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In this short note we generalize, complement and improve recent result on multiplicative metric spaces established by R.P. Agarwal et al. [Ravi P. Agarwal, Erdal Karapinar and Bessem Samet: An essential remark on fixed point results on multiplicative metric spaces. [ABSTRACT FROM AUTHOR]

Some new classes of exponentially bivariational inequalities are introduced and considered in this paper. It is shown that the optimality conditions of differentiable exponentially biconvex functions can be characterized by exponentially bivariational in-equalities. Several inertial iterative are proposed and analyzed for solving exponentially bivariational inequalities by applying the auxiliary principle technique. Convergence criteria is discussed using the pseudo-monotonicity of the operator. Special cases are also highlighted as applications of the main results. Results obtained in this paper can be viewed as significant improvement of previously known results. It is an interesting problem to implement these methods numerically and their comparison with other techniques. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove some common fixed point theorems in S-metric spaces for a pair of self-mappings which is weakly compatible satisfying an implicit relation and give some consequences of the main result. We also give some examples to demonstrate the validity of the results and an application of the main result. The results presented in this paper generalize, extend and enrich several results in the existing literature. It specially generalize the results of Imdad et al. [10] from metric space to the setting of S-metric space. [ABSTRACT FROM AUTHOR]

In this paper we provide an account of some of the fundamental aspects of the mixed variational inequalities with major emphasis on the computational properties, various generalizations, dynamical systems, sensitivity analysis and their applications. Mixed variational inequalities can be viewed as a novel and significant extension of variational principles. A wide class of unrelated problems, which arise in various branches of pure and applied sciences are being investigated in the unified framework of mixed variational inequalities. It is well known that variational inequalities are equivalent to the fixed point problems. This equivalent fixed point formulation has played not only a crucial part in studying the qualitative behavior of complicated problems, but also provide us numerical techniques for finding the approximate solution of these problems. Our main focus is to suggest some new iterative methods for solving mixed variational inequalities and related optimization problems using resolvent methods, resolvent equations, splitting methods, auxiliary principle technique, self-adaptive method and dynamical systems coupled with finite difference technique. Convergence analysis of these methods is investigated under suitable conditions. Sensitivity analysis of the mixed variational inequalities is studied using the resolvent equations method. Iterative methods for solving mixed bivariational inequalities are also introduced and investigated. Our methods of discussing the results are simple ones as compared with other methods and techniques. Results proved in this paper can be viewed as significant and innovative refinement of the known results. Some open problems are also suggested for future research. [ABSTRACT FROM AUTHOR]

In this paper, we formulate a mathematical model of malaria transmission dynamics with impulsive and periodic release of Wolbachia-infected male mosquitoes. Our objective is to evaluate the impact of periodic release of Wolbachia-infected male mosquitoes on malaria transmission. Subsequently, to find out how often and in what quantities Wolbachia-infected male mosquitoes need to be released to effectively reduce malaria transmission. By using the comparison principle, Floquet theory and some of the analytical methods, we obtain the basic reproduction number. Then, we demonstrated that the disease-free periodic solution is globally stable if the reproduction number is less than unity, and we prove the uniform persistence of the disease if the reproduction number is greater than unity. Finally, we perform numerical simulations to illustrate our theoretically pertinent results. [ABSTRACT FROM AUTHOR]

In this paper, we prove some coupled fixed point theorems for contractive type conditions using control function in the setting of partial b-metric spaces and provide some corollaries of the main results. We also give an example to illustrate the result. The results presented in this paper extend and generalize several results from the existing literature (see, for example, [1, 24] and many others). [ABSTRACT FROM AUTHOR]

In the article [M.O. Olatinwo and A.G. Adeagbo-Sheikh: Working functions for a self-organization problem, GrKG/HumanKybernetik, 4(2005), No. 46, 197-208], we determined analytically the behaviour of subsystems of a self-organizing system. A mathematical procedure was initiated to study the behaviour of subsystems of a self-organizing system for which the distance-from-goal expression had been obtained from geometrical consideration. In particular, in that paper, we considered a system of three particles moving in the R²-plane and the system was self-organizing to keep the particles in a straight line. In the present paper, we shall show that a system of n particles (n > 3) is self-organizing to keep the particles in a straight line. This is done by employing the notions of the centre of mass as well as some geometry in R². Our results generalize that of a system of three particles. Indeed, our results can find useful applications in diverse areas, such as in celestial mechanics, artificial intelligence, learning and adaptive control, pattern recognition systems, control systems engineering, automation in general as well as in medicine. [ABSTRACT FROM AUTHOR]

