Let (X , d) be a complete metric space, m ∈ N \ {0}, and γ ∈ R with 0 ≤ γ < 1. A g-contraction is a mapping T : X −→ X such that for all x, y ∈ X there is an i ∈ [1,m] with d(T ix,T iy) <R γid(x, y). The generalized Banach contractions principle states that each g-contraction has a fixed point. We show that this principle is a consequence of Ramsey’s theorem for pairs over, roughly, RCA0 + Σ2-I...

In this paper, we introduce the concept of generalized orthogonal F -Suzuki contraction mapping and prove some fixed point theorems on id="M2"> b -metric spaces. Our results generalize extend well-known in existing literature. As an application our results, show existence a unique solution first-order ordinary d...

The notion of symmetry is the main property a metric function. area fixed point theory has suitable structure for in mathematics. goal this paper to find and common results bicomplex valued b-metric space mixed type rational contractions with control functions. Some well-known literature findings were generalized our findings. We provide an example strengthen validate results. As example, conte...

in this paper, we have dened and studied a generalized form of topological vectorspaces called s-topological vector spaces. s-topological vector spaces are dened by using semi-open sets and semi-continuity in the sense of levine. along with other results, it is provedthat every s-topological vector space is generalized homogeneous space. every open subspaceof an s-topological vector space is ...

In this paper, we introduce the notions of fuzzy $alpha$-Geraghty contraction type mapping and fuzzy $beta$-$varphi$-contractive mapping and establish some interesting results on the existence and uniqueness of fixed points for these two types of mappings in the setting of fuzzy metric spaces and non-Archimedean fuzzy metric spaces. The main results of our work generalize and extend some known ...

n this paper , we propose a generalized iterative method forfinding a common element of the set of fixed points of a singlenonexpannsive mapping and the set of solutions of two variationalinequalities with inverse strongly monotone mappings and strictlypseudo-contractive of browder-petryshyn type mapping. our resultsimprove and extend the results announced by many others.

In this paper, we introduce the notion of weak $psi$-quasi contraction in generalized metric spaces and using this notion we obtain conditions for the existence of fixed points of a self map in $D$-complete generalized metric spaces. We deduce some corollaries from our result and provide examples in support of our main result.