# Fixed Point Theory and Applications

## List of Papers (Total 1,838)

#### 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.

#### 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 examples ...

#### 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.

#### 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.