Hybrid Fixed Point Theorems in Symmetric Spaces via Common Limit Range Property

Demonstratio mathematica

article

Mohammad Imdad¹  Sunny Chauhan²  Ahmed H. Soliman³  M. A. Ahmed⁴ 

[1] DEPARTMENT OF MATHEMATICS ALIGARH MUSLIM UNIVERSITY ALIGARH 202 002;R.H. GOVERNMENT POSTGRADUATE COLLEGE KASHIPUR;DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE AL-AZHAR UNIVERSITY ASSIUT-71524;DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE ASSIUT UNIVERSITY ASSIUT-71516

关键词: and phrases symmetric space;    multi-valued mappings;    quasi-coincidentally commuting mappings;    common limit range property;    coincidence point;    common fixed point;   

DOI  :  10.2478/dema-2014-0075

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

In this paper, we point out that some recent results of Vijaywar et al. (Coincidence and common fixed point theorems for hybrid contractions in symmetric spaces, Demonstratio Math. 45 (2012), 611-620) are not true in their present form. With a view to prove corrected and improved versions of such results, we introduce the notion of common limit range property for a hybrid pair of mappings and utilize the same to obtain some coincidence and fixed point results for mappings defined on an arbitrary set with values in symmetric (semi-metric) spaces. Our results improve, generalize and extend some results of the existing literature especially due to Imdad et al., Javid and Imdad, Vijaywar et al. and some others. Some illustrative examples to highlight the realized improvements are also furnished.

【 授权许可】

CC BY