A fixed point theorem on multiplicative metric space with integral-type inequality
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Authors
Aziz Khan
- Department of Mathematics, University of Peshawar, P. O. Box 25000, Khybar Pakhtunkhwa, Pakistan
Hasib Khan
- College of Engineering, Mechanics and Materials, Hohai University, 211100, Nanjing, P. R. China
Dumitru Baleanu
- Department of Mathematics, Cankaya University, 06530 Ankara, Turkey
Hossein Jafari
- Department of Mathematics, University of Mazandaran, P. O. Box 47416-95447, Babolsar, Iran
Tahir Saeed Khan
- Department of Mathematics, University of Peshawar, P. O. Box 25000, Khybar Pakhtunkhwa, Pakistan
Maysaa Alqurashi
- College of Science, Department of Mathematics, King Saud University, Riyad, Saudi Arabia
Abstract
In this paper, we prove fixed point theorems (FPTs) on multiplicative metric space (MMS) (\(\mathcal{X},\blacktriangle\)) by the help of integral-type contractions of self-quadruple mappings (SQMs), i.e., for \(\wp_1,\wp_2,\wp_3,\wp_4:\mathcal{X}\rightarrow \mathbb{R}\). For this, we assume that the SQMs are weakly compatible mappings and the pairs \(\big(\wp_1,\wp_3\big)\) and \(\big(\wp_2,\wp_4\big)\) satisfy the property \((CLR_{\wp_3\wp_4})\). Further, two corollaries are produced from our main theorem as special cases. The novelty of these results is that for the unique common fixed point (CFP) of the SQMs \(\wp_1,\wp_2,\wp_3,\wp_4\), we do not need to the assumption of completeness of the MMS \((\mathcal{X},\blacktriangle)\). These results generalize the work of Abdou, [A. A. N. Abdou, J. Nonlinear Sci. Appl., \({\bf 9}\) (2016), 2244--2257], and many others in the available literature.
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ISRP Style
Aziz Khan, Hasib Khan, Dumitru Baleanu, Hossein Jafari, Tahir Saeed Khan, Maysaa Alqurashi, A fixed point theorem on multiplicative metric space with integral-type inequality, Journal of Mathematics and Computer Science, 18 (2018), no. 1, 18--28
AMA Style
Khan Aziz, Khan Hasib, Baleanu Dumitru, Jafari Hossein, Khan Tahir Saeed, Alqurashi Maysaa, A fixed point theorem on multiplicative metric space with integral-type inequality. J Math Comput SCI-JM. (2018); 18(1):18--28
Chicago/Turabian Style
Khan, Aziz, Khan, Hasib, Baleanu, Dumitru, Jafari, Hossein, Khan, Tahir Saeed, Alqurashi, Maysaa. "A fixed point theorem on multiplicative metric space with integral-type inequality." Journal of Mathematics and Computer Science, 18, no. 1 (2018): 18--28
Keywords
- Multiplicative metric space
- fractional integral inequalities
- fixed point theorems
MSC
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