%0 Journal Article
%T Some remarks on tripled ﬁxed point theorems for a sequence of mappings satisfying Geraghty contraction with applications
%J Communications in Nonlinear Analysis
%I RGNAA Publishing
%Z 2371-7920
%A Singh, Deepak
%A Chauhan, Varsha
%A Asadi, Mehdi
%D 2017
%\ 06/01/2017
%V 3
%N 2
%P 68-86
%! Some remarks on tripled ﬁxed point theorems for a sequence of mappings satisfying Geraghty contraction with applications
%K Partially ordered metric spaces
%K compatible mappings
%K weakly reciprocally maps
%K tripled coincidence point
%K tripled fixed point
%R
%X The purpose of this paper is threefold. Firstly, we establish a tripled coincidence fixed point theorem for a sequence of mappings involving Geraghty contraction using compatibility and weakly reciprocally continuousmaps in the structure of partially ordered metric spaces. The technique used in A. Roldan et al. [9] andin S. Radenovic [10] are not applicable to the presented theorems, we show that our results cannot beobtained from the existing results in this eld of study and thus our results are completely new and give rise toa new dimension. Secondly, the notable works due to V. Berinde [3], V. Lakshmikantam and L. Ciric [8] andBabu and Subhashini [1] are generalized and extended. Finally, some sufficient conditions are given for theuniqueness of a tripled common fixed point. Consequently, we point out some slip-ups in the main resultsof R. Vats et al.[12] and present a furnished version of the same. Some illustrative examples to highlightthe realized improvements are also furnished. Moreover, existence and uniqueness for the solution of aninitial-boundary-value problem are discussed. On the other hand, as an application to establish existence anduniqueness for the system of integral equations our results are utilized.
%U https://www.cna-journal.com/article_89765_4bd702e3eb13378da52d05c6223e1a68.pdf