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This paper introduces self maps satisfying (CLRα) and (CLRαβ) property in Modified Intuitionistic Fuzzy Soft Metric Space (MIFSMS). Moreover, we have also extended common fixed point theorems for weakly compatible maps satisfying common limit range property in the setting of MIFSMS. We have also given an application utilising our new results. [ABSTRACT FROM AUTHOR]

In this paper, we consider integral boundary value problems of nonlinear fractional differential equations. Existence results of positive solutions for the problem are obtained based on the Guo-Krasnoselskii theorem and the Five functional fixed point theorem. Simple examples follow the main results in successive sections. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the existence of the best proximity points in binormed linear spaces. As a consequence, we obtain some fixed point results. We also provide some illustrations to support our claims. As applications, we obtain the existence of a solution to split feasible and variational inequality problems. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a generalization of a fixed point theorem given by Popescu [O. Popescu, Comput. Math. Appl., vol. 62, no. 10, pp. 3912-3919, 2011]. An example is also given to support our main result. [ABSTRACT FROM AUTHOR]

In this paper we give a classification of endomorphisms and additive mappings of a prime ring satisfying certain algebraic identities. Moreover, we provide an example proving that the primeness hypothesis imposed in our theorems is not superfluous. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of solutions for a tripled system of fractional differential equations with nonlocal integro multi point boundary conditions by using the p-Laplacian operator and the γ-Caputo derivatives. The presented results are obtained by the two fixed point theorems of Banach and Krasnoselskii. An illustrative example is presented at the end to show the applicability of the obtained results. To the best of our knowledge, this is the first time where such problem is considered. [ABSTRACT FROM AUTHOR]

The paper is devoted to prove the existence of solutions for an infinite system of non- linear integral equations. This system is investigated in the WC-Banach algebra C(I; c0), the space of all continuous functions acting from an interval I into the sequence space c0. Making use of the measure of weak noncompactness and the weak topology, we establish some fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operat- ors acting onWC-Banach algebra involving w-contractive operators. [ABSTRACT FROM AUTHOR]

In the present paper, we characterize Lie (Jordan) σ-centralizers of generalized matrix algebras. More precisely, we obtain some conditions under which every Lie σ-centralizer of a generalized matrix algebra can be expressed as the sum of a σ-centralizer and a center- valued mapping. Further, it is shown that under certain appropriate assumptions every Jordan σ-centralizer of a generalized matrix algebra is a σ-centralizer. Finally, the main results are applied to triangular algebras. [ABSTRACT FROM AUTHOR]

The exponential space, which is a Banach function space, can be defined with two very differently looking, but equivalent norms. In this paper, we give estimates for the best constants of the ratio of these two norms. Our result answers a question of C. Bennett, and R. Sharpley. [ABSTRACT FROM AUTHOR]

The concept of a tolerance relation, shortly called tolerance, was studied on various algebras since the seventies of the twentieth century by B. Zelinka and the first author (see e.g. [6] and the monograph [1] and the references therein). Since tolerances need not be transitive, their blocks may overlap and hence in general the set of all blocks of a tolerance cannot be converted into a quotient algebra in the same way as in the case of congruences. However, G. Czédli ([7]) showed that lattices can be factorized by means of tolerances in a natural way, and J. Grygiel and S. Radeleczki ([8]) proved some variant of an Isomorphism Theorem for tolerances on lattices. The aim of the present paper is to extend the concept of a tolerance on a lattice to posets in such a way that results similar to those obtained for tolerances on lattices can be derived. [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]

There are situations when we have to resort to the approximate optimal solution of equations of the type g(t) = t when g is not a self-map, because exact solution of that equation does not exist. The existence of such optimal solutions are ensured by best proximity point theorems. In this paper, we define multivalued Geraghty contraction (MVGC) in a complete metric space and establish the corresponding best proximity point (BPP) result. Our result extends the famous result due to Geraghty on fixed points. [ABSTRACT FROM AUTHOR]

In this paper, we study a coupled system of nonlinear Liouville–Caputo fractional differential equations equipped with a new set of nonlocal boundary conditions involving an arbitrary strip together with two sets of nonlocal multi-points on either part of the strip on the given domain. We emphasize that the boundary conditions considered in this study are formulated with respect to the sum and difference of the unknown functions. We apply the well-known tools of the fixed point theory to derive the main results. Examples are presented for the illustration of the obtained results. [ABSTRACT FROM AUTHOR]

