Turkish Journal of Analysis and Number Theory
ISSN (Print): 2333-1100 ISSN (Online): 2333-1232 Website: http://www.sciepub.com/journal/tjant
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Turkish Journal of Analysis and Number Theory. 2016, 4(5), 118-131
DOI: 10.12691/tjant-4-5-1
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Some Fixed Point Results on Multiplicative (b)-metric-like Spaces

Bakht Zada1, and Usman Riaz1

1Department of Mathematics, University of Peshawar, Peshawar, Pakistan

Pub. Date: September 22, 2016

Cite this paper:
Bakht Zada and Usman Riaz. Some Fixed Point Results on Multiplicative (b)-metric-like Spaces. Turkish Journal of Analysis and Number Theory. 2016; 4(5):118-131. doi: 10.12691/tjant-4-5-1


We give the concept of multiplicative partial metric space, multiplicative metric-like space, multiplicative b-metric space and multiplicative b-metric-like space. Then we build the existence and uniqueness of fixed points in a multiplicative b-metric-like space as well as in a partially ordered multiplicative b-metric-like space. We derive some fixed point results in multiplicative partial metric spaces, multiplicative metric-like spaces and multiplicative b-metric spaces as an application, some examples and an application to existence of solution of integral equations.

Partial metric space metric-like space b-metric space b-metric-like space fixed point integral equation

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[1]  M. A. Alghamdi, N. Hussain, and P. Salimi, Fixed point and coupled fixed point theorems on b-metric-like spaces. Journal of Inequalities and Applications, article 402, (2013).
[2]  Agarwal, El-Gebeily, ORegan, Generalized contractions in partially ordered metric spaces. Appl. Anal., (2008).
[3]  A. E. Bashirov, E. M. Kurpinar, A. Ozyapici, Multiplicative calculus and its applications, J. Math. Anal. Appl., 337 (2008), 36-48.
[4]  S. Czerwik, Contraction mappings in b-metric spaces. Acta Mathematica et Informatica Universitatis Ostraviensis, vol. 1, (1993).
[5]  Daffer, Kaneko, On expansive mappings. Math. Jpn. (1992).
[6]  Ozavsar, Cevikel, Fixed points of multiplicative contraction mappings on multiplicative metric spaces. arXiv:1205.5131v1 [math.GM] (2012).
[7]  Edelstein, On fixed and periodic points under contractive mappings. J. Lond. Math. Soc. 37, (1962).
[8]  S. Gaulyaz, E. Karapinar and V. Rakocevic and P. Salimi, Existence of a solution of integral equations via fixed point theorem. Journal of Inequalities and Appl, (2013).
[9]  Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points. Fixed Point Theory and Applications, (2012).
[10]  Kirk,WA, Srinavasan, PS, Veeramani, Fixed points for mapping satisfying cyclical contractive conditions. Fixed Point Theory 4, (2003).
[11]  Kumar, Garg, Expansion mapping theorems in metric spaces. Int. J. Contemp. Math. Sci. (2009).
[12]  S. G. Matthews, Partial metric topology. Annals of the New York Academy of Sciences. General Topology and Applications, vol. 728, (1994).
[13]  H. K. Pathak, M. S. Khan and R. Tiwari, A common fixed point theorem and its application to nonlinear integral equations. Computers and Mathematics with Applications, (2007).
[14]  H. K. Pathak, S. N. Mishra and A. K. Kalinde, Common xed point theorems with applications to nonlinear integral equations. Demonstratio Math., XXXII (1999).
[15]  S. Shukla, Partial b-metric spaces and fixed point theorems. Mediterranean Journal of Mathematics, (2013).
[16]  Suzuki, A new type of fixed point theorem in metric spaces. Nonlinear Anal. 71(11), (2009).