The concepts of b-metric spaces and ω t -distance mappings play a key role in solving various kinds of equations through fixed point theory in mathematics and other science. In this article, we study some fixed point results through these concepts. We introduce a new kind of function namely, H -simulation function which is used in this manuscript together with the notion of ω t -distance mappings to furnish for new contractions. Many fixed point results are proved based on these new contractions as well as some examples are introduced. Moreover, we introduce an application on matrix equations to focus on the importance of our work.
The ω -distance mapping is one of the important tools that can be used to get new contractions in fixed point theory. The aim of this paper is to use the concept of modified ω -distance mapping to introduce the notion of rational ( α , β ) φ - m ω contraction. We utilize our new notion to construct and formulate many fixed point results for a pair of two mappings defined on a nonempty set A. Our results modify many existing known results. In addition, we support our work by an example.
In this manuscript, we utilize the concept of modified ω -distance mapping, which was introduced by Alegre and Marin [Alegre, C.; Marin, J. Modified ω -distance on quasi metric spaces and fixed point theorems on complete quasi metric spaces. Topol. Appl. 2016, 203, 120–129] in 2016 to introduce the notions of ( ω , φ ) -Suzuki contraction and generalized ( ω , φ ) -Suzuki contraction. We employ these notions to prove some fixed point results. Moreover, we introduce an example to show the novelty of our results. Furthermore, we introduce some applications for our results.
In this Article, we introduce the notion of an ∈φ-contraction which based on modified ω-distance mappings and employ this new definition to prove some fixed point result. Moreover, we introduced an interesting example and an application to highlight the importance of our work.
Interpolative Kannan contractions are a refinement of Kannan contraction, which is considered as one of the significant notions in fixed point theory. Gb-metric spaces is considered as a generalized concept of both concepts b-metric and G-metric spaces therefore, the significant fixed and common fixed point results of the contraction based on this concept is generalized resultsfor both concepts. The purpose of this manuscript, is to take advantage to interpolative Kannan contraction together with the notion of Ωb which equipped with Gb-metric spaces and H simulation functions to formulate two new interpolative contractions namely, (H, Ωb)-interpolative contraction for self mapping f and generalized (H, Ωb)-interpolative contraction for pair of self mappings (f1, f2). We discuss new fixed and common fixed point theorems. Moreover, to demonstrate the applicability and novelty of our theorems, we formulate numerical examples and applications to illustrate the importance of fixed point theory in applied mathematics and other sciences.
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