The object of the present paper is to generalize projective curvature tensor of paraKenmotsu manifold with the help of a new generalized (0,2) symmetric tensor Z introduced by Mantica and Suh. Various geometric properties of generalized projective curvature tensor of para-Kenmotsu manifold have been studied. It is shown that a generalized projectively φ symmetric para-Kenmotsu manifold is an Einstein manifold. [ABSTRACT FROM AUTHOR]

In this paper, we prove the stability of Hadamard homomorphisms and Hadamard derivations in Banach algebras. This is applied to investigate Hadamard isomorphisms between Banach algebras. [ABSTRACT FROM AUTHOR]

In the present paper, we proposed a new sequence of summation-integral type operators involving Apostol-Genocchi polynomials. We study some approximation results of the proposed operators using first and second-order modulus of continuity, the global rate of convergence using Voronovskaja-type asymptotic theorem, Lipschitz-type space, and Ditzian-Totik modulus of smoothness. Lastly, we study the weighted approximation. [ABSTRACT FROM AUTHOR]

In this paper, some new estimations of Hermite-Hadamard-Fejér type inequalities for higher order differentiable preinvex functions are established via fractional integral operators. The main motivation point of the study is that our findings, which include generalized preinvex functions for Hermite-Hadamard-Fejér type inequalities by means of fractional integral operators, are the rare results in the literature. The coincidence of the special cases of the our main theorems with the earlier works in the literature is also demonstrated as a verification of our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study the ∗-identities with a pair of generalized derivations on ∗-ideals of prime rings with involution. In particular, we prove that if a noncommutative prime ∗-ring admit two generalized derivations F and G such that [F (x),G(x* )] = 0 for all x ∈ I, where I is a nonzero ∗-ideal of R, then there exists λ ∈ C such that F = λG. Finally, we provide an example which shows that the primeness of R is crucial in our results. [ABSTRACT FROM AUTHOR]

In this paper, we extend the result of Romaguera [21] with the aid of best proximity point theory on partial metric spaces by considering the approach of Haghi et al. [9], and so celebrated Boyd-Wong fixed point theorem [7]. We first introduce two concepts called generalized proximal BW-contraction and generalized best BW-contraction. Then, we obtain some best proximity point theorems for such mappings. To illustrate the effectiveness of our results, we provide some nontrivial and interesting examples. Finally, unlike homotopy applications existing in the literature, we present for the first time an application of the best proximity result to the homotopy theory. [ABSTRACT FROM AUTHOR]

In the paper, we will discus some τ-topological properties of the set F (S0,T,H) := {x ∈ X : S0x ∈ Tx+Hx}, where T is multivalued operator, S0 and H are two single valued operators acting on a Hausdorff locally convex space X and τ is a weaker Hausdorff locally convex topology on X. Moreover, when X is a τ-angelic space with the so-called τ-Krein-Šmulian property, we will provide some new variants of fixed point theorems for multivalued operators. Our results are formulated in terms of τ-upper semicontinuity, τ-S0-demicom-pactness and families of axiomatic measures of noncompactenss. [ABSTRACT FROM AUTHOR]

In this paper, we mainly consider the oscillation of numerical solutions for a nonlinear delay differential equation which is generalized from a delay Lotka-Volterra type single species population growth model. By studying the corresponding difference scheme of the equation discretized by θ-method, forward Euler method and backward Euler method, some sufficient conditions under which the numerical solutions oscillate are obtained. Furthermore, we prove that the positive non-oscillatory numerical solutions tend to the equilibrium of the original differential equation. Finally, some numerical experiments are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a two dimensional discrete-time predator-prey system with weak Allee effect, affecting the prey population, is considered. The existence of the positive fixed points of the system and topological classification of coexistence positive fixed point are examined. By using the bifurcation theory, it is shown that the discrete-time predator-prey system with Allee effect undergoes flip and Neimark-Sacker bifurcations depending on the parameter a. The parametric conditions for existence and direction of bifurcations are investigated. Numerical simulations including bifurcation diagrams, phase portraits and maximum Lyapunov exponents of the system are performed to validate analytical results. The computation of the maximum Lyapunov exponents confirm the presence of chaotic behaviour in the considered system. Finally, the OGY feedback control method is implemented to stabilize chaos existing in the system. [ABSTRACT FROM AUTHOR]

In this paper, we prove two new general fixed point theorems in rectangular b-metric spaces. As applications, we answer two open questions in rectangular b-metric spaces posed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of integration with respect to a given derivation on a lattice. More precisely, we give the definitions of integrable elements of a lattice and their integral sets. We investigate several characterizations and properties of integrations on a lattice. Also, we give a lattice structure to the family of integral sets with respect to a given integration. Further, we provide a representation theorem for the lattice of fixed points of an isotone derivation based on the family of integral sets. As an application of this notion of integration, we use the integrable elements of a Boolean lattice to determine the necessary and sufficient conditions under which a linear differential equation on this Boolean lattice has a solution. [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]

