Related papers: Weak and strong convergence theorems for generaliz…

We develop a framework for quantitative convergence analysis of Picard iterations of expansive set-valued fixed point mappings. There are two key components of the analysis. The first is a natural generalization of single-valued averaged…

Weintroduce a new class of mappings called cyclic p-$\phi$-contraction mappings and investigate the existence and uniqueness of fixed point for such mappings defined on metric spaces, uniformly convex Banach spaces, or reflex ive Banach…

In this paper, first some results of [5] are extended for subadditive separating maps between C(X;E) and C(Y;E), such that E is a unital Banach algebra. Then we give some conditions under which a strongly subadditive map has a unique fixed…

Let $C$ be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space $E$ with dual space $E^*$. We present a novel hybrid method for finding a common solution of a family of equilibrium problems, a…

The weakly contractive metric type fixed point result in Berinde [Nonlinear Anal. Forum, 9 (2004), 45-53] is "almost" covered by the related altering metric one due to Khan et al [Bull. Austral. Math. Soc., 30 (1984), 1-9]. Further…

In this paper, the notions of $p$-cyclic $\phi$-contraction and $p$-cyclic Kannan nonexpansive mappings are introduced, and the existence of coupled best proximity points for such mappings is established.

We prove a basic property of continuous multilinear mappings between topological vector spaces, from which we derive an easy proof of the fact that a multilinear mapping (and a polynomial) between topological vector spaces is weakly…

This paper introduces the concept of quasi $\alpha$-firmly nonexpansive mappings in Wasserstein spaces over $\mathbb R^d$ and analyzes properties of these mappings. We prove that for quasi $\alpha$-firmly nonexpansive mappings satisfying a…

We propose the concepts of vicinal mappings and firmly vicinal mappings in metric spaces. We obtain fixed point and convergence theorems for these mappings in complete geodesic spaces with curvature bounded above by one and apply our…

In 1994, M. M. Popov [On integrability in F-spaces, Studia Math. no 3, 205-220] showed that the fundamental theorem of calculus fails, in general, for functions mapping from a compact interval of the real line into the lp-spaces for 0<p<1,…

We prove the convergence case of Khintchine's theorem, with general approximation functions that are not necessarily monotonic, for analytic nonplanar manifolds over local fields of positive characteristic. Our approach is based on the…

In this paper, we study the existence of solutions for generalized vector quasi-equilibrium problems. Firstly, we prove that in the case of Banach spaces, the assumptions of continuity over correspondences can be weakened. The theoretical…

We consider the conformal decomposition of Einstein's constraint equations introduced by Lichnerowicz and York, on a closed manifold. We establish existence of non-CMC weak solutions using a combination of a priori estimates for the…

For a finite and positive measure space $(\Omega,\Sigma,\mu)$ and any weakly compact convex subset of $L\sp\infty(\Omega,\Sigma,mu)$, a fixed point theorem for a class of nonexpansive self-mappings is proved. An analogous result is obtained…

In this paper, we consider the class of generalized {\Phi}-strongly monotone mappings and the methods of approximating a solution of equations of Hammerstein type. Auxiliary mapping is defined for nonlinear integral equations of Hammerstein…

We establish common fixed point theorems for two pairs of weakly compatible self-mappings using an auxiliary function of two variables. Unlike classical results, our theorems do not assume continuity of the mappings and require completeness…

Let $X$ be a metric space. Recently in~[1] it was considered a new type of mappings $T\colon X\to X$ which can be characterized as mappings contracting perimeters of triangles. These mappings are defined by the condition based on the…

Inspired by the work of Suzuki in [Proc. Amer. Math. Soc. 136 (2008), 1861--1869] we prove a fixed point theorem for contractive mappings that generalizes a theorem of Geraghty in [Proc. Amer. Math. Soc., 40 (1973), 604--608] and…

In this paper we give a new proof, relying on Banach's contraction mapping principle, of a celebrated theorem of Andr\'e Bloch. Also, via the same contraction mapping principle, we give a proof of a Bloch type theorem for normalised Wu…

In this paper, we introduce a new contraction condition that combines the framework of Singh's extension with the classical Chatterjea contraction. This generalized form, called the Singh-Chatterjea contraction, is defined on the p-th…