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In this paper we consider an asymptotic version of α-ψ contractive mappings in vector metric spaces and give some fixed point theorems on this spaces.

In this paper we consider an asymptotic version of α-ψ contractive mappings in vector metric spaces taking value in Riesz spaces. and prove fixed point theorem on this spaces.

This manuscript was built to generalize Ekeland variational principle for mixed monotone functions in the setting of partially ordered complete metric spaces. The results obtained are applied to give different proofs for tripled fixed points of mixed monotone mappings in the mentioned space by using a variational technique. The results presented in our manuscripts generalize and expand many of the findings presented in the earlier period. For the sobriety and enhancement of our paper, two examples are given and the existence and uniqueness of the solution to a periodic boundary value problem are studied as applications.

The aim of this work is to give some fixed point results based on the technique of measure of noncompactness which extend the classical Darbo’s theorem. With the help of our Darbo-type theorem, we obtain the existence of solution of implicit fractional integral equations in C ( I , l p α ) (collection of all continuous functions from I = [ 0 , a ] ( a > 0 ) to l p α ), where l p α is a tempered sequence space. Finally, we present a numerical example to see the validity and practicability of our existence result.

In this article, we establish that any uniformly local Mizoguchi-Takahashi contraction is actually a set-valued contraction due to Feng and Liu on a metrically convex complete metric space. Through an example, we demonstrate that this result need not hold on any arbitrary metric space. Furthermore, when the metric space is compact, we derive that any Mizoguchi-Takahashi local contraction and Nadler local contraction are equivalent. Moreover, a result related to invariant best approximation is established., Keywords: Fixed points; Set-valued map; metrically convex metric space; uniformly local contractions

In this paper, we introduce the concept of multi-valued almost E-contractions. We then present some approximate fixed point and fixed point results for such mappings in metric spaces. Our results generalize and improve several well-known results in literature. We also provide several illustrative examples to compare our findings with some earlier results. An application to homotopy theory is given.

We determine the common fixed point of two maps satisfying Hardy-Roger type contraction in a complete partial b-metric space without exploiting any variant of continuity or commutativity, which is indispensable in analogous results. Towards the end, we give examples and an application to solve a Cantilever beam problem employed in the distortion of an elastic beam in equilibrium to substantiate the utility of these improvements.

In the present paper, we study the existence and convergence of the best proximity point for cyclic Θ \Theta -contractions. As consequences, we extract several fixed point results for such cyclic mappings. As an application, we present some solvability theorems in the topic of variational inequalities.

In this paper, we introduce a new method to analyze the convergence of the standard finite element method for Hamilton-Jacobi-Bellman equation with noncoercive operators with nonlinear source terms with the mixed boundary conditions. The method consists of combining Bensoussan-Lions algorithm with the characterization of the solution, in both the continuous and discrete contexts, as fixed point of contraction. Optimal error estimates are then derived, first between the continuous algorithm and its finite element counterpart and then between the continuous solution and the approximate solution.

In this paper, using a new shrinking projection method and generalized resolvents of maximal monotone operators and generalized projections, we consider the strong convergence for finding a common point of the fixed points of a Bregman quasi-nonexpansive mapping, and common fixed points of a infinite family of Bregman weak relatively nonexpansive mappings, and common zero points of a finite family of maximal monotone mappings, and common solutions of an equilibrium problem in a reflexive Banach space., 28 pages. arXiv admin note: substantial text overlap with arXiv:2107.13254

