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In 2020, Olia et al. [Olia, Z. E. D. D., Gordji, M. E. and Bagha, D. E. (2020). Banach fixed point theorem on orthogonal cone metric spaces. FACTA Universitatis (NIS) Ser. Math. Inform, 35, 1239-1250] examined orthogonal cone metric spaces. They assumed that P is a normal cone with normal constant K and that self mapping T is orthogonal continuous on the orthogonal cone metric space X in their study. This study now presentes certain required definitions on orthogonal cone metric spaces that were not previously given in [9]. The examples that show the link between existing and new definitions have also been included. The results are also generalized by eliminating the normalcy condition and utilizing point orthogonal continuity instead of general orthogonal continuity in the major results of [9]. The fundamental finding of the study is then generalized by removing the requirement of orthogonal continuity and introducing normality. In addition, certain outcomes of stated theorems are proven, and some examples are provided to demonstrate these theorems. [ABSTRACT FROM AUTHOR]

The goal of this paper is to develop new fixed points for quasi upper semicontinuous set-valued mappings and compact continuous (single-valued) mappings, and related applications for useful tools in nonlinear analysis by applying the best approximation approach for classes of semiclosed 1-set contractive set-valued mappings in locally p-convex and p-vector spaces for p ∈ (0 , 1 ] . In particular, we first develop general fixed point theorems for quasi upper semicontinuous set-valued and single-valued condensing mappings, which provide answers to the Schauder conjecture in the affirmative way under the setting of locally p-convex spaces and topological vector spaces for p ∈ (0 , 1 ] ; then the best approximation results for quasi upper semicontinuous and 1-set contractive set-valued mappings are established, which are used as tools to establish some new fixed points for nonself quasi upper semicontinuous set-valued mappings with either inward or outward set conditions under various boundary situations. The results established in this paper unify or improve corresponding results in the existing literature for nonlinear analysis, and they would be regarded as the continuation of the related work by Yuan (Fixed Point Theory Algorithms Sci. Eng. 2022:20, 2022)–(Fixed Point Theory Algorithms Sci. Eng. 2022:26, 2022) recently. [ABSTRACT FROM AUTHOR]

This paper proposes new existence and uniqueness results for an initial value problem (IVP) of fractional differential equations of nonlinear variable order. Riemann–Liouville-type fractional derivatives are considered in the problem. The new fundamental results achieved in this work are obtained by using the inequalities technique and the fixed point theory. In addition, uniform stability criteria for the solutions are derived. The accomplished results are new and complement the scientific research in the field. A numerical example is composed to show the efficacy and potency of the proposed criteria. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and stability of solutions for impulsive pantograph fractional integro-differential equation via ψ-Hilfer fractional derivative in a appropriate Banach space. Our approach is based on fixed point theorems of Darbo’s and Mönch via Kuratowski measure of non-compactness. An example is given to illustrate our approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose a system of equations containing two kernels. In our transformation of the system, we use the integrable dichotomy condition, where we extract the term of the integration matrix from one of the kernels. We then use the fixed-point theory to prove that the system has periodic solutions that are unique under sufficient conditions. An illustrative example at the end of the article is given. [ABSTRACT FROM AUTHOR]

In this paper, the problem of the existence and uniqueness of solutions for a nonlinear fractional-order coupled delayed system with a new kind of boundary condition is studied. For this reason, we transform the above problem into an equivalent fixed point problem using the integral operator. Moreover, by applying fixed point theorems, a novel set of sufficient conditions that guarantee the existence and uniqueness of solutions of the coupled system is derived. Eventually, an example is presented to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we establish two fixed point theorems of Himmelberg's type for multivalued maps. Using abstract measures of weak noncompactness, these results are applied to derive some fixed point theorems of Sadovskii's type. [ABSTRACT FROM AUTHOR]

The purpose if this paper is to present a fixed point result constructed by finite sequences. Using iterated function systems and related fractal operators, a mixed patterns generated by the a finite sequence patterns construct the sets of patterns built by black and white squares. A complete metric space related to a mixed pattern sequence is defined using the distance based on difference of the black squares' area. The main result of the paper highlights that these fractal operators has unique fixed points for the sets generated by the mixed patterns. Moreover, the main theorem is also applied for Vicsek fractals such that results also hold for mixed Vicsek patterns. Motivated by various studies on growing graph sequences and related large structures, this paper underlines a new connection between fixed point theory and network science. Using circle patterns, the paper also interprets the main result on sets mixed patterns based on touching circles. Thus, the paper focuses a fixed point theorem on the sets mixed patterns built by iterated function systems and the distances calculated between the areas of these geometric shapes. [ABSTRACT FROM AUTHOR]

