In this paper, we define a Halpern–Ishikawa type iterative method for approximating a fixed point of a Lipschitz pseudocontractive non-self mapping T in a real Hilbert space settings and prove strong convergence result of the iterative method to a fixed point of T under some mild conditions. We give a numerical example to support our results. Our results improve and generalize...

In this paper, some strong and Δ-convergence results are proved for Suzuki generalized nonexpansive mappings in the setting of \(\mathit{CAT}(0)\) spaces using the K iteration process. We also give an example to show the efficiency of the K iteration process. Our results are the extension, improvement and generalization of many well-known results in the literature of fixed point...

In this paper, we study an inertial algorithm for approximating a common fixed point for a countable family of relatively nonexpansive maps in a uniformly convex and uniformly smooth real Banach space. We prove a strong convergence theorem. This theorem is an improvement of the result of Matsushita and Takahashi (J. Approx. Theory 134:257–266, 2005) and the result of Dong et al...

Our purpose in this paper is (i) to introduce the concept of further generalized hybrid mappings, (ii) to introduce the concept of common attractive points (CAP), and (iii) to write and use Picard-Mann iterative process for two mappings. We approximate common attractive points of further generalized hybrid mappings by using iterative process due to Khan (Fixed Point Theory Appl...

We consider the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings in real Hilbert spaces. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common solution of the considered problems. A numerical example is presented to illustrate the convergence result. Our...

In this paper, we introduce some operations on a fuzzy neutrosophic soft set (\(\mathfrak{fns}\)-set) by utilizing the theories of fuzzy sets, soft sets and neutrosophic sets. We introduce \(\mathfrak{fns}\)-mappings by using a cartesian product with relations on \(\mathfrak{fns}\)-sets and establish some results on fixed points of an \(\mathfrak{fns}\)-mapping. We present an...

In this paper, we propose two strongly convergent algorithms which combines diagonal subgradient method, projection method and proximal method to solve split equilibrium problems and split common fixed point problems of nonexpansive mappings in a real Hilbert space: fixed point set constrained split equilibrium problems (FPSCSEPs) in real Hilbert spaces. The computations of first...

In this paper, motivated and inspired by Samet et al., we introduce the notion of generalized weakly contractive mappings in metric spaces and prove the existence and uniqueness of fixed point for such mappings, and we obtain a coupled fixed point theorem in metric spaces. These theorems generalize many previously obtained fixed point results. An example is given to illustrate...

In 1980, Hegedüs and Szilágyi proved some fixed point theorem in complete metric spaces. Introducing a new contractive condition, we generalize Hegedüs-Szilágyi’s fixed point theorem. We discuss the relationship between the new contractive condition and other contractive conditions. We also show that we cannot extend Hegedüs-Szilágyi’s fixed point theorem to Meir-Keeler type.

In this paper, we establish some fixed point results for fuzzy mappings in a complete dislocated b-metric space. Our results generalize and extend the results of Joseph et al. (SpringerPlus 5:Article ID 217, 2016). We also give examples to support our results, and applications relating the results to a fixed point for multivalued mappings and fuzzy mappings are studied.

In this paper, we introduce a new class of \(\alpha_{qs^{p}}\)-admissible mappings and provide some fixed point theorems involving this class of mappings satisfying some new conditions of contractivity in the setting of b-metric-like spaces. Our results extend, unify, and generalize classical and recent fixed point results for contractive mappings.

We give characterizations of the contractive conditions, by using convergent sequences. Since we use a unified method, we can compare the contractive conditions very easily. We also discuss the contractive conditions of integral type by a unified method.

This work is for giving the probabilistic aspect to the known b-metric spaces (Czerwik in Atti Semin. Mat. Fis. Univ. Modena 46(2):263-276, 1998), which leads to studying the fixed point property for nonlinear contractions in this new class of spaces.

We apply the topological degree theory for condensing maps to study approximation of solutions to a fractional-order semilinear differential equation in a Banach space. We assume that the linear part of the equation is a closed unbounded generator of a \(C_{0}\)-semigroup. We also suppose that the nonlinearity satisfies a regularity condition expressed in terms of the Hausdorff...

In this paper, we prove the existence of a common best proximity point for a pair of multivalued non-self mappings in partially ordered metric spaces. Also, we provide some interesting examples to illustrate our main results.

In this paper we present several coincidence type results for morphisms (fractions) in the sense of Gorniewicz and Granas.

In this paper, we study the existence of solutions for systems of random semilinear impulsive differential equations. The existence results are established by means of a new version of Perov’s, a nonlinear alternative of Leray-Schauder’s fixed point principles combined with a technique based on vector-valued metrics and convergent to zero matrices. Also, we give a random abstract...

A dislocated cone metric space over Banach algebra is introduced as a generalisation of a cone metric space over Banach algebra as well as a dislocated metric space. Fixed point theorems for Perov-type α-quasi contraction mapping, Kannan-type contraction as well as Chatterjee-type contraction mappings are proved in a dislocated cone metric space over Banach algebra. Proper...

In this paper, we obtain a unique common coupled fixed point theorem by using \((\psi , \alpha , \beta )\)-contraction in ordered partial metric spaces. We give an application to integral equations as well as homotopy theory. Also we furnish an example which supports our theorem.

In this paper, we obtain some generalizations of fixed point results for Kannan, Chatterjea and Hardy-Rogers contraction mappings in a new class of generalized metric spaces introduced recently by Jleli and Samet (Fixed Point Theory Appl. 2015:33, 2015).

In this article, a Krasnoselskii-type and a Halpern-type algorithm for approximating a common fixed point of a countable family of totally quasi-ϕ-asymptotically nonexpansive nonself multi-valued maps and a solution of a system of generalized mixed equilibrium problem are constructed. Strong convergence of the sequences generated by these algorithms is proved in uniformly smooth...

The purpose of this work is to introduce and study an iterative method to approximate solutions of a hierarchical fixed point problem and a variational inequality problem involving a finite family of nonexpansive mappings on a real Hilbert space. Further, we prove that the sequence generated by the proposed iterative method converges to a solution of the hierarchical fixed point...

We extend Nadler’s fixed point theorem to ν-generalized metric spaces. Through the proof of the above extension, we understand more deeply the mathematical structure of a ν-generalized metric space. In particular, we study the completeness of the space. We also improve Caristi’s and Subrahmanyam’s fixed point theorems in the space.

Herein, we search for some best proximity point results for a novel class of non-self-mappings \(T:A \longrightarrow B\) called generalized proximal α-β-quasi-contractive. We illustrate our work by an example. Our results generalize and extend many recent results appearing in the literature. Several consequences are derived. As applications, we explore the existence of best...