The concept of coupled 𝔉-orthogonal contraction mapping is introduced in this paper, and some coupled fixed point theorems in orthogonal metric spaces are proved. The obtained results generalize and extend some of the well-known results in the literature. An example is presented to support our results. Furthermore, we apply our result to obtain the existence theorem for a common solution of the integral equations: ζ ( v ) = ð ( v ) + ∫ 0 M Ξ ( v , β ) Ω ( β , ζ ( β ) , ξ ( β ) ) d β , v ∈ [ 0 , H ] , ξ ( v ) = ð ( v ) + ∫ 0 M Ξ ( v , β ) Ω ( β , ξ ( β ) , ζ ( β ) ) d β , v ∈ [ 0 , H ] , \left\{\begin{array}{ll}\zeta \left({\mathfrak{v}})=ð\left({\mathfrak{v}})+\underset{0}{\overset{{\mathfrak{M}}}{\displaystyle \int }}\Xi \left({\mathfrak{v}},\beta )\Omega \left(\beta ,\zeta \left(\beta ),\xi \left(\beta )){\rm{d}}\beta ,& {\mathfrak{v}}\in \left[0,{\mathscr{H}}],\\ \xi \left({\mathfrak{v}})=ð\left({\mathfrak{v}})+\underset{0}{\overset{{\mathfrak{M}}}{\displaystyle \int }}\Xi \left({\mathfrak{v}},\beta )\Omega \left(\beta ,\xi \left(\beta ),\zeta \left(\beta )){\rm{d}}\beta ,& {\mathfrak{v}}\in \left[0,{\mathscr{H}}],\end{array}\right. where (a) ð : M → R ð:{\mathfrak{M}}\to {\mathbb{R}} and Ω : M × R × R → R \Omega :{\mathfrak{M}}\times {\mathbb{R}}\times {\mathbb{R}}\to {\mathbb{R}} are continuous; (b) Ξ : M × M \Xi :{\mathfrak{M}}\times {\mathfrak{M}} is continuous and measurable at β ∈ M , ∀ \beta \in {\mathfrak{M}},\hspace{0.33em}\forall v ∈ M {\mathfrak{v}}\in {\mathfrak{M}} ; (c) Ξ ( v , β ) ≥ 0 , ∀ v , β ∈ M \Xi \left({\mathfrak{v}},\beta )\ge 0,\hspace{0.33em}\forall {\mathfrak{v}},\beta \in {\mathfrak{M}} and ∫ 0 H Ξ ( v , β ) d β ≤ 1 , ∀ v ∈ M {\int }_{0}^{{\mathscr{H}}}\Xi \left({\mathfrak{v}},\beta ){\rm{d}}\beta \le 1,\hspace{0.33em}\forall {\mathfrak{v}}\in {\mathfrak{M}} .

Objectives We investigated the existence and uniqueness of a fixed point for the mapping satisfying generalized rational type contraction conditions in metric space endowed with partial order. Suitable examples are presented to justify the results obtained. Result Some new fixed point results have been obtained for a mapping fulfilling generalized contractions. The uniqueness of the fixed point is also the part of the study based on an ordered relation. One example is given for a result which is not valid in the usual metric space.

In this paper we study a class of impulsive systems of stochastic differential equations with infinite Brownian motions. Sufficient conditions for the existence and uniqueness of solutions are established by mean of some fixed point theorems in vector Banach spaces. An example is provided to illustrate the theory.

This paper is devoted to discuss Hilfer fractional evolution equations through its controllability and stability in a Banach space. We achieve our claims and conclusions by first demonstrating the nature and uniqueness of the suggested set of equations with their mild solutions. The outcomes of existence and uniqueness are obtained with the aid of the propagation family theory, non-compactness calculation methods and the fixed point technique. An example is also provided for the description of our main results.

We introduce existence and convergence theorems on two modified proximal point algorithms for convex functions in Hadamard spaces.

In this article, we prove a weak convergence theorem of Mann's type iteration for infinite families of extended generalized hybrid mappings in a Banach space satisfying Opial's condition. This theorem solves a problem posed by Hojo and Takahashi [8]. Using this result, we get well-known and new weak convergence theorems in a Banach space. In particular, we obtain a weak convergence theorem of Mann's type iteration for finite families of extended generalized hybrid mappings in a Banach space.

We state existence and convergence theorems for finding fixed points of spherically nonspreading mappings in CAT(1) spaces. These results can be applied to convex optimization in such spaces.

