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

The Journal of Nonlinear Sciences and its Applications

HasibKhan¹  ErdalKarapinar²  DumitruBaleanu³  AzizKhan⁴  Tahir SaeedKhan⁴ 

[1] College of Engineering, Mechanics and Materials, Hohai University, 210098, Nanjing, P. R. China;Department of Mathematics,Atilim University, 06586 Incek, Ankara, Turkey;Department of Mathematics, Cankaya University, 06530 Ankara, Turkey;Department of Mathematics, University of Peshawar, P. O. Box 25000, Khyber Pakhtunkhwa, Pakistan

关键词: Weakly compatible mappings;    common limit range property;    fixed point theorems;   

DOI  :  10.22436/jnsa.010.11.07

学科分类：社会科学、人文和艺术（综合）

来源: Shomal University

【 摘 要 】

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.

【 授权许可】

Unknown