4/10/2021 0 Comments Ecut 6 Kryak
In this manuscript, the idea of weakly contraction is used for in tuitionistic fuzzy mappings in association with ( T, N, ) cut set of an IF-set 27.We intend to prove common fixed point theorem for a pair of intuitionistic fuzzy mappings satisfying weakly contractive condition in a complete metric space which generalizes many results existing in the literature.
Moreover, concrete results on existence of the solution of a delay differential equation and a system of Riemann-Liouville Cauchy type problems have been derived. Ecut 6 Kryak Free Public FullDiscover the worlds research 20 million members 135 million publications 700k research projects Join for free Public Full-text 1 Available via license: CC BY-NC-ND 4.0 Content may be subject to copyright. Romaguera Abstract The purpose of this article is to extend the results derived through for- mer articles with respect to the notion of weak contraction into intu- itionistic fuzzy weak contraction in the con text of ( T, N, ) cut set of an intuitionistic fuzzy set. We intend to pro ve common xed point the- orem for a pair of intuitionistic fuzzy mappings satisfying weakly con- tractive condition in a complete metric space which generalizes man y results existing in the literature. Moreover, concrete results on exis- tence of the solution of a delay dierential equation and a system of Riemann-Liouville Cauchy t ype problems have been derived. In addi- tion, we also present illustrative examples to substan tiate the usability of our main result. ![]() Keywords: common xed point; intuitionistic fuzzy set-v alued maps; ( T, N, ) cut set; weakly contractive condition; delay dier- ential equation; Riemann-Liouville fractional dierential equa- tions. ![]() In 1997, Alber and Guerr-Delabriere 3 proposed the notion of weak contractive mappings on Hilbert spaces and studied the existence of xed point results in the context of weakly con tractive single v alued maps on Hilbert spaces as a generalization of Banach Contraction Principle. Howev er, in 2001, Rhoades 30 presented some results of 3 to arbitrary Banach spaces. Later on, Bae 10 established the xed points of weakly contractiv e multivalued mappings and Beg and Abbas 19 demonstrated the xed point results for a pair of single valued mappings one is w eakly contractive relativ e to the other. On the other hand, there are many complicated practical problems in the domain of real world such as engineering, economics, social sciences, medical science and many other elds that inv olve data which are not alw ays precise. T o overcome these diculties, classical mathematical notions may not be ap- plied eectively, because there are numerous types of vagueness appear in these domains. However, in response to this fact, Zadeh 39 developed the concept of fuzzy set as an extension of conven tional set theory. Over the years, sev- eral mathematicians extended this notion in dierent directions, for instance, L -fuzzy set, intuitionstic fuzzy set, fuzzy soft set and hesitant fuzzy soft set. Consequently, in 1981, Heilpern 20 initiated the idea of fuzzy mapping and proved a xed point theorem for fuzzy con traction mappings as an extension of multiv alued mappings of Nadlers contraction principle. Thus, this result motivated sev eral researchers to study and establish the xed point results satisfying a fuzzy contractive inequalities ( see, 1, 6, 7 ). One of the generalizations of fuzzy set theory 39 is the notion of intuition- istic fuzzy set (IF-set) introduced by Atanasso v 5. Moreover, IF-sets cre- ate a valuable mathematical structure to deal with inaccuracy and hesitancy originating from insucient decision information and as a consequence,it has remarkable applications in v arious elds like image proccessing 21, medical diagnosis 18, drug selection 22, decision analysis 26, etc. Until now, research on IF-set has been very activ e and many results hav e been proved with dierent aspects. Recently, Azam et al. Later on, Azam and Rehana 9 presented existence of common coincidence point for three intuitionistic fuzzy set valued maps and they also studied existence results for a system of integral equations.
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