The foremost goal of this paper is to study the sufficient conditions for controllability of Hilfer fractional Langevin dynamical system with impulse. The main results are obtained by using the generalized fractional calculus and fixed point theory. Finally, a pair of examples are equipped to demonstrate the importance of the obtained theoretical result. The homotopy perturbation method (HPM) is successfully used in the numerical example. [ABSTRACT FROM AUTHOR]

The scaling exponent of a hierarchy of cities used to be regarded as a fractional. This paper investigates a newly constructed system of equation for Hepatitis B disease in sense of Atanganaa–Baleanu Caputo (ABC) fractional order derivative. The proposed approach has five distinctive quantities, namely, susceptible, acute infections, chronic infection, immunized and vaccinated populace. By applying some well-known results of fixed point theory, we find the Ulam–Hyers type stability and qualitative analysis of the candidate solution. The deterministic stability for the proposed system is also computed. We apply well-known transform due to Laplace and decomposition techniques (LADM) and Adomian polynomial for nonlinear terms for computing the series solution for the proposed model. Graphical results show that LADM is an efficient and robust method for solving nonlinear problems. [ABSTRACT FROM AUTHOR]

In this paper we examine two basic topological properties of partial metric spaces, namely compactness and completeness. Our main result claims that in these spaces compactness is equivalent to sequential compactness. We also show that Hausdorff compact partial metric spaces are metrizable. In the second part of this article we discuss the significance of bottom sets of partial metric spaces in fixed point theorems for mappings acting in these spaces. [ABSTRACT FROM AUTHOR]

In this paper, we present a framework for investigating the mild solution of stochastic integrodifferential equations with nonlocal initial conditions in Hilbert spaces. In order to obtain the existence results, we have made use of the ideas of fixed point theorems, stochastic analysis, and the resolvent operator in the sense of Grimmer. Finally, an example is provided to demonstrate the findings that were produced. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the existence of positive solutions for the semipositone fractional boundary value problem with n point fractional integral boundary conditions. The existence of positive solutions is established using the five functionals fixed point theorem. An example is given to ratify that our main result is theoretically feasible. [ABSTRACT FROM AUTHOR]

This paper presents a survey for some recent research on the controllability of nonlinear fractional evolution systems (FESs) in Banach spaces. The prime focus is exact controllability and approximate controllability of several types of FESs, which include the basic systems with classical initial and nonlocal conditions, FESs with time delay or impulsive effect. In addition, controllability results via resolvent operator are reviewed in detail. At last, the conclusions of this work and the research prospect are presented, which provides a reference for further study. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of weak partial-quasi k-metrics, which generalizes both k-metric and weak metric. Also, we present some examples to support our results. Furthermore, we obtain some fixed point theorems in weak partial-quasi k-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider existence criteria of three positive solutions of three-point boundary value problems for p-Laplacian dynamic equations on time scales. To show our main results, we apply the well-known Leggett-Williams fixed point theorem. Moreover, we present some results for the existence of single and multiple positive solutions for boundary value problems on time scales, by applying fixed point theorems in cones. The conditions we used in the paper are different from those in [Dogan A. On the existence of positive solutions for the one-dimensional p-Laplacian boundary value problems on time scales. Dynam Syst Appl 2015; 24: 295-304]. [ABSTRACT FROM AUTHOR]

Let T be a time scale not bounded below and above such that to e T. In this paper, we provide new sufficient conditions and use the Banach fixed point theorem to establish the stability results about the zero solution for the following Levin-Nohel intego-dynamic equation with variable delay ... where xΔ is Δ-derivative on T. An asymptotic stability theorem with a necessary and sufficient condition is proved. In addition, the case of the equation with several delays is studied. The results obtained here extend the work of Bessioud, Ardjouni, Djoudi [10] [ABSTRACT FROM AUTHOR]

