Some fixed point results for a generalized ψ-weak contraction mappings in orbitally metric spaces

Samet and Vetro [Samet B, Vetro C. Berinde mappings in orbitally complete metric spaces. Chaos Solitons Fract 2011;44:1075–9.] studied a fixed point theorem for a self-mapping satisfying a general contractive condition of integral type in orbitally complete metric spaces. In this paper, we introduce the notion of a generalized ψ-weak contraction mapping and establish some results in orbitally complete metric spaces. Our results generalize several well-known comparable results in the literature. As an application of our results we deduce the result of Samet and Vetro. Some examples are given to illustrate the useability of our results.     

The common fixed point of single-valued generalized φf-weakly contractive mappings

Fixed point and coincidence results are presented for single-valued generalized ${\phi }_f$-weakly contractive mappings on complete metric spaces $(X,d)$, where $\phi :[0,\infty )\to [0,\infty )$ is a lower semicontinuous function with $\phi \left(0\right)=0$ and $\phi \left(t\right)>0$ for all $t>0$ and $f:E\to X$ is a function such that $E?X$ is nonempty and closed. Our results extend previous results given by Rhoades (2001) [1] and by Zhang and Song (2009) [2].     

On the split common fixed point problem for strict quasi-ϕ-pseudocontractive mappings in Banach spaces

Numerical Algorithms - The purpose of this paper is to propose an algorithm for solving the split common fixed point problem for strict quasi-?-pseudocontractive mappings in Banach spaces. It...     

Existence and approximation of fixed points of multivalued generalized α-nonexpansive mappings in Banach spaces

Numerical Algorithms - We consider the theoretical and numerical aspects of the quadrature rules associated with a sequence of polynomials generated by a special RII recurrence relation. We also...     

On an equation characterizing multi-Jensen-quadratic mappings and its Hyers–Ulam stability via a fixed point method

In this paper, we unify the system of functional equations defining a multi-Jensen-quadratic mapping to obtain a single equation. We also prove, using the fixed point method, the generalized Hyers–Ulam stability of this equation both in Banach spaces and in complete non-Archimedean normed spaces.     

On generalization of Darbo–Sadovskii type fixed point theorems for iterated mappings in Fréchet spaces

In this paper, we give new Darbo–Sadovskii type fixed point theorems for iterated mappings in Fréchet spaces. Moreover, we solve two open questions proposed in Ariza-Ruiz and Garcia-Falset (Fixed Point Theory, 2018).     

On a generalization of a Greguš fixed point theorem

Let C be a closed convex subset of a complete convex metric space X. In this paper a class of selfmappings on C, which satisfy the nonexpansive type condition (2) below, is introduced and investigated. The main result is that such mappings have a unique fixed point.     

Hybrid projection method for generalized mixed equilibrium problem and fixed point problem of infinite family of asymptotically quasi-?-nonexpansive mappings in Banach spaces

In this paper, we consider a hybrid projection method for finding a common element in the set of fixed points of a infinite family of asymptotically quasi-?-nonexpansive mappings and in the set of solutions of a generalized mixed equilibrium problem. Some strong convergence theorems of common elements are established in a uniformly smooth and strictly convex Banach space which has the Kadec-Klee property. The results presented in the paper improve and extend some recent results.     

On the ℂ-differentiability of mappings of Banach spaces

We study the monogeneity conditions for -differentiable mappings of domains of a Banach space and establish criteria of -differentiability of a mapping at a point.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 10, pp. 1336–1342, October, 1994.     

Commutators of Toeplitz Operators On A~p(ψ)

Let denote the positive continous function on ［0,1）. be called normal, if there exist two constants a and b (0＜a＜b) such that (t)(1-t2)a decreases and (t)(1-t2)b increases on ［0,1）. Let dm denote the normalized area measure on the open unit disk D in the complex plane. Define dmp as the measure on D: dmp=p(｜z｜)1-｜z｜2dm(z). For 1p＜∞, let Lp() denote the Banach space of measurable functions f with norm ‖f‖p,φ＝∫D｜f｜pdmpφ1/p＜∞. Ap() denote the closed subspac…     

On the Various Realizations of the Basic Representation of An−1(1) and the Combinatorics of Partitions

The infinite dimensional Lie algebra l _n = A _n–1 ⁽¹⁾ can be realized in several ways as an algebra of differential operators. The aim of this note is to show that the intertwining operators between the realizations of l _n corresponding to all partitions of n can be described very simply by using combinatorial constructions.     

Two refinements of Frink’s metrization theorem and fixed point results for Lipschitzian mappings on quasimetric spaces

Aequationes mathematicae - Quasimetric spaces have been an object of thorough investigation since Frink’s paper appeared in 1937 and various generalisations of the axioms of metric spaces are...     

Convergence theorems for fixed points of uniformly continuous generalized Φ-hemi-contractive mappings

Let E be a real normed linear space, K be a nonempty subset of E and be a uniformly continuous generalized Φ-hemi-contractive mapping, i.e., , and there exist x^∗∈F(T) and a strictly increasing function , Φ(0)=0 such that for all x∈K, there exists j(x−x^∗)∈J(x−x^∗) such that

〈Tx−x^∗,j(x−x^∗)〉?‖x−x^∗‖2−Φ(‖x−x^∗‖).     

On generalized Ekeland’s variational principle and equivalent formulations for set-valued mappings

We propose a very weak type of generalized distances called a weak τ-function and use it to weaken the assumptions about lower semicontinuity in existing versions of Ekeland’s variational principle and equivalent formulations.