This paper is devoted to the study of the existence and nonexistence of positive solutions for a second-order m-point eigenvalue impulsive boundary value problem. We use the fixed point theorems on the cones in order to achieve our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve some fixed point results given by I.A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babes¸-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia's theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babes¸-Bolyai Univ. Cluj- Napoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia's fixed point theorem. 2010 Mathematics Subject Classification: 47H10, 47H09, 34K05, 34K12, 45D05, 45G10, [ABSTRACT FROM AUTHOR]

Inspired by the paper of Fazli and Nieto in [Open Math. 17 (2019) 499--512], we establish new existence and uniqueness result for a type of fractional Bagley--Torvik differential equation. Reported result not only generalizes previous results but also adopts different technique. We finish this study by concluding remarks which discuss the preference of our theorem compared to previous results. An example is constructed with specific parameters that requires weaker conditions for the existence of a unique solution. Meanwhile, we construct an iterative sequence that converges to the unique solution and can not be commented via the results of Fazli and Nieto. [ABSTRACT FROM AUTHOR]

In this paper, we solve a new Jensen type m-dimensional multiplicative inverse functional equation and then its various stability problems in the setting of non-negative real numbers and non-Archimedean spaces via fixed point method. The functional equation dealt in this study is linked with the famous relationship between arithmetic and harmonic mean of m values. The role of harmonic mean is very significant in many other fields such as traffic flow theory, industrial engineering, communication system, etc. By inversing the arithmetic mean of reciprocal values, we attain the harmonic mean. This property could be analyzed as an inverse problem via the functional equation dealt in this investigation. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to consider a system of N -fixed point equations in metric spaces. The existence and uniqueness of solution and an iterative algorithm for approximating the solution are studied. This system of N -fixed point equations is an extension of the classical of fixed point equation x = T x. The results of this paper improve several important works recently published in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we will prove some fixed point results using a Pompeiu type metric on Pcl(X), for multi-valued operators satisfying two conditions: contractivity and monotonicity. The approach is based on a fixed point theorem for a multi-valued operator in the setting of a b-metric space. Several qualitative properties(well-posedness, Ulam-Hyers stability) are also obtained. In the second part of this paper, we will consider the extended coupled fixed point problem for a multi-valued operator. We will consider the problem of the existence of the solutions. Data dependence and well-posedness of the extended coupled fixed point problem are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, some new weighted Simpson's type integral inequalities are presented for the class of harmonically-preinvex functions by using power-mean integral inequality and Holder's integral inequality. [ABSTRACT FROM AUTHOR]

In this paper, we study the complex dynamical behaviors of a discrete-time SIR epidemic model. Analysis of the model demonstrates that the Diseases Free Equilibrium (DFE) point is globally asymptotically stable if the basic reproduction number is less than one while the Endemic Equilibrium (EE) point is globally asymptotically stable if the basic reproduction number is greater than one. The results are further substantiated visually with numerical simulations. Furthermore, numerical results demonstrate that the discrete model has more complex dynamical behaviors including multiple periodic orbits, quasi-periodic orbits and chaotic behaviors. The maximum Lyapunov exponent and chaotic attractors also confirm the chaotic dynamical behaviors of the model. [ABSTRACT FROM AUTHOR]

The aim of this paper is to improve some fixed point results given by I. A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babeş-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia's theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babeş-Bolyai Univ. ClujNapoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia's fixed point theorem. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis of the following linear 2m-th order parabolic equation ∂tu+(-1) m ∑ N k=1 ∂ 2m xk u = f, subject to Dirichlet type condition ∂ l νu = 0, l = 0,1,...,m-1, on the lateral boundary, where m is a positive integer. The right-hand side f of the equation is taken in the Lebesgue space L p, 1 < p < +∞. The problem is set in a domain of the form Q = (t, x1,..., xN) ∈ R N+1 : 0 ≤ q x 2 1 +...+x 2 N < t α with α > 1/2m. [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]

In this paper, we study the existence of a non-trivial solution in W 1,p(x) 0 (Ω) for the problem ( ∆p(x)u = f(x,u,∇u) in Ω, u = 0 in Ω. The proof is based on Schaefer's fixed point theorem. [ABSTRACT FROM AUTHOR]

