# Fixed Point Theory and Applications

## List of Papers (Total 1,827)

#### Rectangular cone b-metric spaces over Banach algebra and contraction principle

Rectangular cone b-metric spaces over a Banach algebra are introduced as a generalization of metric space and many of its generalizations. Some fixed point theorems are proved in this space and proper examples are provided to establish the validity and superiority of our results. An application to solution of linear equations is given which illustrates the proper application of the ...

#### Fixed points of set-valued maps in locally complete spaces

We prove an extension of the Pareto optimization criterion to locally complete locally convex vector spaces to guarantee the existence of fixed points of set-valued maps.

#### Best proximity points for proximal contractive type mappings with C-class functions in S-metric spaces

In this paper, we use the concept of C-class functions to establish the best proximity point results for a certain class of proximal contractive mappings in S-metric spaces. Our results extend and improve some known results in the literature. We give examples to analyze and support our main results.

#### Some applications via fixed point results in partially ordered $S_{b}$ -metric spaces

In this paper we give some applications to integral equations as well as homotopy theory via fixed point theorems in partially ordered complete $S_{b}$-metric spaces by using generalized contractive conditions. We also furnish an example which supports our main result.

#### Remarks on contractive type mappings

We present an analog of Banach’s fixed point theorem for $CJM$ contractions in preordered metric spaces. These results substantially extend theorems of Ran and Reurings’ (Proc. Am. Math. Soc. 132(5): 1435-1443, 2003) and Nieto and Rodríguez-López (Order 22: 223-239, 2005).

#### Fixed point theorems for F-expanding mappings

Recently, Wardowski (Fixed Point Theory Appl. 2012:94, 2012) introduced a new concept of F-contraction and proved a fixed point theorem which generalizes the Banach contraction principle. Following this direction of research, in this paper, we present some new fixed point results for F-expanding mappings, especially on a complete G-metric space.

#### F-cone metric spaces over Banach algebra

The paper deals with the achievement of introducing the notion of F-cone metric spaces over Banach algebra as a generalization of $N_{p}$-cone metric space over Banach algebra and $N_{b}$-cone metric space over Banach algebra and studying some of its topological properties. Also, here we define generalized Lipschitz and expansive maps for such spaces. Moreover, we investigate ...

#### Weak convergence theorems for split feasibility problems on zeros of the sum of monotone operators and fixed point sets in Hilbert spaces

In this paper, we consider a type of split feasibility problem by focusing on the solution sets of two important problems in the setting of Hilbert spaces that are the sum of monotone operators and fixed point problems. By assuming the existence of solutions, we provide a suitable algorithm for finding a solution point. Some important applications and numerical experiments of the ...

#### Fixed set of set valued mappings with set valued domain in terms of start set on a metric space with a graph

In this article, we define the new concept of a fixed set for a set valued map with set valued domain in the setting of metric space endowed with a directed graph. This notion of fixed set is analogous to the notion of a fixed point for a multivalued map and not for a classical single-valued map. We also introduce the new concept of the start set of a graph whose vertices are ...

#### Generalized α-nonexpansive mappings in Banach spaces

We consider a new type of monotone nonexpansive mappings in an ordered Banach space X with partial order ⪯. This new class of nonlinear mappings properly contains nonexpansive, firmly-nonexpansive and Suzuki-type generalized nonexpansive mappings and partially extends α-nonexpansive mappings. We obtain some existence theorems and weak and strong convergence theorems for the Mann ...

#### Pseudo-metric space and fixed point theorem

The aim of this paper is to give a generalized version of Caristi fixed point theorems in pseudo-metric spaces. Our results generalize and improve many of well-known theorems. As an application of our results, we give a new existence theorem to the generalized nonlinear complementarity problem and a solution of differential inclusion in the distributions setting.

#### Common coupled fixed point results for operators without mixed monotone type properties and application to nonlinear integral equations

We establish some new common coupled fixed point theorems for a pair of operators not assumed to satisfy mixed monotone type properties in the ordered Banach space setting. For that purpose, the notions of weakly inflationary and weakly deflationary operators are introduced in the two-dimensional setting, and existence and uniqueness common coupled fixed point theorems for such ...

