Type Fixed Point Theorem Research Articles

Hyers–Ulam stability for coupled random fixed point theorems and applications to periodic boundary value random problems

Abstract In this paper, we prove some existence, uniqueness and Hyers–Ulam stability results for the coupled random fixed point of a pair of contractive type random operators on separable complete metric spaces. The approach is based on a new version of the Perov type fixed point theorem for contractions. Some applications to integral equations and to boundary value problems are also given.

The large contraction principle and existence of periodic solutions for infinite delay Volterra difference equations

In this article, we establish sufficient conditions for the existence of periodic solutions of a nonlinear infinite delay Volterra difference equation: $$\Delta x(n) = p(n) + b(n)h(x(n)) + \sum^{n}_{k = -\infty}B(n, k)g(x(k)).$$ We employ a Krasnosel'ski\u{i} type fixed point theorem, originally proved by Burton. The primary sufficient condition is not verifiable in terms of the parameters of the difference equation, and so we provide three applications in which the primary sufficient condition is verified.

Theory of Hybrid Fractional Differential Equations with Complex Order

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the existence of mild solutions of initial value problems for hybrid fractional differential equations. Finally, an application to solve one-variable linear fractional Schrodinger equation with complex order is given.

English

The concept of measures of noncompactness is applied to prove the existence of a solution for a boundary value problem for an infinite system of second order differential equations in $\ell _{p}$ space. We change the boundary value problem into an equivalent system of infinite integral equations and result is obtained by using Darbo's type fixed point theorem. The result is illustrated with help of an example.

Continuous selections and retractive representations for the fixed points sets of set valued Reich's contractions

We refine a continuous selection approach adopted earlier to fixed points of set valued Banach's contractions. An extension of selection and representation results to continuous set valued Reich's contractions is given. A new Krasnoselskii - Melvin type fixed point theorem is stated as a corollary.

A Mizoguchi–Takahashi Type Fixed Point Theorem in Complete Extended b-Metric Spaces

In this paper, we prove a new fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U, which generalizes Nadler’s fixed point theorem. We also establish some fixed point results, which generalize our first result. Furthermore, we establish Mizoguchi–Takahashi’s type fixed point theorem for a multi-valued mapping from a complete extended b-metric space U into the non empty closed and bounded subsets of U that improves many existing results in the literature.

Nadler and Kannan Type Set Valued Mappings in M-Metric Spaces and an Application

This article intends to initiate the study of Pompeiu–Hausdorff distance induced by an M-metric. The Nadler and Kannan type fixed point theorems for set-valued mappings are also established in the said spaces. Moreover, the discussion is supported with the aid of competent examples and a result on homotopy. This approach improves the current state of art in fixed point theory.

Caristi, Nadler and H + -Type Contractive Mappings and Their Fixed Points in θ-Metric Spaces

A new proper generalization of metric called as θ -metric is introduced by Khojasteh et al. (Mathematical Problems in Engineering (2013) Article ID 504609). In this paper, first we prove the Caristi type fixed point theorem in an alternative and comparatively new way in the context of θ -metric. We also investigate two θ -metrics on CB ( X ) (family of nonempty closed and bounded subsets of a set X). Furthermore, using the obtained θ -metrics on CB ( X ) , we prove two new fixed point results for multi-functions which generalize the results of Nadler and Lim type in the context of such spaces. In order to illustrate the usability of our results, we equipped them with competent examples.

Existence of weak solutions for an infinite system of second order differential equations

‎ ‎In this paper‎, ‎we investigate the existence of weak solutions for a boundary value problem of an infinite system of second order differential equations‎. ‎As the main tool‎, ‎a new Krasnosel'skii type fixed point theorem in Frechet spaces is established in conjunction with the technique of measures of weak noncompactness‎.

Maia type fixed point theorems for Prešić type operators

Maia type fixed point theorems for Prešić type operators

Ekeland’s variational principle and fixed point theorems in partial b-metric spaces

In this paper, a new version of Ekeland’s variational principle is presented in partial b-metric spaces via Cantor’s intersection theorem. As a consequence, some Caristi type fixed point theorems are proved in partial b-metric spaces. Furthermore, the construction and number of fixed points are discussed.