In this paper, we extend the relation-theoretic contraction principle due to Alam and Imdad (J. Fixed Point Theory Appl. 17 (2015) 693-702) for Matkowski contractions employing a locally T-transitive binary relation. Our results improve and enrich several fixed point theorems of the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider the higher-order multi-point fractional boundary value problem. We establish the criteria for the existence of at least one and three positive solutions for higher order nonlinear m-point fractional boundary value problem by using the Krasnosel'skii fixed point theorem and the Legget-Williams fixed point theorem, respectively. [ABSTRACT FROM AUTHOR]

In this paper, by considering theWardowski's technique, we present fixed point results for multivalued mapping on a space with two metrics. Also, taking into account β-admissibility of a multivalued mapping, we provide some more general results. [ABSTRACT FROM AUTHOR]

In this paper, we aim to study the existence of global attractors for the time discretized modified three-dimensional (3D) Bénard systems. Using the backward implicit Euler scheme, we obtain the time discretization systems of 3D Benard systems. Then, by the Galerkin method and the Brouwer fixed point theorem, we prove the existence of the solution to this time-discretized systems. On this basis, we proved the existence of the attractor by the compact embedding theorem of Sobolev. Finally, we discuss the limiting behavior of the solution as N tends to infinity. [ABSTRACT FROM AUTHOR]

In this paper, first we prove a common fixed point theorem for pairs of weakly compatible mappings satisfying a generalized -weak contraction condition that involves cubic terms of metric functions. Secondly, we prove some results using different variants of R-weakly commuting mappings. At the end, we give an application in support of our results. [ABSTRACT FROM AUTHOR]

In this paper, firstly, we introduce the concept of a complex valued fuzzy b-metric space, which is inspired by the work of Shukla et al. [24]. Also, we investigate some of its topological properties which strengthen this concept. Next, we establish some fixed point theorems in the context of complex valued fuzzy b-metric spaces and give suitable examples to illustrate the usability of the obtained main results. These results extend and generalize the corresponding results given in the existing literature. Moreover, we provide some applications on the existence and uniqueness of solutions for a certain type of nonlinear integral equations. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate oscillatory properties of even-order advanced differential equations. The key idea of our approach is to conduct a comparison with first order equations and use the Riccati transformation technique. Some new oscillation criteria are shown. Two examples are presented in order to clarify the main results. [ABSTRACT FROM AUTHOR]

In this paper, a general fixed point theorem for quasi-contractions in b-metric spaces, which is a sharp improvement of Amini-Harandi's result, Mitrovic and Hussain's result, and is a generalization of many b-metric fixed point theorems in the literature, is proved. The technique overcomes some limits in b-metric fixed point theory compared to metric fixed point theory. The obtained results are also supported by examples. [ABSTRACT FROM AUTHOR]

The aim of this paper is to initiate the study of best proximity point and optimal coincidence point results of some a Pata-proximal admissible contraction of type-I and type-II in the framework of complete metric space. Some examples are presented to support the results obtained herein. Our results unify, extend and generalize various existing results in literature. [ABSTRACT FROM AUTHOR]

In this paper we generalize the well-known class of quasi contractions pairs, by using the so-called Geraghty's property and by controlling the contractive inequality with an altering distance function. For this class, in the setting of b-metric spaces, we prove the existence and uniqueness a of common fixed point assuming some non commutative notions. Finally, for this class of mappings we prove the b-convergence of the Jungck-Mann iterative scheme under suitable conditions on the b-metric space and on the altering distance function. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of an admissible extended Z-contraction mapping in the setting of extended b-metric spaces. As an application, we consider Ulam stability problems based on our contractions. The presented results cover several existing results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we construct an iteration scheme involving a hybrid pair of nonexpansive mappings. For this scheme, we prove some convergence theorems in CAT(0) spaces. In process, we remove a restricted condition (also called end-point condition) in previous several existing results. Thus, several relevant results cited in the literature generalize and improve. [ABSTRACT FROM AUTHOR]

The paper gives multiplicity results for the impulsive boundary value problem x" = f(t,x), for a.e. t ∈ [0,T], such that x(t) ∈ int K, x'(s +) = -x'(s-), if s ∈ (0,T), x(s) ∈ ∂K, x(0) = A, x(T) = B, where K ⊂ R is a compact interal, f is Carathéodory function on [0,T]?× K and A, B ∈ int K. This problem can be understood as a problem in one-dimensional billiard space and it is also a generalization of oscillator with obstacles from below and from above and absolutely elastic impacts. A simple condition for the existence of solution with exact number of impacts is given, as well as the multiplicity result. The results are obtained by a transformation into problem without impulses (without impacts) and using Schauder fixed point theorem. [ABSTRACT FROM AUTHOR]