Some Fixed Point Theorems in b-metric Space

Pankaj Kumar Mishra^1, , Shweta Sachdeva¹ and S. K. Banerjee¹

¹Department of Mathematics, University of Petroleum & Energy Studies, P.O. Bidholi, Via Prem Nagar, Dehradun (Uttarakhand), India

Cite this paper:
Pankaj Kumar Mishra, Shweta Sachdeva and S. K. Banerjee. Some Fixed Point Theorems in b-metric Space. Turkish Journal of Analysis and Number Theory. 2014; 2(1):19-22. doi: 10.12691/tjant-2-1-5

Abstract

In this paper we have obtained some fixed point theorems on b- metric space which is an extension of a fixed point theorem by Hardy [13] and Reich [20].

Keywords:
b-metric space fixed point

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Hassen Aydi, Monica-Felicia Bota, Erdal Karapinar, and Slobodanka Mitrović, A fixed point theorem for set-valued quasicontractions in b-metric spaces, Fixed Point Theory and Application (2012), no. 88.
[2]	Vasile Berinde, Generalized contractions in quasimetric spaces, (1993), no. 3, 3-9.
[3]	Monica Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Babes-Bolyai University Mathematica Studia LIV (2009), no. 3, 1-14.
[4]	Boriceanu M. Fixed point theory on spaces with vector-valued b-metrics, Demonstratio Mathematica XLII (2009), no. 4, 285-301.
[5]	Boriceanu M. Strict fixed point theorems for multivalued operators in b-metric spaces. International Journal of Modern Mathematics 4 (2009), no. 2, 285-301.
[6]	M. Bota, A. Molnar, and C. Varga, On ekeland's variational principle in b-metric spaces, Fixed Point Theory 12 (2011), no. 2, 21-28.
[7]	Renu Chugh, Vivek kumar, and Tamanna Kadian, Some fixed point theorems for multivalued mappings in generalized b-metric spaces, International Journal of Mathematical Archive 3 (2012), no. 3, 1198-1210.
[8]	S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1 (1993), 5-11.
[9]	Czerwik S., Nonlinear set-valued contraction mappings in b-metric spaces, Atti. Sem. Mat. Fis. Univ. Modena 46 (1998), 263-276.
[10]	S. Czerwik, Krzyszt Dlutek, and S. L. Singh, Round-off stability of iteration procedures for operators in b-metric spaces, J. Natur. Phys. Sci. 11 (1997), 87-94.
[11]	Czerwik S, Dlutek K, and Singh S L. Round-off stability of iteration procedures for set-valued operators in b-metric spaces, J. Natur. Phys. Sci. 15 (2001), 1-2.
[12]	Wei Shih Du and Erdal Karapýnar, A note on cone b-metric and its related results: generalizations or equivalence ?, Fixed Point Theory and Application 2012, no. 210.
[13]	G. E. Hardy and T. D. Rogers, A generalization of fixed point theorem of reich, Canadian Mathematical Bulletin 16 (1973), 201-206.
[14]	Mehmet Kir and Hukmi Kiziltunc, On some well known fixed point theorems in b-metric spaces, Turkish Journal of Analysis and Number Theory, 1 (2013), no. 1, 13{16.
[15]	Ion Marian Olaru and Adrian Branga, Common fixed point results in b-k-metric spaces, General Mathematics 19 (2011), no. 4, 51-59.
[16]	Memudu O. Olatinwo and Christopher O. Imoru, A generalisation of some results on multi-valued weakly Picard mappings in b-metric space, Fasciculi-Mathematici 40 (2008), 45-56.
[17]	Mădălina Păcurar, A fixed point result for φ-contractions on b-metric spaces without the boundedness assumption, Fascicyli Mathematici 43 (2010), 125-137.
[18]	Pacurar M. Sequences of almost contractions and fixed pointsin b-metric spaces, Analele Universităţ de Vest, Timi_soara, Seria Matematică Informatică XLVIII (2010), no. 3, 125-137.
[19]	K. P. R. Rao and K. R. K. Rao, A common fixed point theorem for two hybridpairs of mappings in b-metric spaces, International Journal of Analysis 2013, no. 404838.
[20]	Simeon Reich, Some remarks concerning contraction mappings, Canadian Mathematical Bulletins 14 (1971), no. 1, 121-124.
[21]	Jamal Rezaei Roshan, Vahid Parvaneh, Shaban Sedghi, Nabi Shobkolaei, and Wasfi Shatanawi, Common fixed points of almost generalized (ψ,φ)s-contractive mappings in ordered b-metric spaces, Fixed Point Theory and Application 2013, no. 159.
[22]	Lu Shi and Shaoyuan Xu, Common fixed point theorems for two weakly com-patible self-mappings in cone b-metric spaces, Fixed Point Theory and Applications 2013, no. 120.
[23]	Shyam Lal Singh, Stephen Czerwik, and Krzysztof Król, Coincidences and fixed points of hybrid contractions, Tamsui Oxford Journal of Mathematical Sciences 24 (2008), no. 4, 401-416.