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

Khan, Aziz ¹ ; Khan, Hasib ² ; Baleanu, Dumitru ³ ; Karapinar, Erdal ⁴ ; Khan, Tahir Saeed ¹

¹ Department of Mathematics, University of Peshawar, P. O. Box 25000, Khyber Pakhtunkhwa, Pakistan
² College of Engineering, Mechanics and Materials, Hohai University, 210098, Nanjing, P. R. China;Shaheed Benazir Bhutto University Sheringal, Dir Upper, 18000, Khyber Pakhtunkhwa, Pakistan
³ Department of Mathematics, Cankaya University, 06530 Ankara, Turkey;Institute of Space Sciences, P. O. BOX, MG-23, 76900 Magrrele-Bucharest, Romania
⁴ Department of Mathematics, Atilim University, 06586 Incek, Ankara, Turkey

Journal of nonlinear sciences and its applications, Tome 10 (2017) no. 11, p. 5690-5700.

Résumé

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.

Détail

DOI : 10.22436/jnsa.010.11.07

Classification : 47H10, 54H25
Keywords: Weakly compatible mappings, common limit range property, fixed point theorems

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