This paper aims to study the sufficient conditions for the existence and uniqueness of solutions to the multipoint coupled boundary value problem of nonlinear Caputo–Hadamard fractional differential equations associating with nonlocal integral boundary conditions. The required conditions are obtained by using classical results of functional analysis and fixed point theory. Furthermore, the Hyers–Ulam stability of solutions is discussed, and sufficient conditions for the stability are developed. Obtained results are supported by examples and illustrated in the last section. [ABSTRACT FROM AUTHOR]

In this paper, we use Suzuki-type contraction to prove three fixed point theorems for generalized contractions in an ordered space equipped with two metrics; we obtain some generalizations of the Kannan fixed point theorem. Our results on partially ordered metric spaces generalize and extend some results of Ran and Reurings as well as of Nieto and Rodríguez-López. To illustrate the effectiveness of our main result, we give an application to matrix equations which involves monotone mappings. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of solutions to new inclusion prob- lems involving both Caputo and Hadamard fractional derivatives, and separated boundary conditions. We apply the modern tools of the fixed point theory to study the cases when the multi-valued map (the right hand-side of the inclusions) takes convex as well as non-convex values. Examples illustrating the abstract results are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam stability for the following cubic functional equation with involution f(2x + y) + f(2x + σ(y)) - 2f(x + y) - 2f(x + σ(y)) - 12f(x) = 0 in modular spaces by using a fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept of W-nonexpansive mappings and obtain fixed point theorems for nonexpansive mappings for non-convex set. Our results resolve fixed pointed problem that nonexpansive mappings be not on closed convex set, and it extends fixed point theorems for nonexpansive mappings. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove fixed point theorem for an extended Kannan and Chatterjea type T-contraction mapping in a cone metric space. Our results generalize recent results existing in the literature of T-contraction mappings in cone metric space. [ABSTRACT FROM AUTHOR]

This paper aims to study the existence of the solutions for an Impulsive Sequential Fractional Differential Equations of order 1 < q ≤ 2 involving separate boundary conditions. Our analysis relies on some fixed point theorems. In addition, an example is provided to illustrate the results of this study. [ABSTRACT FROM AUTHOR]

It is a well-known fact that the topology induced by a fuzzy metric is metrizable. Nevertheless, the problem of how to obtain a classical metric from a fuzzy one in such a way that both induce the same topology is not solved completely. A new method to construct a classical metric from a fuzzy metric, whenever it is defined by means of an Archimedean t -norm, has recently been introduced in the literature. Motivated by this fact, we focus our efforts on such a method in this paper. We prove that the topology induced by a given fuzzy metric M and the topology induced by the metric constructed from M by means of such a method coincide. Besides, we prove that the completeness of the fuzzy metric space is equivalent to the completeness of the associated classical metric obtained by the aforementioned method. Moreover, such results are applied to obtain fuzzy versions of two well-known classical fixed point theorems in metric spaces, one due to Matkowski and the other one proved by Meir and Keeler. Although such theorems have already been adapted to the fuzzy context in the literature, we show an inconvenience on their applicability which motivates the introduction of these two new fuzzy versions. [ABSTRACT FROM AUTHOR]

In this paper, we firstly introduce a model of four-point boundary value problem for generalized singular Lane–Emden systems on whole line. By establishing Green’s function G ( t , s ) for problem − ( ρ ( t ) x ′ ( t ) ) ′ = 0 , lim t → − ∞ x ( t ) − k x ( ξ ) = 0 , lim t → + ∞ x ( t ) − l x ( η ) = 0 , we prove that G ( t , s ) ≥ 0 under some assumptions which actually generalize a corresponding result in Liu (2004). We then obtain sufficient conditions to guarantee existence of positive solutions of this kind of models. Finally, three examples are given at the end of the paper to illustrate main theorems. [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam stability for the following cubic functional equation with involution f(2x + y) + f(2x + σ(y)) - 2f(x + y) - 2f(x + σ(y)) - 12f(x) = 0 in modular spaces by using a fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the functional inequality N(f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 6f(y); t) ≥ N(f(2x + y) + f(2x - y) - 2f(x + y) - 2f(x - y) - 12f(x); kt) for some fixed nonzero real number k and prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces by fixed point methods. [ABSTRACT FROM AUTHOR]

This paper aims to study the existence of the solutions for an Impulsive Sequential Fractional Differential Equations of order 1 < q ≤ 2 involving separate boundary conditions. Our analysis relies on some fixed point theorems. In addition, an example is provided to illustrate the results of this study. [ABSTRACT FROM AUTHOR]

