MATEMATIČKI VESNIK, Vol. 69, No. 2, pp. 75

MATEMATIČKI VESNIK
Vol. 69, No. 2, pp. 75–88 (2017)

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Fixed points of generalized $T A C$ -contractive mappings in $b$ -metric spaces

G. V. R. Babu and T. M. Dula

G.V.R.B.: Department of Mathematics, Andhra University, Visakhapatnam-530 003, India. E-mail: gvr_babu@hotmail.com and T.M.D.: Present address: Department of Mathematics, Andhra University, Visakhapatnam-530 003, India. Permanent address: Department of Mathematics, Wollega University, Nekemte-395, Ethiopia. E-mail: dulamosissa@gmail.com

Abstract: We introduce generalized $T A C$ -contractive mappings in $b$ -metric spaces and we prove some new fixed point results for this class of mappings. We provide examples in support of our results. Our results extend the results of [S. Chandok, K. Tas and A. H. Ansari, Some fixed point results for $T A C$ -type contractive mappings, J. Function Spaces, Vol. 2016, Article ID 1907676, 6 pages] from the metric space setting to $b$ -metric spaces and generalize a result of [D. Djorić, Common fixed point for generalized $(ψ, φ)$ -weak contractions, Appl. Math. Lett. 22 (2009) 1896–1900].

Keywords: $b$ -metric space; cyclic $(α, β)$ -admissible mapping; generalized $T A C$ -contractive mapping; fixed point.

Classification (MSC2000): 47H10; 54H25

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Electronic fulltext finalized on: 24 Feb 2017. This page was last modified: 17 Mar 2017.

© 2017 Mathematical Society of Serbia (Društvo matematičara Srbije)
© 2017 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition

Fixed points of generalized TAC-contractive mappings in b-metric spaces

G. V. R. Babu and T. M. Dula

Fixed points of generalized $T A C$ -contractive mappings in $b$ -metric spaces