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In the present paper we prove some new fixed point theorems for self-mappings defined on a complete metric space with a w-distance. These results extend some previous fixed point theorems in this field to more general contractive conditions in the setting of w-distances for selfmappings which satisfy certain weaker Meir–Keeler conditions.

The propose of this work is to study unified Feng-Liu type fixed point theorems using $$(\alpha ,\eta )$$ -muti-valued admissible mappings with more general contraction condition in complete metric spaces. The obtained results generalize and improve several existing theorems in the literature. We use these results in metric spaces endowed with binary relations and partially ordered sets. Some non-trivial example have been presented to illustrate facts and show genuineness of our work. At the end, the established results will be used to obtain existence solutions for a fractional-type integral inclusion.

In the publication of this article [Fixed Point Theory Appl. 2017:26, 2017], there is an error in Section 3. The error: Corollary 3.22 Let $( X,\sigma_{b} ) $ be a complete b-metric-like space with parameter $s \ge 1$ , and let f, g be two self-maps of X with $\psi \in \Psi $ , $\varphi \in \Phi $ satisfying the condition $$ \psi \bigl( \alpha_{qs^{p}}\sigma_{b} ( fx,fy ) \bigr) \le \lambda \psi \bigl( M ( x,y ) \bigr) $$ for all $x,y \in X$ , where $M ( x,y ) $ is defined as in (3.15) and $q > 1$ . Then f and g have a unique common fixed point in X. Should instead read: Corollary 3.22 Let $( X,\sigma_{b} ) $ be a complete b-metric-like space with parameter $s \ge 1$ , $f:X \to X$ be a self-mapping, and $\alpha :X \times X \to \mathopen[ 0,\infty \mathclose) $ . Suppose that the following conditions are satisfied: Then f has a fixed point $x \in X$ . Moreover, f has a unique fixed point if property $U_{qs^{p}}$ is satisfied. This has now been included in this erratum.

In this paper we point out that a number of fixed point papers, involving several maps, are special cases of a general result proved several years ago by the author and G. F. Jungck, and one proved by Aliouche and Popa [1].

In this paper we investigate the degree of approximation of a function belonging to the generalized Zygmund class \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$Z_{p}^{(\omega)}$\end{document}Zp(ω) (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p \ge1$\end{document}p≥1) by Hausdorff means of its Fourier series. We also deduce a corollary and mention a few applications of our main results.

We show that, under appropriate conditions, one can create a hybrid between two given iterations which can perform better than either of the original ones. This fact provides a freedom of choice. We also give numerical examples in which we compare our hybrid with the dedicated Lee-Seung iteration.

The fixed point theorems presented in this paper generalize recent results of Dutta and Choudhury [3], Branciari [2], Banach [1], Rhoades [9], Khan et al. [6], Kada [5] and Rhoades and Abbas [10].

Recently, Filipovic et al. [M. Filipovic, L. Paunovic, S. Radenovic, M. Rajovic, Remarks on 'Cone metric spaces and fixed point theorems of T-Kannan and T-Chatterjea contractive mappings', Math. Comput. Modelling. 54 (2011) 1467-1472] proved several fixed and periodic point theorems for solid cones on cone metric spaces. In this paper several fixed and periodic point theorems for T-contraction of two maps on cone metric spaces with solid cone are proved. The results of this paper extend and generalize well-known comparable results in the literature.

In this article we establish two coincidence point theorems for four mappings satisfying a generalized weakly contractive condition in ordered metric space, and apply it to find new coincidence point and common fixed point results. We furnish suitable examples to demonstrate the validity of the hypotheses of our results. Also we give an existence theorem for common solution of two integral equations.

In this paper we show that by renorming an ordered Banach space, every cone $P$ can be converted to a normal cone with constant $K=1$ and consequently due to this approach every cone metric space is really a metric one and every theorem in metric space is valid for cone metric space automatically.

We obtain necessary conditions for a doubly triangular matrix A to have the property that a double series ΣΣ λmnbmn is summable |A|k whenever the series ΣΣbmn is bounded |A|k.

We prove the existence of coincidence points and common fixed points for multivalued f-weak contraction mappings which assume closed values only. As an application, related common fixed point, invariant approximation, random coincidence point and random invariant approximation results are also obtained. Our results provide extensions as well as substantial improvements of several well known results in the existing literature.

We prove a fixed point theorem for a generalized weakly contractive mapping and a fixed point theorem for a pair of weakly contractive mappings. We also show that these mappings satisfy properties P and Q.

Mittal, Rhoades [5] , [6] , [7] , [8] and Mittal et al. [9] , [10] have initiated a study of error estimates E n ( f ) through trigonometric-Fourier approximation (tfa) for the situations in which the summability matrix T does not have monotone rows. In this paper we continue the work. Here we extend two theorems of Leindler [4] , where he has weakened the conditions on { p n } given by Chandra [2] , to more general classes of triangular matrix methods. Our Theorem also partially generalizes Theorem 4 of Mittal et al. [11] by dropping the monotonicity on the elements of matrix rows, which in turn generalize the results of Quade [15] .

In this paper, we consider the concept of a $\Omega$-distance on a complete partially ordered G-metric space and prove some fixed point theorems.

In 1930 Knopp presented the following matrix characterization for the core of ordinary sequences. If A is a nonnegative regular matrix then the core of [Ax] is contained in the core of [x], provided that [Ax] exists. Patterson in 1999 extended Knopp’s results to double sequences via four dimensional matrices. In a manner similar to the Knopp’s and Patterson’s results we present multidimensional extensions of Bustoz’s singular dimensional Gibbs phenomenon results. These results include a notion of what it means for a four dimensional matrix transformation to induce the double Gibbs phenomenon in s. In addition, necessary and sufficient conditions for a four dimensional matrix to induce the double Gibbs phenomenon is also presented.