In this paper we generalize the notion of O-set and establish some fixed point theorems for ⊥ - α - ψ-contraction multifunction in the setting of orthogonal modular metric spaces. As consequences of these results we deduce some theorems in orthogonal modular metric spaces endowed with a graph and partial order. Finally, we establish some theorems for integral type contraction multifunctions and give some examples to demonstrate the validity of the results. [ABSTRACT FROM AUTHOR]

In this paper, we first establish a new fixed point theorem in cones of Banach spaces. Then, we apply the fixed point theorem to study the existence and uniqueness of monotone positive solutions for an elastic beam equation u(4)(t) = f(t; u(t); u'(t)) with superlinear boundary conditions. An example is given to illustrate our main result. Compared with some earlier results (cf. [10]), the biggest differences are that we consider such equation with superlinear boundary conditions and remove some restrictive conditions. [ABSTRACT FROM AUTHOR]

Abstract In this paper we investigate a free boundary problem describing S–K–T competition ecological model with two competing species and with cross-diffusion and self-diffusion in one space dimension, where one species is made up of two groups separated by a free boundary, and the other has a single group. The system under consideration is strongly coupled and the coefficients of the equations are allowed to be discontinuous. We first show the global existence and uniqueness of the solutions for the corresponding diffraction problem by approximation method, Galerkin method and Schauder fixed point theorem, and then prove the local existence of the solutions for the free boundary problem by Schauder fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we prove the generalized Hyers-Ulam stability for the following cubic functional equation with involution f(2x + y) + f(2x + σ(y)) - 2f(x + y) - 2f(x + σ(y)) - 12f(x) = 0 in modular spaces by using a fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the functional inequality N(f(x + 2y) - 3f(x + y) + 3f(x) - f(x - y) - 6f(y); t) ≥ N(f(2x + y) + f(2x - y) - 2f(x + y) - 2f(x - y) - 12f(x); kt) for some fixed nonzero real number k and prove the generalized Hyers-Ulam stability for it in fuzzy Banach spaces by fixed point methods. [ABSTRACT FROM AUTHOR]

This paper aims to study the existence of the solutions for an Impulsive Sequential Fractional Differential Equations of order 1 < q ≤ 2 involving separate boundary conditions. Our analysis relies on some fixed point theorems. In addition, an example is provided to illustrate the results of this study. [ABSTRACT FROM AUTHOR]

In this paper, we extend the concept of mixed monotone mappings and then we consider certain fixed point theorems for a pair of mappings in metric spaces with a partial ordering. As an application, we study existence of solutions for the following fourth-order two-point boundary value problems for elastic beam equations:... where f is a continuous mapping of [0, 1]×R×R into R. Moreover, using these fixed point theorems, we prove several existence results for the solutions of various boundary value problems. [ABSTRACT FROM AUTHOR]

In this paper, we first establish a new fixed point theorem in cones of Banach spaces. Then, we apply the fixed point theorem to study the existence and uniqueness of monotone positive solutions for an elastic beam equation u(4)(t) = f(t,u(t),u'(t)) with superlinear boundary conditions. An example is given to illustrate our main result. Compared with some earlier results (cf. [10]), the biggest differences are that we consider such equation with superlinear boundary conditions and remove some restrictive conditions. [ABSTRACT FROM AUTHOR]

In this paper, we consider the existence of positive solutions to a singular semipositone boundary value problem of nonlinear fractional differential equations. By using Krasnoselskii's fixed point theorem, some sufficient conditions for the existence of positive solutions and the eigenvalue intervals on which there exists a positive solution are obtained. In addition, two examples are presented to demonstrate the application of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we use Schauder and Banach fixed point theorems to study the existence, uniqueness and stability of bounded nonhomogeneous iterative functional differential equations of the form x' (t) = λ1x(t) + λ2x[2](t)+...+λnx[n](t)+f(t). [ABSTRACT FROM AUTHOR]

In this paper, we consider a discrete population model and obtain a couple of criteria to guarantee our model being stable, including the global attractor, the extreme stability, and the periodicity. [ABSTRACT FROM AUTHOR]

