Search

We investigate a nonlinear integral equation derived through moment approximation from the individual-based representation of spatial logistic dynamics. The equation describes how the densities of pairs of individuals represented by points in continuous space are expected to equilibrate under spatially explicit birth–death processes characterized by constant fecundity with local natal dispersal and variable mortality determined by local competition. The equation is derived from a moment hierarchy truncated by a moment closure expressing the densities of triplets as a function of the densities of pairs. Focusing on results for individuals inhabiting two-dimensional habitats, we explore the solvability of the equation by introducing a dedicated space of functions that are integrable up to a constant. Using this function space, we establish sufficient conditions for the existence of solutions of the equation within a zero-centered ball. For illustration and further insights, we complement our analytical findings with numerical results.

In this manuscript, we prove the existence and uniqueness of a common best proximity point for a pair of non-self mappings satisfying the iterative mappings in a complete fuzzy multiplicative metric space. We consider the pair of non-self mappings $ X:\mathcal{P}\rightarrow \mathcal{G} $ and $ Z:\mathcal{P }\rightarrow \mathcal{G} $ and the mappings do not necessarily have a common fixed-point. In a complete fuzzy multiplicative metric space, if $ \mathcal{\varphi } $ satisfy the condition $ \mathcal{\varphi } \left(b, Zb, \varsigma \right) = \mathcal{\varphi }\left(\mathcal{P}, \mathcal{ G}, \varsigma \right) = \mathcal{\varphi }\left(b, Xb, \varsigma \right) $, then $ b $ is a common best proximity point. Further, we obtain the common best proximity point for the real valued functions $ \mathcal{L}, \mathcal{M}:(0, 1]\rightarrow \mathbb{R} $ by using a generalized fuzzy multiplicative metric space in the setting of $ (\mathcal{L}, \mathcal{M}) $-iterative mappings. Furthermore, we utilize fuzzy multiplicative versions of the $ (\mathcal{L}, \mathcal{M}) $-proximal contraction, $ (\mathcal{L}, \mathcal{M}) $-interpolative Reich-Rus-Ciric type proximal contractions, $ (\mathcal{L}, \mathcal{M}) $-Kannan type proximal contraction and $ (\mathcal{L}, \mathcal{M}) $-interpolative Hardy-Rogers type proximal contraction to examine the common best proximity points in fuzzy multiplicative metric space. Moreover, we provide differential non-trivial examples to support our results.

The aim of this article is to introduce a new type of operator similar to those of A. Petruşel and G. Petruşel type (Fixed point results for decreasing convex orbital operators, J. Fixed Point Theory Appl. 23 (2021), no. 35) and prove some fixed-point theorems which generalize and complement several results in the theory of nonlinear operators.

In this article, we consider the following two-point discrete fractional boundary value problem with constant coefficient associated with Dirichlet boundary conditions. \begin{equation*} \begin{cases} -\big{(}\nabla^{\nu}_{\rho(a)}u\big{)}(t) + \lambda u(t) = f(t, u(t)), \quad t \in \mathbb{N}^{b}_{a + 2}, \\ u(a) = u(b) = 0, \end{cases} \end{equation*} \noindent where $1 < \nu < 2$, $a,b \in \mathbb{R}$ with $b-a\in\mathbb{N}_{3}$, $\mathbb{N}^b_{a+2} = \{a+2,a+3,\hdots,b\}$, $|\lambda| < 1$, $\nabla^{\nu}_{\rho(a)}u$ denotes the $\nu^{\text{th}}$-order Riemann--Liouville nabla difference of $u$ based at $\rho(a)=a-1$, and $f : \mathbb{N}^{b}_{a + 2} \times \mathbb{R} \rightarrow \mathbb{R}^{+}$. \noindent We make use of Guo--Krasnosels'ki\v{\i} and Leggett--Williams fixed-point theorems on suitable cones and under appropriate conditions on the non-linear part of the difference equation. We establish sufficient requirements for at least one, at least two, and at least three positive solutions of the considered boundary value problem. We also provide an example to demonstrate the applicability of established results.

The aim of this article is to study the results of the fixed-point in coupled and tripled measure of noncompactness (MNC). We will use the technique of MNC for coupled and tripled MNC. Also, we tend to prove some results of coupled and tripled MNC for the family of JS-contractive-type mappings. Moreover, an application with an example is provided to illustrate the results.

Recently, Karapinar, Aydi and De Hierro introduced the notions of interpolative Kannan-type contractions and interpolative CRR-type contractions and proved that they possess a fixed point when the space is complete. In this paper, we show that the existence of fixed points for interpolative Kannan-type and CRR-type contractions remains true for a metric space which is not necessarily complete and we give a more precise result concerning the behaviour of Picard sequences of arbitrary initial point. We also study some particular classes of interpolative Kannan-type and CRR-type contractions.

Abstract This research is conducted for studying some qualitative specifications of solution to a generalized fractional structure of the standard snap boundary problem. We first rewrite the mathematical model of the extended fractional snap problem by means of the G $\mathbb{G}$ -operators. After finding its equivalent solution as a form of the integral equation, we establish the existence criterion of this reformulated model with respect to some known fixed point techniques. Then we analyze its stability and further investigate the inclusion version of the problem with the help of some special contractions. We present numerical simulations for solutions of several examples regarding the fractional G $\mathbb{G}$ -snap system in different structures including the Caputo, Caputo–Hadamard, and Katugampola operators of different orders.

