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...

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...

In this article, we introduce a new notion of weakly soft susc-contraction in metric spaces and prove fixed point theorem which assure the existence points for type susc-contraction. Our results generalize many recent literature.

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.

Different versions of Wiener’s Tauberian theorem are discussed for the generalized group algebra LI(G,A) (of integrable functions on a locally compact abelian group G taking values in a commutative semisimple regular Banach algebra A) using A-valued Fourier transforms. A weak form of Wiener’s Tauberian property is introduced and it is proved that LI(G,A) is weakly Tauberian if and only if A is....

Interpolative Kannan contractions are a refinement of contraction, which is considered as one the significant notions in fixed point theory. Gb-metric spaces generalized concept both concepts b-metric and G-metric therefore, common results contraction based on this resultsfor concepts. The purpose manuscript, to take advantage interpolative together with notion Ωb equipped H simulation function...