In this paper, some new classes of exponentially general nonconvex variational inequalities are introduced and investigated. Several special cases are discussed as applications of these nonconvex variational inequalities. Projection technique is used to establish the equivalence between the noncovex variational inequalities and fixed point problem. This equivalent formulation is used to discuss the existence of the solution. Several inertial type methods are suggested and analyzed for solving exponentially general nonconvex variational inequalities. using the technique of the projection operator and dynamical systems. Convergence analysis of the iterative methods is analyzed under suitable and appropriate weak conditions. In this sense, our result can be viewed as improvement and refinement of the previously known results. Our methods of proof are very simple as compared with other techniques. [ABSTRACT FROM AUTHOR]

The objective of the present paper is to study Ricci soliton, N-Ricci soliton and Yamabe soliton with respect to a metric connection on para-Sasakian manifold. Moreover, the paper concerns with the study of Ricci soliton and Yamabe soliton with torse forming vector fields on para-sasakian manifold admitting the metric connection. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new self-adaptive algorithm for approximating a common element of the set of solutions of generalized mixed equilibrium problems, split common null point and common fixed point of a finite family of quasi-ɸ-nonexpansive mappings in 2-uniformly smooth and uniformly convex real Banach space. Our proposed algorithm is constructed in such a way that its convergence analysis does not require a prior estimate of the operator norm. Furthermore, we establish a strong convergence result under some mild conditions. Our result improves and generalizes many existing results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we discuss SPK iterative algorithm for approximating fixed point of monotone generalized (α, β)-nonexpansive mapping in the setting of partially ordered hyperbolic spaces. Indeed, we present some convergence results for SPK iterative algorithm for monotone generalized (α, β)-nonexpansive mapping. Moreover, we provide an application of our results to nonlinear integral equations. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new fixed point technique based on the composition operators for characterizing common fixed point sets involving two nonlinear maps in Banach spaces without commuting assumption. We use our new result as tool to obtain the strong convergence of the sequence generated by a modified Mann algorithm for solving common fixed point problems involving firmly nonexpansive, quasi-nonexpansive and demicontractive mappings in Banache spaces. Application to constrained optimization problem is provided to support our main results. Finally, we give a numerical result to illustrate the main theorem. [ABSTRACT FROM AUTHOR]

In the present paper we study n-Ricci solitons on three-dimensional para-Kenmotsu manifolds with the curvature condition R.Q = 0. Also we study conformal flat, projectively flat and concircularly flat n-Ricci soliton on a three-dimensional paraKenmotsu manifold. Finally, we construct an example of a three-dimensional para-Kenmotsu manifold which admits n-Ricci solitons. [ABSTRACT FROM AUTHOR]

In this paper we develop the notion of Jacobson radical to fuzzy hyperrings and studies its basic properties. In this regards, we investigate some results and definitions related to fuzzy hyperideals of fuzzy hyperrings. Then we generalize the classical case of Jacobson radical rings and ideals to fuzzy case of Jacobson radical of hyperrings and hyperideals. We will proceed focuses on the relationships of between them and studies their properties. Also, we prove a fuzzy hyperring R is semisimple if and only if it is a artinian fuzzy hyperring and Jl(R) = {0} and R be a left artinian fuzzy hyperring. Also, it is proved that R is semisimple if and only if J(R) = 0. In particular, it is shown that R/J(R) is semisimple. Also, it is prove ff R is a left artinian fuzzy hyperring, then its radical J(R) is the unique largest nilpotent left, right, or two-sided fuzzy hyperideal in R and it is shown that, if R is a fuzzy hyperring with J = J(R). Finally, it is proved R is left artinian if and only if R it is left noetherian, J is nilpotent, and R/J is semisimple. [ABSTRACT FROM AUTHOR]

In this paper we present the curvature tensors of (k, μ)-paracontact manifold satisfying the conditions R ⋅ W1* = 0, R ⋅ W2 = 0, R ⋅ W3 = 0, R ⋅ W4 = 0 and R ⋅ W5 = 0. According these cases, (k, μ)-paracontact manifolds have been characterized. We think that some interesting results on a (k, μ)-paracontact metric manifold are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of extended rectangular cone b-metric spaces, then prove the fixed point theorems in such spaces. And we give an example to show the validity of our main result. Moreover, we prove the fixed point theorems in orbitally complete extended rectangular cone b-metric spaces, which are generations of previous results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove a relation-theoretic version of the famous fixed point result of Mizoguchi and Takahashi in the metric spaces endowed with an arbitrary binary relation. The fixed point result of this paper generalizes the famous results of Nadler [7], Mizoguchi and Takahashi [6] and several other fixed point results for set-valued mappings defined on the spaces endowed with various kinds of binary relations. [ABSTRACT FROM AUTHOR]