In this paper, we establish the existence and uniqueness of solution for a nonlinear coupled system of implicit fractional differential equations including ψ-Caputo fractional operator under nonlocal conditions. Schaefer's and Banach fixed-point theorems are applied to obtain the solvability results for the proposed system. Furthermore, we extend the results to investigate several types of Ulam stability for the proposed system by using classical tool of nonlinear analysis. Finally, an example is provided to illustrate the abstract results.

In this paper, we aim to review Meir–Keeler contraction mappings results on various abstract spaces, in particular, on partial metric spaces, dislocated (metric-like) spaces, and M-metric spaces. We collect all significant results in this direction by involving interesting examples. One of the main reasons for this work is to help young researchers by giving a framework for Meir Keeler’s contraction.

The intent of this manuscript is to present new rational symmetric ϖ−ξ-contractions and infer some fixed-points for such contractions in the setting of Θ-metric spaces. Furthermore, some related results such as Suzuki-type rational symmetric contractions, orbitally Υ-complete, and orbitally continuous mappings in Θ-metric spaces are introduced. Ultimately, the theoretical results are shared to study the existence of the solution to a fractional-order differential equation with one boundary stipulation.

In this paper we prove the existence and uniqueness of coincident (fixed) points for nonlinear mappings of any number of arguments under a (ψ, θ, φ)-weak contraction condition without O-compatibility. The obtained results extend, improve and generalize some well-known results in the literature to be discussed below. Moreover, we present an example to show the efficiency of our results.

In recent years, complex-valued fuzzy metric spaces (in short CVFMS) were introduced by Shukla et al. (Fixed Point Theory 32 (2018)). This setting is a valuable extension of fuzzy metric spaces with the complex grade of membership function. They also established fixed-point results under contractive condition in the aforementioned spaces and generalized some essential existence results in fixed-point theory. The purpose of this manuscript is to derive some fixed-point results for multivalued mappings enjoying the least upper bound property in CVFMS. Furthermore, we studied the existence theorem for a unique solution to the Fuzzy fractional Volterra–Fredholm integro-differential equations (FCFVFIDEs) as an application to our derived result involving the Caputo derivative.

The main result of this paper is a fixed-point theorem for multivalued contractions obtained through an inequality with rational terms. The contraction is an F-type contraction. The results are obtained in a metric space endowed with a graph. The main theorem is supported by illustrative examples. Several results as special cases are obtained by specific choices of the control functions involved in the inequality. The study is broadly in the domain of setvalued analysis. The methodology of the paper is a blending of both graph theoretic and analytic methods.

The purpose of this paper is to introduce a new type of contraction called fuzzy F-contraction. As compared to the F-contraction in the existing literature, our fuzzy F-contraction is much simpler and more straightforward, since it contains only one condition—that is, the function F is strictly increasing. Moreover, some fixed-point theorems for fuzzy F-contraction are presented. Further, some examples are given to illustrate its validity and superiority. In addition, by applying a very significant lemma, we show that our proofs of most fixed-point theorems are shorter and more elegant than ones in the literature.

In this article, the authors give sufficient conditions for existence and attractivity of mild solutions for second order semi-linear functional evolution equation in Banach spaces using Schauder's fixed point theorem. An example is provided to illustrate the result.

Recently, Mlaiki et al. introduced the notion of a controlled metric type space which is a generalization of the b-metric space. In this work, we define the controlled partial metric type space and give some fixed-point theorems for extensions of Kannan contraction in this space with suitable conditions. Moreover, as an application, we derive a fixed-point theorem for graphic contraction on the considered metric space endowed with a graph.

In this work, we concern ourselves with the problem of solving a general system of variational inequalities whose solutions also solve a common fixed-point problem of a family of countably many nonlinear operators via a hybrid viscosity implicit iteration method in 2 uniformly smooth and uniformly convex Banach spaces. An application to common fixed-point problems of asymptotically nonexpansive and pseudocontractive mappings and variational inequality problems for strict pseudocontractive mappings is also given in Banach spaces.

We consider a dynamic frictionless contact problem for thermo-elastic-viscoplastic materials with damage and adhesion. The contact is modeled with normal compliance condition. We derive a weak formulation of the system, then we prove existence and uniqueness of the solution. The proof is based on arguments of monotonicity and fixed point.

In this article, we give some results concerning the continuity of the nonlinear Volterra and Fredholm integral operators on the space $L^{1}[0,infty)$. Then by using the concept of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes of nonlinear integral equations. Our results extend some previous works.

In this paper sufficient conditions are given ensuring the controllability of mild solutions defined on a bounded interval for two classes of first order semilinear functional and neutral functional differential equations involving evolution operators when the delay is infinite using the nonlinear alternative of Leray-Schauder type.

In this paper, we establish the existence of positive solution for the semipositone second-order three-point boundary value problem $u''(t)+lambda f(t,u(t))=0$, $0