# Fixed Point Theory and Applications

## List of Papers (Total 1,854)

#### Some convergence results using K iteration process in $\mathit{CAT}(0)$ spaces

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...

#### Inertial algorithm for approximating a common fixed point for a countable family of relatively nonexpansive maps

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...

#### On solving the split generalized equilibrium problem and the fixed point problem for a countable family of nonexpansive multivalued mappings

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...

#### Fixed points of fuzzy neutrosophic soft mapping with decision-making

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...

#### Hybrid projected subgradient-proximal algorithms for solving split equilibrium problems and split common fixed point problems of nonexpansive mappings in Hilbert spaces

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...

#### Fixed point theorems for generalized weakly contractive mappings in metric spaces with applications

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...

#### A generalization of Hegedüs-Szilágyi’s fixed point theorem in complete metric spaces

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.

#### Fixed point results for fuzzy mappings in a b-metric space

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.

#### Characterizations of contractive conditions by using convergent sequences

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.

#### Probabilistic b-metric spaces and nonlinear contractions

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.

#### On approximate solutions for a class of semilinear fractional-order differential equations in Banach 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...

#### Common best proximity point theorem for multivalued mappings in partially ordered metric spaces

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.

#### Coincidence theory for compact morphisms

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

#### Random semilinear system of differential equations with impulses

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...

#### Some generalizations for $(\alpha - \psi,\phi )$ -contractions in b-metric-like spaces and an application

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.

#### Dislocated cone metric space over Banach algebra and α-quasi contraction mappings of Perov type

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...

#### Applications and common coupled fixed point results in ordered partial metric spaces

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.

#### On some fixed point theorems in generalized metric spaces

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).

#### Relaxed iterative algorithms for a system of generalized mixed equilibrium problems and a countable family of totally quasi-Phi-asymptotically nonexpansive multi-valued maps, with applications

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...

#### Hybrid steepest iterative algorithm for a hierarchical fixed point problem

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...

#### Nadler’s fixed point theorem in ν-generalized metric spaces

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.

#### Best proximity point theorems for generalized α-β-proximal quasi-contractive mappings

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...

#### A note on Ćirić type nonunique fixed point theorems

In this paper, we suggest some nonunique fixed results in the setting of various abstract spaces. The proposed results extend, generalize and unify many existing results in the corresponding literature.

#### Some fixed point results for fuzzy homotopic mappings

The first purpose of this paper is to define a homotopy for fuzzy spaces. We continue our work by showing that the property of having a fixed point is invariant by this homotopy. These theorems generalize and improve well-known results.