In the year 1998, M. Matsumoto [11] has studied the conditions for some Finsler spaces with (α, β)-metric to be of Douglas type. The purpose of the present paper is devoted to find the various conditions for a Finsler space Fn with a special (α, β)-metric to be a Douglas space for assumptions α² = 0(modβ), in the entire paper. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the uniqueness results of difference-differential polynomials of entire functions sharing a value with ignoring multiplicities. The results of this paper improve and generalize the results of X. Qian and Y.S. Ye [3] and K. Zhang, H.X. Yi [10] and many others. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the growth condition as well as the distribution of zeros of the most general polynomial generated by shifts, q-shifts and derivatives of a meromorphic function. Meanwhile the results obtained in this paper not only generalize but also improve the earlier results of Zheng and Xu [20] by removing the conditions on the zeros and poles of a meromorphic function. [ABSTRACT FROM AUTHOR]

Variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of problems arising in pure and applied sciences. In this paper, we introduce and consider a new class of exponentially general variational inequalities. Some new iterative methods are proposed and analyzed using the auxiliary principle technique. Our results present a significant improvement of previously known results for solving variational inequalities and related optimization problems. Several open problems have been suggested for further research in these areas. [ABSTRACT FROM AUTHOR]

In this paper, we establish some fixed point theorems with the help of α-admissible mapping satisfying (ψ,Φ) contractive condition of integral type in Gb-metric space. Our results are supported by examples. [ABSTRACT FROM AUTHOR]

In this paper, approximative K-frames for separable Hilbert spaces have been introduced and some results for the frame operators are established. Also, the interchangeability of approximative Bessel sequences has been discussed. [ABSTRACT FROM AUTHOR]

In this paper, we examine topology of Sb-metric spaces and prove some results. We also extend some fixed point theorems to Sb-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper for mixed hyperbolic-parabolic type equation, a non-local boundary problem with integral boundary condition is studied. Many physical problems are expressed only in mixed-type equations. The physical process is expressed in the hyperbolic type equation in one part of the region and in the parabolic type in the other part. The problem is reduced to the non-local boundary-value problem. In this paper the uniqueness, existence and stability of the solution are shown. [ABSTRACT FROM AUTHOR]

In this paper, C*-valued-algebra S-metric space is an extension of the S-metric space. The purpose of this paper is to establish and prove some fixed point theorems for mappings under different contractive conditions. Some examples are given to prove the validity of the results obtained. Our results promote and improve relevant conclusions. [ABSTRACT FROM AUTHOR]

In this paper, we consider a system of quasi variational inequalities involving two arbitrary mappings. It is shown that the system of quasi variational inequalities are equivalent to the fixed point problem using the projection method. We use this alternative formulation to suggest some new inertial projection methods. The convergence criteria of the new methods is analyzed under some appropriate conditions. Several special cases are discussed as applications of the results. It is interesting problem to consider the implementation of the proposed methods with other similar techniques. The concept of this paper may inspire future research in this area. Results obtained in this paper can be viewed as refinement and improvement of previously known results. [ABSTRACT FROM AUTHOR]

In this paper, as a continuation of research on Γ-semirings with apartness in Bishop's constructive framework, we determine the concepts of (left, right) weak interior co-ideals (i.e. a constructive dual of (left, right, res.) weak interior ideals) in Γ-semirings with apartness as a generalization of the concept of co-ideals and the concept of interior co-ideals in Γ-semiring with apartness and analyze some of their fundamental properties. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the qualitative properties of some polynomials generated by a q-shift difference and differentials of a meromorphic function. Our results generalize and supplement the results of Zheng and Xu (J. Math. Res. Appl., 42(2022), No. 1, 31-40). [ABSTRACT FROM AUTHOR]

In this paper, we obtain common fixed point results in b-metric space as well as in dislocated b-metric space for Geraghty type and ψ-Geraghty type contractions. These results extend some existing results in the literature. Moreover, some examples and an application for non-linear integral equations are also given. [ABSTRACT FROM AUTHOR]

