# Fixed Point Theory and Applications

## List of Papers (Total 1,871)

#### A strong convergence theorem for generalized-Φ-strongly monotone maps, with applications

Let X be a uniformly convex and uniformly smooth real Banach space with dual space $$X^{*}$$. In this paper, a Mann-type iterative algorithm that approximates the zero of a generalized-Φ-strongly monotone map is constructed. A strong convergence theorem for a sequence generated by the algorithm is proved. Furthermore, the theorem is applied to approximate the solution of a convex...

#### An inertial S-iteration process

In this paper, we establish a new iteration method, called an InerSP (an inertial S-iteration process), by combining a modified S-iteration process with the inertial extrapolation. This strategy is for speeding up the convergence of the algorithm. We then prove the convergence theorems of a sequence generated by our new method for finding a common fixed point of nonexpansive...

#### Observations on relation-theoretic coincidence theorems under Boyd–Wong type nonlinear contractions

In this article, we carry out some observations on existing metrical coincidence theorems of Karapinar et al. (Fixed Point Theory Appl. 2014:92, 2014) and Erhan et al. (J. Inequal. Appl. 2015:52, 2015) proved for Lakshmikantham–Ćirić-type nonlinear contractions involving $$(f,g)$$-closed transitive sets after proving some coincidence theorems satisfying Boyd–Wong-type nonlinear...

#### The Maslov index and the spectral flow—revisited

We give an elementary proof of a celebrated theorem of Cappell, Lee and Miller which relates the Maslov index of a pair of paths of Lagrangian subspaces to the spectral flow of an associated path of self-adjoint first-order operators.We particularly pay attention to the continuity of the latter path of operators, where we consider the gap-metric on the set of all closed operators...

#### Iterative approximation of attractive points of further generalized hybrid mappings in Hadamard spaces

In this paper, we study the class of further generalized hybrid mappings due to Khan (Fixed Point Theory Appl. 2018:8, 2018) in the setting of Hadamard spaces. We prove a demiclosed principle for such mappings in Hadamard spaces. Furthermore, we also prove the Δ-convergence of the sequence generated by the S-iteration process for finding attractive points of further generalized...

We study a semilinear fractional order differential inclusion in a separable Banach space E of the form $${}^{C}D^{q}x(t)\in Ax(t)+ F\bigl(t,x(t)\bigr),\quad t\in [0,T],$$ where $${}^{C}D^{q}$$ is the Caputo fractional derivative of order $$0 < q < 1$$, $$A \colon D(A) \subset E \rightarrow E$$ is a generator of a $$C_{0}$$-semigroup, and $$F \colon [0,T] \times E \multimap E... #### Bernstein-type theorem for ϕ-Laplacian In this paper we obtain a solution to the second-order boundary value problem of the form \(\frac{d}{dt}\varPhi'(\dot{u})=f(t,u,\dot{u})$$, $$t\in [0,1]$$, $$u\colon \mathbb {R}\to \mathbb {R}$$ with Sturm–Liouville boundary conditions, where $$\varPhi\colon \mathbb {R}\to \mathbb {R}$$ is a strictly convex, differentiable function and $$f\colon[0,1]\times \mathbb {R}\times... #### On modeling and complete solutions to general fixpoint problems in multi-scale systems with applications This paper revisits the well-studied fixed point problem from a unified viewpoint of mathematical modeling and canonical duality theory, i.e., the general fixed point problem is first reformulated as a nonconvex optimization problem, its well-posedness is discussed based on the objectivity principle in continuum physics; then the canonical duality theory is applied for solving... #### \(F(\psi,\varphi)$$ -Contractions for α-admissible mappings on M-metric spaces

In this paper, we introduce certain α-admissible mappings which are $$F(\psi,\varphi)$$-contractions on M-metric spaces, and we establish some fixed point results. Our results generalize and extend some well-known results on this topic in the literature.

#### Caristi type cyclic contraction and common fixed point theorems in bipolar metric spaces with applications

In this paper, we obtain the existence and uniqueness of the solution for three self mappings in a complete bipolar metric space under a new Caristi type contraction with an example. We also provide applications to homotopy theory and nonlinear integral equations.

#### Boundary value problems for singular second order equations

We investigate strongly nonlinear differential equations of the type $$\bigl(\Phi \bigl(k(t) u'(t) \bigr) \bigr)'= f \bigl(t,u(t),u'(t) \bigr), \quad\text{a.e. on } [0,T],$$ where Φ is a strictly increasing homeomorphism and the nonnegative function k may vanish on a set of measure zero. By using the upper and lower solutions method, we prove existence results for the Dirichlet...

#### Common fixed point theorems for a finite family of multivalued mappings in an ordered Banach space

In this paper, we prove some common fixed point theorems for a finite family of multivalued and single-valued mappings operating on ordered Banach spaces. Our results extend and generalize many results in the literature on fixed point theory and lead to existence theorems for a system of integral inclusions.

#### Convergence theorems of subgradient extragradient algorithm for solving variational inequalities and a convex feasibility problem

Let C be a nonempty closed and convex subset of a uniformly smooth and 2-uniformly convex real Banach space E with dual space $$E^{*}$$. In this paper, a Krasnoselskii-type subgradient extragradient iterative algorithm is constructed and used to approximate a common element of solutions of variational inequality problems and fixed points of a countable family of relatively...

#### Halpern–Ishikawa type iterative method for approximating fixed points of non-self pseudocontractive mappings

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...

#### Fixed point theorems for a class of generalized weak cyclic compatible contractions

In this manuscript, we establish a coincidence point and a unique common fixed point theorem for $$(\psi ,\varphi )$$-weak cyclic compatible contractions. We also present a fixed point theorem for a class of Λ-weak cyclic compatible contractions via altering distance functions. Our results extend and improve some well-known results in the literature. We provide examples to...

#### Infinitely split Nash equilibrium problems in repeated games

In this paper, we introduce the concept of infinitely split Nash equilibrium in repeated games in which the profile sets are chain-complete posets. Then by using a fixed point theorem on posets in (J. Math. Anal. Appl. 409:1084–1092, 2014), we prove an existence theorem. As an application, we study the repeated extended Bertrant duopoly model of price competition.

#### 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...

#### Iterative approximation of common attractive points of further generalized hybrid mappings

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...

#### 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.