13--28
• Opis fizyczny: Bibliogr. 24 poz.

Twórcy

autor

Babu G. V. R.

• Department of Mathematics, Andhra University, Visakhapatnam-530 003, India

autor

Tolera M. D.

• Department of Mathematics, Andhra University, Visakhapatnam-530 003, India
• Department of Mathematics, Wollega University, Nekemte-395, Ethiopia

Bibliografia

• [1] Ahmad J., Al-Rawashdeh A., Azam A., New fixed point theorems for generalized F-contractions in complete metric spaces, Fixed Point Theory Appl., 80(2015).
• [2] Alber Ya.I., Guerre-Delabriere S., Principle of weakly contractive maps in Hilbert spaces, New Results in Operator Theory and Its Applications, Oper. Theory Adv. Appl. 98, Birkhauser, Basel, (1997), 7-22.
• [3] Ansari A.H., Note on ϕ-ψ-contractive type mappings and related fixed point, Proceedings of the 2nd Regional Conference on Math. and Appl., (2014), 377-380.
• [4] Babu G.V.R., Sailaja P.D., A fixed point theorem of generalized weakly contractive maps in orbitally complete metric spaces, Thai J. of Math., 9(1)2011, 1-10.
• [5] Chandok S., Tas K., Ansari A.H., Some Fixed Point Results for TAC-type contractive mappings, J. Funct. Spaces, Volume 2016, Article ID 1907676, 6 pages.
• [6] Czerwik S., Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1(1993), 5-11.
• [7] Doric D., Common fixed point for generalized (ψ, ϕ)-weak contractions, Appl. Math. Lett., 22(2009), 1896-1900.
• [8] Dutta P.N., Choudhury B.S., A generalization of contraction principle in metric spaces, Fixed Point Theory Appl., (2008), Article ID 406368, 8 pages.
• [9] Hieu N.T., Dung N.V., Some fixed point results for generalized rational type contraction mappings in partially ordered b−metric spaces, Facta Univ. Ser. Math. Inform., 30(1)(2015), 49-66.
• [10] Huang H., Ansari A.H., Dolicanin-Dekic D., Radenovic S., Some fixed point results for rational type and subrational type contractive mappings, Acta Univ. Sapientiae Math., 9(1)(2017), 185-201.
• [11] Huang H., Deng G., Chen Z., Radenovic S., On some recent fixed point results for α−admissible mappings in b−metric spaces, J. Comput. Anal. Appl., 25(2)(2018), 255-268.
• [12] Hussain N., Kutbi M.A., Salimi P., Fixed point theory in α-complete metric spaces with applications, Abstr. Appl. Anal., (2014), Article ID 280817.
• [13] Jaggi D.S., Some unique fixed point theorems, Indian J. of Pure and Appl. Math., 8(1977), 223-230.
• [14] Karapinar E., Kumam P., Salimi P., On α − ψ Meir-Keeler contractive mappings, Fixed Point Theory Appl., 94(2013), 12 pages.
• [15] Khan M.S., Swaleh M.S., Sessa S., Fixed point theorems by altering distances between the points, Bull. Aust. Math. Soc., 30(1984), 1-9.
• [16] Kirk W.A., Srinivasan P.S., Veeramani P., Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4(2003), 79-89.
• [17] Pansuwon A., Sintunavarat W., Parvaneh V., Cho Y.J., Some fixed point theorems for (α, θ, k)-contractive multi-valued mappings with some applications, Fixed Point Theory Appl., 132(2015).
• [18] Piri H., Kumam P., Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl., 2014, Article ID 210 (2014).
• [19] Piri H., Rahrovi S., Generalized multivalued F-weak contraction on complete metric spaces, Sahand Commun. Math. Anal. (SCMA), 2(2)(2015), 1-11.
• [20] Rhoades B.E., Some theorems on weakly contractive maps, Nonlinear Anal., 47(2001), 2683-2693.
• [21] Samet B., Vetro C., Vetro P., Fixed point theorems for α−ψ-contractive type mappings, Nonlinear Anal., 75(2012), 2154-2165.
• [22] Singh S.L., Kamal R., De la Sen M., Chugh R., A fixed point theorem for generalized weak contractions, Filomat, 29(7)(2015), 1481-1490.
• [23] Wardowski D., Fixed point theory of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012, Article ID 94 (2012).
• [24] Wardowski D., Van Dung N., Fixed points of F-weakly contractions on complete metric spaces, Demonstr. Math., Vol. XLVII, (1)(2014).