In this paper, we introduce a new one-step iterative process to approximate the common fixed points of two multivalued nonexpansive mappings. We will also prove a strong convergence theorem in a uniformly convex Banach space under the multivalued version of so-called Condition (A′).

The existence of coincidence points and common fixed points for four mappings satisfying generalized contractive conditions without exploiting the notion of continuity of any map involved therein, in a cone metric space is proved. These results extend, unify and generalize several well known comparable results in the existing literature.

The notions of weak*-nonexpansive mapping and generalized R -multivalued mapping are introduced. Fixed points, common fixed points and some properties of the set of fixed points (common fixed points) of these maps are studied.

Using the setting of a generalized metric space, a fixed point theorem is proved for one map, and several fixed point theorems are proved for two maps. These results generalize several well known comparable results in the literature.

In this paper we extend a fixed point theorem of Imdad and Kumar, for a pair of non-self maps, to non-normal cone spaces.

We establish the convergence of Krasnoselskij iteration for various classes of non-Lipschitzian operators.

A fixed point theorem of Ciric, Diviccaro et al., Fisher and Sessa, Gregus, Jungck, and Mukherjee and Verma is generalized to weakly compatible maps. As applications, common fixed point and approximation results for Gregus type I-contractions are obtained. Our results unify and generalize various known results to the more general classes of noncommuting mappings.

We obtain sufficient conditions for the series ∑ a n λ n to be absolutely summable of order k by a triangular matrix.

Weobtain sufficient conditions for the series ∑∑ amn , which is absolutely summable of order k by a double triangular matrix method A , to be such that ∑∑ amnλmn is absolutely summable of order k by a double triangular matrix B . As corollaries we obtain a number of inclusion theorems. Mathematics subject classification (2000): 40G99, 40G05, 40D15.

The paper deals with absolute summability factors for infinite series. The main result obtained in this paper generalizes a recent paper of Mazhar.

We obtain sufficient conditions for the series ]]> ]]> \sum a_{n}\lambda_{n}$ to be absolutely summable of order $k$ by a triangular matrix.

The power series summability method is one of the most important and general methods in Summability Theory. In this work we will extend the power series method by considering the Burmann series method (i.e. f s ( z n ) = 1 f ( z n ) ∑ k = 0 ∞ s k b k [ h ( z n ) ] k , where f ( z n ) = ∑ k = 0 ∞ b k [ h ( z n ) ] k and | h ( z n ) | 1 ). Using the generalization we obtain a Tauberian theorem which contains, as special cases, some standard theorems for Abel, Borel, and Sonnenschein methods. We use the Abel and Borel matrix methods to illustrate this theorem.

We give a general condition which enables one to easily establish fixed point theorems for a pair of maps satisfying a contractive inequality of integral type.

We show that the convergence of Mann, Ishikawa iterations are equivalent to the convergence of a multistep iteration, for various classes of operators.

We obtain a theorem on a local property of \N, p(n)\(k), summability of factored Fourier series and a summability factor theorem for Fourier series. (C) 2003 Elsevier Inc. All rights reserved.

We show that the Ishikawa iteration and the corresponding Mann iteration are equivalent when applied toψ-uniformly pseudocontractive orψ-uniformly accretive maps.

Given a finite family of nonexpansive self-mappings of a Hilbert space, a particular quadratic functional, and a strongly positive selfadjoint bounded linear operator, Yamada et al. defined an iteration scheme which converges to the unique minimizer of the quadratic functional over the common fixed point set of the mappings. In order to obtain their result, they needed to assume that the maps satisfy a commutative type condition. In this paper, we establish their conclusion without the assumption of any type of commutativity.

We prove [1, Theorems 1 and 2] under weaker conditions and in a simpler way than we did in the cited paper.

We show that the convergence of Mann iteration is equivalent to the convergence of Ishikawa iteration for various classes of non-Lipschitzian operators.

We show that certain Mann and Ishikawa iteration schemes are equivalent for various classes of functions.

The purpose of this erratum is to correct both the mathematical and typographical errors made in 2006.

We prove an equivalent definition of summability of a numerical series by a weighted mean method in terms of ordinary convergence of another series. Our result includes a classical one by Hardy as a particular case. In the proof we make intrinsic use of infinite matrices, and our proof is therefore different from Hardy's.

The purpose of this paper is to introduce a new Kirk type iterative algorithm called Kirk multistep iteration and to study its convergence. We also prove some theorems related to the stability results for the Kirk multistep and Kirk-SP iterative processes by employing certain contractive-like operators. Our results generalize and unify some other results in the literature.

In this paper, we prove that the convergence of a new iteration and S-iteration can be used to approximate the fixed points of contractive-like operators. We also prove some data dependence results for these new iteration and S-iteration schemes for contractive-like operators. Our results extend and improve some known results in the literature. MSC:47H10.

We study the rate of approximation to functions inLpand, in particular, inLip(α,p)by weighted means of their Walsh-Fourier series, whereα>0and1≤p≤∞. For the casep=∞,Lpis interpreted to beCW, the collection of uniformlyWcontinuous functions over the unit interval[0,1). We also note that the weighted mean kernel is quasi-positive, under fairly general conditions.

In this article, we shall show that the metrics defined by Feng and Mao, and Du are equivalent. We also provide some examples for one of the metrics.

In this article, we study coupled coincidence and coupled common fixed point theorems in ordered generalized metric spaces for nonlinear contraction condition related to a pair of altering distance functions. Our results generalize and modify several comparable results in the literature. 2000 MSC: 54H25; 47H10; 54E50.