Existence, Uniqueness and Stability of Nonlinear Implicit Fractional Dynamical Equation with Impulsive condition on Time Scales

Abstract The main motive of this research article is to establish the existence, uniqueness and stability results for the non-linear fractional differential equation with impulsive condition on time scales. Banach, Leray-Schauder’s alternative type fixed point theorems are used to examine these results. Further, we give the existence and uniqueness of solution for the corresponding non-local problem. Moreover, to outline the utilization of these outcomes some examples are given.

Unique common fixed points for four non-continuous mappings satisfying Ψ-implicit contractive condition on non-complete multiplicative metric spaces

In this paper, we introduce a class Ψ of 5-dimensional real functions and consider a ψ-implicit contractive condition, and then discuss and obtain a unique common fixed point theorem for four non-continuous mappings defined on non-complete multiplicative metric spaces. Finally, we give several Ciric type fixed point theorems on non-complete multiplicative metric spaces.

Complex valued dislocated metric spaces

In this paper, we introduce complex valued dislocated metric spaces. We prove Banach contraction principle, Kannan and Chatterjea type fixed point theorems in this new space. Moreover, we give some applications of the results to differential equations and iterated functions.

Common Fixed Points of Intuitionistic Fuzzy Maps for Meir-Keeler Type Contractions

The main purpose of this paper is to establish and prove some new common fixed point theorems for intuitionistic fuzzy maps in the context of (α,β)-cut sets of intuitionistic fuzzy sets on a complete metric space in association with the Hausdorff metric. Furthermore, the technique of Meir-Keeler (shortly, M-K) contraction is applied to obtain common fixed point of intuitionistic fuzzy compatible maps and fixed points of Kannan type intuitionistic fuzzy set-valued contractive mappings. Our results generalize M-K type fixed point theorem along with its various generalizations. Some nontrivial examples have been furnished in the support of the main results.

On generalization of Darbo–Sadovskii type fixed point theorems for iterated mappings in Fréchet spaces

In this paper, we give new Darbo–Sadovskii type fixed point theorems for iterated mappings in Frechet spaces. Moreover, we solve two open questions proposed in Ariza-Ruiz and Garcia-Falset (Fixed Point Theory, 2018).

Meir–Keeler theorems in fuzzy metric spaces

In this paper, we propose the concept of fuzzy Meir–Keeler contractive mappings in fuzzy metric spaces, which covers fuzzy ψ-contractive mappings and fuzzy H-contractive mappings as special cases. With the aid of the proposed concept, we obtain some Meir–Keeler type fixed point theorems. The derived theorems improve and extend the corresponding ones developed by D. Mihet, D. Wardowski and V. Gregori, et al. And an example in the end of the paper illustrates the validity of our results.

Fixed Point Theorems Under Caristi’s Type Map on C∗ -Algebra Valued Fuzzy Soft Metric Space

In this paper, we present the extension of Caristi’s fixed point theorems for mappings defined on C∗-algebra-valued Fuzzy soft metric spaces. We establish the existence of simple proof of caristi’s type fixed point theorems in C∗-algebra-valued Fuzzy soft metric spaces and we give some examples which supports our main results.

Maia type fixed point theorems for Ćirić-Prešić operators

Abstract The main aim of this paper is to obtain Maia type fixed point results for Ćirić-Prešić contraction condition, following Ćirić L. B. and Prešić S. B. result proved in [Ćirić L. B.; Prešić S. B. On Prešić type generalization of the Banach contraction mapping principle, Acta Math. Univ. Comenian. (N.S.), 2007, v 76, no. 2, 143–147] and Luong N. V. and Thuan N. X. result in [Luong, N. V., Thuan, N. X., Some fixed point theorems of Prešić-Ćirić type, Acta Univ. Apulensis Math. Inform., No. 30, (2012), 237–249]. We unified these theorems with Maia’s fixed point theorem proved in [Maia, Maria Grazia. Un’osservazione sulle contrazioni metriche. (Italian) Rend. Sem. Mat. Univ. Padova 40 1968 139–143] and the obtained results are proved is the present paper. An example is also provided.

Nonsmooth variational inequalities on Hadamard manifolds

ABSTRACTNonsmooth variational inequality problem (NVIP) and Minty nonsmooth variational inequality problem (MNVIP) in terms of a bifunction are considered in the setting of Hadamard manifolds. We first establish a Browder type fixed point theorem in the setting of Hadamard spaces, and then by using it we prove some existence results for solutions of NVIP and MNVIP. We give some relations among NVIP, MNVIP and nonsmooth optimization problem. The gap functions for NVIP and MNVIP are also studied in the setting of Hadamard manifolds.