In this paper, we extend Darbo's fixed point theorem in Banach space via the concept of the class of operators O(f;.) and obtain a tripled fixed point theorem. The main tool applied in our investigation is the technique of measures of noncompactness. Finally, as an application of our obtained results, we analyze the existence of solutions for a system of integral equations. [ABSTRACT FROM AUTHOR]

This paper deals with a new class of non-linear impulsive sequential fractional differential equations with multi-point boundary conditions using Caputo fractional derivative, where impulses are non instantaneous. We develop some sufficient conditions for existence, uniqueness and different types of Ulam stability, namely Hyers–Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability and generalized Hyers–Ulam–Rassias stability for the given problem. The required conditions are obtained using fixed point approach. The validity of our main results is shown with the aid of few examples. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the class of α-h-F-ψ-Greaghty contractions where the pair (F; h) is up class of type I and establish several fixed point theorems for this newly introduced class. Our results extend some recent results of Asadi et al. [1] as well as other corresponding results. [ABSTRACT FROM AUTHOR]

In this paper, we study a integral boundary value problem of fractional differential equation with the nonlinearity depending on fractional derivatives of lower order on an infinite interval. We establish a proper compactness criterion in a special function space. By using the Schauder fixed point theorem and Banach contraction mapping principle, we show the existence and uniqueness results of solutions. Two examples are also provided to illustrate the main results. The results obtained generalize and include some known results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a possible applicability of the newly established fractional differentiation in the field of epidemiology. To do this, we extend the model describing the Lassa hemorrhagic fever by changing the derivative with the time fractional derivative for the inclusion of memory. Detailed analysis of existence and uniqueness of exact solution is presented using the Banach fixed point theorem. Finally, some numerical simulations are shown to underpin the effectiveness of the used derivative. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of multi-valued impulsive stochastic partial functional integrodifferential equations with infinite delay in the α-norm. Using stochastic analysis, analytic semigroup and fixed point strategy with the properties of fractional powers of closed operators, we establish the existence and uniqueness results of mild solutions for these equations with not instantaneous impulse. Then, the existence of optimal mild solutions is also proved. Particularly, the compactness of the operator semigroups is not needed. Finally, an example to illustrate the applications of main results is given. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce and study a class of fuzzy fractional differential inclusions with projection operators, which captures the desired features of both fuzzy differential inclusions and fractional-order projective dynamical systems within the same framework. The existence of solutions for the open situation is proved by using continuous selection theorem. Moreover, the existence of solutions for the closed situation is showed by employing Lipschitzean selection theorem and fixed point theorem, respectively. Furthermore, an application and a numerical example are also given. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some new existence, uniqueness, and multiplicity results of radial solutions of an elliptic system coupled by Monge-Ampère equations using the fixed point theorem. [ABSTRACT FROM AUTHOR]

The purpose of this paper is first to reformulate the fixed point theorem (see Theorem 1 of [J. Brzdȩk, J. Chudziak and Z. Páles, A fixed point approach to stability of functional equations, Nonlinear Anal. 74 2011, 17, 6728–6732]) in β-Banach spaces. We also show that this theorem is a very efficient and convenient tool for proving the hyperstability results of the general linear equation in β-Banach spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. [ABSTRACT FROM AUTHOR]

In this paper we develop various new fixed point theorems for a class of operator equations with three general mixed monotone operators,namely $A(x,x)+B(x,x) +C(x,x)=x$ on ordered Banach spaces, where A, B, C are the mixed monotone operators. A is such that for any $t\in(0,1)$, there exists $\varphi(t)\in(t,1]$ such that for all $x,y\in P$, $A(tx,t^{-1}y)\geq\varphi(t)A(x,y)$; B is hypo-homogeneous, i.e. B satisfies that for any $t\in(0,1)$, $x,y\in P$, $B(tx,t^{-1}y)\geq tB(x,y)$; C is concave-convex, i.e. C satisfies that for fixed y, $C(\cdot,y):P\rightarrow P$ is concave; for fixed x, $C(x,\cdot)$: $P\rightarrow P$ is convex. Also we study the solution of the nonlinear eigenvalue equation $A(x,x)+B(x,x)+C(x,x)=\lambda x$ and discuss its dependency to the parameter. Our work extends many existing results in the field of study. As an application, we utilize the results obtained in this paper for the operator equation to study the existence and uniqueness of positive solutions for a class of nonlinear fractional differential equations with integral boundary conditions. [ABSTRACT FROM AUTHOR]