This paper employs a hybrid numerical technique based on uniform Haar wavelets and θ-weighted scheme for numerical solution of non-homogeneous Buckmaster equation. In the solution process, after applying θ-weighted scheme to Buckmaster equation, the time derivative is approximated by the forward difference and then non-linear terms in this equation are linearized by Taylor series expansion. Thereafter, Haar wavelet collocation method has been employed to solve the resulting ordinary differential equation. To verify the competence of the present technique to solve Buckmaster equation, some test problems have been solved and the present results have been compared with the exact results. It can be seen from the numerical simulation that the computed solutions are in excellent agreement with the exact solutions for very small number of collocation points. [ABSTRACT FROM AUTHOR]

In [11], Gray introduced two interesting classes of Riemannian manifolds which generalize the concept of Einstein manifolds. In this paper, we prove that the projection of the Einstein-like class type defined on a warped product induces Einstein-like type on the base manifolds whereas the fiber manifold does under some conditions. [ABSTRACT FROM AUTHOR]

In this paper, we establish a unique fixed point and some common fixed point theorems in the setting of S-metric spaces. The results presented in this paper generalize, extend and unify some previous results in the existing literature. We also present one of the possible applications of our result to explain well-posedness and limit shadowing property of fixed point problems. We give some examples to support our results. [ABSTRACT FROM AUTHOR]

he object of the present paper is to introduce a new non-metric linear connection named as Zamkovoy connection in Lorentzian para-Sasakian manifolds (briey, LP-Sasakian manifolds). In this paper we obtain expressions for Riemannian curvature tensor (R*), Ricci tensor (S*), Ricci operetor (Q*) and scalar curvature (r*) with respect to Zamkovoy connection in LP-Sasakian manifolds. Moreover, we study generalized recurrent and generalized concircular φ-recurrent LP-Sasakian manifolds with respect to Zamkovoy connection. Besides these, we discuss an LP-Sasakian manifold M satisfying W*(X; Y ):R* = 0, for all vector fields X, Y on M, where W* denotes concircular cur- vature tensor with respect to Zamkovoy connection. [ABSTRACT FROM AUTHOR]

Some new concepts of the higher order strongly log convex functions involving an arbitrary bifuction are considered in this paper. Some properties of the higher order strongly convex functions are investigated under suitable conditions. The optimality conditions for the diffFerentiable higher order strongly log-convex functions are characterized by variational inequalities. It is proved that the parallelogram laws for Banach spaces can be obtained as novel applications of higher order strongly affine convex functions. Some important special cases are discussed. Results obtained in this paper can be viewed as refinement and improvement of previously known results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study composite implicit iterative process with errors for two finite families of non-Lipschitzian asymptotically quasi-nonexpansive type mappings. In this paper, we have obtained a necessary and sufficient condition to converge to common fixed points for proposed scheme and mappings and also obtained a strong convergence theorem by using Condition (B') in the framework of real Banach spaces. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present three concepts of nonuniform polynomial dichotomies for linear discrete systems and their correspondents in the uniform case. With the aid of particular discrete systems defined on infinite dimensional Banach spaces, we emphasize the connections between the presented concepts. The main result of the paper is given by a boundedness result of the dichotomic sequence of projections. [ABSTRACT FROM AUTHOR]

Let f(z), g(z), h(z) are three entire functions of non zero finite order and fn(z) the iterations of f(z), with respect to g(z) and h(z) also T(r; f), T(r; g), T(r; h), T(r; fn) are there respective characteristic functions. In this paper we study comparative growth properties of T(r; fn), with respect to T(r; f), T(r; g) and T(r; h) in terms of generalist order. [ABSTRACT FROM AUTHOR]

In this paper, we prove some unifying fixed point theorems of Ćirić's type in a complete b-metric space for mappings possessing non-unique fixed points by employing general contractive inequality conditions as well as the notion of comparison functions. The right-hand side of each of the contractive inequality condition being introduced is Akram-Zafar-Siddiqui while the left-hand side of each is Akram-Zafar-Siddiqui type to certain extent. Our results unify, generalize and improve several unique and non-unique fixed point theorems in the literature. Also, the results obtained are extensions of such unique and non-unique fixed point theorems from the metric space setting to the b-metric space environment. [ABSTRACT FROM AUTHOR]