#### Some extensions of the Meir-Keeler theorem

Meir and Keeler formulated their fixed point theorem for contractive mappings with purely metric condition. This idea was extended by numerous mathematicians. In this paper, we present a simple method of proving such theorems and give new results.

#### Strong and weak convergence theorems for split equality generalized mixed equilibrium problem

In this paper, we consider split equality generalized mixed equilibrium problem, which is more general than many problems such as split feasibility problem, split equality problem, split equilibrium problem, and so on. We propose a new modified algorithm to obtain strong and weak convergence theorems for split equality generalized mixed equilibrium problem for nonexpansive mappings ...

#### Viscosity approximations methods for $(\psi,\varphi)$ -weakly contractive mappings

In this paper, we study viscosity approximations with $(\psi,\varphi)$-weakly contractive mappings. We show that Moudafi’s viscosity approximations follow from Browder and Halpern type convergence theorems. Our results generalize a number of convergence theorems including a strong convergence theorem of Song and Liu (Fixed Point Theory Appl. 2009:824374, 2009).

#### Four mappings and generalized contractions

In the paper general theorems on common fixed point for four mappings are presented. The results are compact and they extend and unify the respective part of the fixed point theory.

#### Random fixed point theorems in partially ordered metric spaces

We present the random version in partially ordered metric spaces of the classical Banach contraction principle and some of its generalizations to ordered metric spaces. The results are used to prove the existence of solutions for random differential equations with boundary conditions.

#### Approximation of zeros of bounded maximal monotone mappings, solutions of Hammerstein integral equations and convex minimization problems

Let E be a real normed space with dual space $E^{*}$ and let $A:E\rightarrow2^{E^{*}}$ be any map. Let $J:E\rightarrow2^{E^{*}}$ be the normalized duality map on E. A new class of mappings, J-pseudocontractive maps, is introduced and the notion of J-fixed points is used to prove that $T:=(J-A)$ is J-pseudocontractive if and only if A is monotone. In the case that E is a ...

#### Functional type Caristi-Kirk theorem on two metric spaces and applications

In this paper, we give some generalizations of the functional type Caristi-Kirk theorem (see Functional Type Caristi-Kirk Theorems, 2005) for two mappings on metric spaces. We investigate the existence of some fixed points for two simultaneous projections to find the optimal solutions of the proximity two functions via Caristi-Kirk fixed point theorem.

#### Contributions to the fixed point theory of diagonal operators

In this paper, we introduce the notion of diagonal operator, we present the historical roots of diagonal operators and we give some fixed point theorems for this class of operators. Our approaches are based on the weakly Picard operator technique, difference equation techniques, and some fixed point theorems for multi-valued operators. Some applications to differential and integral ...

#### The split common fixed point problem for asymptotically nonexpansive semigroups in Banach spaces

In this paper, we propose an iteration method for finding a split common fixed point of asymptotically nonexpansive semigroups in the setting of two Banach spaces, and we obtain some weak and strong convergence theorems of the iteration scheme proposed. The results presented in the paper are new and improve and extend some recent corresponding results.

#### System of generalized mixed equilibrium problems, variational inequality, and fixed point problems

The purpose of this paper is to introduce a new iterative algorithm for finding a common element of the set of solutions of a system of generalized mixed equilibrium problems, the set of common fixed points of a finite family of pseudo contraction mappings, and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a real Hilbert space. We ...

#### On multiplicative metric spaces: survey

The purpose of this survey is to prove that the fixed point results for various multiplicative contractions are in fact equivalent to the corresponding fixed point results in (standard) metric spaces. For example, such are recent results established by He et al. (Fixed Point Theory Appl. 2014:48, 2014), Mongkolkeha and Sintunavarat (J. Nonlinear Sci. Appl. 8:1134-1140, 2015) and ...

#### Discussion of several contractions by Jachymski’s approach

We discuss several contractions of integral type by using Jachymski’s approach. We give alternative proofs of recent generalizations of the Banach contraction principle due to Ri (Indag. Math. 27:85-93, 2016) and Wardowski (Fixed Point Theory Appl. 2012:94, 2012).