In this paper, we introduce two iterative methods (one implicit method and one explicit method) for finding a common element of the zero point set of a set-valued maximal monotone operator, the solution set of the variational inequality problem for a continuous monotone mapping, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative methods to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets. The main theorems develop and complement some well-known results in the literature.

This work intends to treat the existence of mild solutions for the Hilfer fractional hybrid differential equation (HFHDE) with linear perturbation of first and second type in partially ordered Banach spaces. First, we establish the results concerning the actuality of fixed point of sum and product of operators via the concepts of measure of noncompactness and simulation functions in partially ordered spaces. Then combining these fixed point theorems with the concepts in fractional calculus, new existence results for mild solutions of HFHDE’s are established. Furthermore, the presented fixed point results and existence results improve and extend the present state-of-art in the literature. Competent examples in support of theory are illustrated for better understanding.

Altun et al. explored the existence of fixed points for multivalued F F -contractions and proved some fixed point theorems in complete metric spaces. This paper extended the results of Altun et al. in partial metric spaces and proved fixed point theorems for multivalued F F -contraction mappings. Some illustrative examples are provided to support our results. Moreover, an application for the existence of a solution of an integral equation is also enunciated, showing the materiality of the obtained results.

In this work it was proved Matkowski’s fixed point theorem. The consequences of this theorem are also presented.

We deal with some impulsive Caputo-Fabrizio fractional differential equations in b b -metric spaces. We make use of α - ϕ \alpha \text{-}\phi -Geraghty-type contraction. An illustrative example is the subject of the last section.

In this article, we prove the generalized Hyers-Ulam-Rassias stability for the following composite functional equation:f(f(x)−f(y))=f(x+y)+f(x−y)−f(x)−f(y),f(f\left(x)-f(y))=f\left(x+y)+f\left(x-y)-f\left(x)-f(y),whereffmaps from a(β,p)\left(\beta ,p)-Banach space into itself, by using the fixed point method and the direct method. Also, the generalized Hyers-Ulam-Rassias stability for the compositess-functional inequality is discussed via our results.

In this paper, we convert the recent COVID-19 model with the use of the most influential theories, such as variable fractional calculus and fuzzy theory. We propose the fuzzy variable fractional differential equation for the COVID-19 model in which the variable fractional-order derivative is described using the Caputo-Fabrizio in the Caputo sense. Furthermore, we provide the results on the existence and uniqueness using Lipschitz conditions. Also, discuss the stability analysis of the present new COVID-19 model by employing Hyers-Ulam stability.

A generalized metric type space is a generic name for various spaces similar to hyperconvex metric spaces or extensions of them. The purpose of this article is to introduce some KKM theoretic works on generalized metric type spaces and to show that they can be improved according to our abstract convex space theory. Most of these works are chosen on the basis that they can be improved by following our theory. Actually, we introduce abstracts of each work or some contents, and add some comments showing how to improve them.

In this paper, we consider a certain fixed point theorem that contains some rational expressions. The main aim of this paper is to prove a fixed point theorem without using the Picard iteration.

In this paper, we obtain a fixed point theoremω-ψ-interpolative Hardy-Rogers contractive of Suzuki type mappings. In the following, we present an example to illustrate the new theorem is applicable. Subsequently, some results are given. These results generalize several new results present in the literature.

In this paper, we prove some fixed point theorems for a Meir-Keeler type Contraction in rectangularM−metric space. Thus, our results extend and improve very recent results in fixed point theory.

In this study, a new iterative method for third-order boundary value problems based on embedding Green’s function is introduced. The existence and uniqueness theorems are established, and necessary conditions are derived for convergence. The accuracy, efficiency and applicability of the results are demonstrated by comparing with the exact results and existing methods. The results of this paper extend and generalize the corresponding results in the literature.

In this paper, we prove some common fixed point theorems on bicomplex metric space. Our results generalize and expand some of the literature’s well-known results. We also explore some of the applications of our key results.

In this paper, we will establish, in two and three dimensions, the local well-posedness result in [math] of the nonlinear regularized Schrödinger equation using the Strichartz estimates for the regularized Schrödinger equation on exterior domains established previously. