In this paper, we introduce the notion of generalized (α, φ, ψ)- Geraghty contractive type mappings in setup Sb-metric spaces and α-orbital admissible with respect to φ. Furthermore, fixed-point theorems for such complete are proven without assuming subadditivity ψ. Some examples provided supporting our main results. Also, gave an application integral equations as well Homotopy.

The fixed point theorems in metric spaces are playing a major role to construct methods in mathematics to solve problems in applied mathematics and sciences. So the attraction of metric spaces to a large numbers of mathematicians is understandable. Some generalizations of the notion of a metric space have been proposed by some authors. In 2006, Mustafa in collaboration with Sims introduced a ne...

Given a subvariety V of the complex algebraic torus G n m defined by polynomials of total degree at most d and a power map φ : G n m → G n m , the points x whose forward orbits O φ (x) belong to V form its stable subvariety S(V, φ). The main result of the paper provides an upper bound T = T (n, d, φ) for the number of iterations of the power map φ required to " cut off " the points of V that do...

Let BN be the unit ball in the N-dimensional complex space, for ψ, a holomorphic function in BN , and φ, a holomorphic map from BN into itself, the weighted composition operator on the weighted Hardy space H(β,BN ) is given by (Cψ,φ) f = ψ(z) f (φ(z)), where f ∈H2(β,BN ). This paper discusses the spectrum of Cψ,φ when it is compact on a certain class of weighted Hardy spaces and when the compos...

We show in this paper that the module structure and the orthogonality structure of a Hilbert C∗-module determine its inner product structure. Let A be a C∗-algebra, and E and F be Hilbert A-modules. Assume Φ : E → F is an A-module map satisfying 〈Φ(x),Φ(y)〉A = 0 whenever 〈x, y〉A = 0. Then Φ is automatically bounded. In case Φ is bijective, E is isomorphic to F . More precisely, let JE be the cl...

We consider the Schrödinger map initial-value problem { ∂tφ = φ×∆φ on R × R; φ(0) = φ0, where φ : R × R → S →֒ R is a smooth function. In all dimensions d ≥ 2, we prove that the Schrödinger map initial-value problem admits a unique global smooth solution φ ∈ C(R : H∞ Q ), Q ∈ S, provided that the data φ0 ∈ H∞ Q is smooth and satisfies the smallness condition ‖φ0−Q‖Ḣd/2 ≪ 1. We prove also that th...

Let Φ be a finite root system of rank n and let m be a positive integer. It is proved that the generalized cluster complex ∆m(Φ), introduced by S. Fomin and N. Reading, is (m + 1)-Cohen-Macaulay, in the sense of Baclawski. This statement was conjectured by V. Reiner. More precisely, it is proved that the simplicial complex obtained from ∆m(Φ) by removing any subset of its vertex set of cardinal...

A fixed-point theorem on compact compositions of acyclic maps on admissible (in the sense of Klee) convex subset of a t.v.s. is applied to obtain a cyclic coincidence theorem for acyclic maps, generalized “onNeumann type intersection theorems, the Nash type equilibrium theorems, and the “onNeumann minimax theorem. Our new results generalize earlier works of Lassonde [l], Simons [2], and Park [3...

‎In this work‎, ‎we investigate admitting center map on multiplicative metric space‎ ‎and establish some fixed point theorems for such maps‎. ‎We modify the Banach contraction principle and‎ ‎the Caristi's fixed point theorem for M-contraction admitting center maps and we prove some‎ ‎useful theorems‎. ‎Our results on multiplicative metric space improve and modify‎ ‎s...