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EMPLOYING COMMON LIMIT RANGE PROPERTY WITH VARIANTS OF R-WEAKLY COMMUTING MAPPINGS IN METRIC SPACES
Sunny Chauhan,Jelena VujakoviĆ,Shamsul Haq 한국수학교육학회 2015 純粹 및 應用數學 Vol.22 No.2
The object of this paper is to emphasize the role of `common limit range property' and utilize the same with variants of R-weakly commuting mappings for the existence of common fixed point under strict contractive conditions in metric spaces. We also furnish some interesting examples to validate our main result. Our results improve a host of previously known results including the ones contained in Pant [Contractive conditions and common fixed points, Acta Math. Acad. Paed- agog. Nyházi. (N.S.) 24(2) (2008), 257{266 MR2461637 (2009h:54061)]. In the process, we also derive a fixed point result satisfying Φ-contractive condition.
Some remarks on results of Pant and Pant along with generalization for hybrid mappings
Kamal Wadhwa,Ved Prakash Bhardwaj 원광대학교 기초자연과학연구소 2017 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.14 No.3
In the present note, we pose some remarks on results of Pant and Pant [23]. After resolving some errors; we provide their results using common limit in the range property. Further, we generalize their results for hybrid pairs of mappings in fuzzy metric space. we also provide some examples for the validity of our results.
Nashine, Hemant Kumar,Kadelburg, Zoran Korean Mathematical Society 2015 대한수학회보 Vol.52 No.3
We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized ${\Phi}$-contractive conditions i Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.
Hemant Kumar Nashine,Zoran Kadelburg 대한수학회 2015 대한수학회보 Vol.52 No.3
We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized Φ-contractive conditions in Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.
Om Prakash Chauhan,Deepak Singh,Vishal Joshi,Garima Singh,Rajendra Kumar Sharma 경남대학교 수학교육과 2018 Nonlinear Functional Analysis and Applications Vol.23 No.4
In this article, we define the notion of a non-negative function satisfying property of oneness. Utilizing this concept, certain unified fixed point results are established. Furthermore generalized φ-contractions mapping and some fixed point results in the framework of symmetric space are also presented. Some well-known results from the existence literature are obtained through our introduced setting. Results are substantiated by some innovative examples with the aid of visualization of surfaces. Moreover applications of obtained theory for the existence for the system of integral equations as well as for the system of functional equations occurred in dynamic programming are also presented.