In 2021, F. Abbas introduced a new class of open sets in topological spaces called h-open sets and explored some properties of these sets. In this paper, we introduced new notions such as strongly h-continuous functions, pre-h-open functions, pre-h-closed functions, h-irresolute-homeomorphism and investigated several properties of these functions. Moreover, we introduced a new class of spaces known as h-irresolute topological vector spaces via these h-open sets. We studied and explored various properties and characterizations of this newly introduced space. Furthermore, we defined an h-extremally disconnected space and proved that an h-irresolute topological vector space X is h-extremally disconnected if and only if h-closures of disjoint pair of h-open sets are disjoint. [ABSTRACT FROM AUTHOR]

The work of this paper consists to present analytical and numerical results on the weak solution for a vibrating beam system. Using the variational method, we show that the weak solution exists, is unique and is continuous in time. Moreover, by combining the finite element method and the one we call "discrete multiplier method", we develop a numerical method stable and convergent which preserves faithfully the dissipativity of energy and the property of exponential stability obtained in the continuous case by the authors in [2]. We perform numerical simulations in order to validate this method. [ABSTRACT FROM AUTHOR]

The aim of this paper is to discuss the notion of approximate continuous Sequential Henstock Stieltjes integrals of certain class of functions which are generalisations of some of the existing Henstock-type integrals in the literature. An example to show the applicability of this integral is given. [ABSTRACT FROM AUTHOR]

In this paper, we study some comparative growth properties of composite entire functions on the basis of relative (p, q)-th order and relative (p, q)-th lower order of entire function with respect to another entire function, where p and q are any two positive integers, here we also take relative L order and relative L* order form, to prove some comparative growth properties. [ABSTRACT FROM AUTHOR]

The symmetric division deg index (or sdd-index) of a graph G is one of the 148 discrete Adriatic indices introduced by Vukičević and Gašperov, defined as SDD(G) = Suv∊E(G) (dG(u)/dG(v) + dG(v)/dG(u)), and has a good correlation with the total surface area of polychlorobiphenyls, where dG(u) is the degree of a vertex u in G and E(G) is the edge set of G. In this paper, the sdd-index is expressed over the vertex set. Using this new expression, we derive explicit formulae for the sdd-index and sdd-coindex of some derived graphs, and also some new bounds for the sdd-index. [ABSTRACT FROM AUTHOR]

In this paper we introduce two new classes of operators which are called strongly order continuous and order-to-unbounded order continuous operators and we study their lattice properties. With under some conditions, we show that order continuity is equivalent to strongly order continuity of operators on Riesz spaces. We show that the collection of all strongly continuous linear functionals on a Riesz space E is a band of E~. [ABSTRACT FROM AUTHOR]

This paper establishes some important latest innovations in the existence and uniqueness results by means of Krasnoselskii's fixed point and the Banach fixed point theorems for Caputo fractional Volterra-Fredholm integro-differential equations with initial condition. New conditions on the nonlinear terms are given to pledge the equivalence. Finally, an illustrative example is also presented. [ABSTRACT FROM AUTHOR]

In this paper, we shall prove a unique fixed point theorem for generalized (ψ-φ)-weakly contractive mappings satisfying C-class function in the setting of complete metrically convex metric spaces. The result obtain in this paper generalizes the corresponding results of Khan [17], Khan and Imdad [16], Rhoades [22], Alber and Guerre-Delabriere [3] and others. [ABSTRACT FROM AUTHOR]

Some new concepts of the higher order strongly uniform convex functions with an increasing modulus ø(.) vanishing only at 0 are considered in this paper. Some properties of the higher order strongly uniformly convex functions are investigated under suitable conditions. The parallelogram laws for Banach spaces are obtained as applica- tions of higher order strongly affine uniform convex functions as novel applications. It is shown that the minimum of the higher order strongly uniform convex functions can be characterized by the variational inequalities. Some important special cases as appli- cations of our results are discussed. Results obtained in this paper can be viewed as refinement and improvement of previously known results. [ABSTRACT FROM AUTHOR]

In this paper, we define and introduce some new concepts of the exponen- tially harmonic convex functions. We investigate several properties of the exponentially harmonic convex functions and discuss their relations with convex functions. Optimality conditions are characterized by a class of variational inequalities, called exponentially harmonic variational inequalities. Several interesting results characterizing the exponen- tially convex functions are obtained. Results obtained in this paper can be viewed as significant improvement of previously known results. [ABSTRACT FROM AUTHOR]

In this paper, we prove Clunie lemmas for a polynomial generated by shifts, q-shifts of a meromorphic function and their derivatives which in turn allow us to study the growth of a solution of larger class of difference-differential equations. The results obtained in this paper generalize earlier results on Clunie lemmas. [ABSTRACT FROM AUTHOR]