Fixed points of weakly compatible mappings satisfying a generalized common limit range property


Authors

Aziz Khan - Department of Mathematics, University of Peshawar, P. O. Box 25000, Khyber Pakhtunkhwa, Pakistan. Hasib Khan - College of Engineering, Mechanics and Materials, Hohai University, 210098, Nanjing, P. R. China. - Shaheed Benazir Bhutto University Sheringal, Dir Upper, 18000, Khyber Pakhtunkhwa, Pakistan. Dumitru Baleanu - Department of Mathematics, Cankaya University, 06530 Ankara, Turkey. - Institute of Space Sciences, P. O. BOX, MG-23, 76900 Magrrele-Bucharest, Romania. Erdal Karapinar - Department of Mathematics, Atilim University, 06586 Incek, Ankara, Turkey. Tahir Saeed Khan - Department of Mathematics, University of Peshawar, P. O. Box 25000, Khyber Pakhtunkhwa, Pakistan.


Abstract

In this paper, we produce new fixed point theorems for \(2n\) self-mappings \(\wp^a_1,\wp^a_2,\ldots,\wp^a_n\), \(\gamma^b_1,\gamma^b_2,\ldots,\gamma^b_n:\mathcal{X}\rightarrow\mathcal{X}\) on a metric space \((\mathcal{X},\rho )\), satisfying a generalized common limit range (CLR) property or CLR\(_{\wp^a_k\gamma^b_l}\) for \(k,l=2,\ldots,n\). Along with the newly introduced property CLR\(_{\wp^a_k\gamma^b_l}\) for \(k,l=2,\ldots,n\) for the \(2n\) self-mappings, we also assume that the pairs \((\wp^a_1,\gamma^b_1),(\wp^a_2,\gamma^b_2),\ldots,(\wp^a_n,\gamma^b_n)\) are weakly compatible. From the main result, we produce three more corollaries as its special cases. These results generalize the work of Sarwar et al. [M. Sarwar, M. Bahadur Zada, I. M. Erhan, Fixed Point Theory Appl., \({\bf 2015}\) (2015), 15 pages] and many others in the available literature. Two examples are also presented for the applications of our new FPTs.


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ISRP Style

Aziz Khan, Hasib Khan, Dumitru Baleanu, Erdal Karapinar, Tahir Saeed Khan, Fixed points of weakly compatible mappings satisfying a generalized common limit range property, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 11, 5690--5700

AMA Style

Khan Aziz, Khan Hasib, Baleanu Dumitru, Karapinar Erdal, Khan Tahir Saeed, Fixed points of weakly compatible mappings satisfying a generalized common limit range property. J. Nonlinear Sci. Appl. (2017); 10(11):5690--5700

Chicago/Turabian Style

Khan, Aziz, Khan, Hasib, Baleanu, Dumitru, Karapinar, Erdal, Khan, Tahir Saeed. "Fixed points of weakly compatible mappings satisfying a generalized common limit range property." Journal of Nonlinear Sciences and Applications, 10, no. 11 (2017): 5690--5700


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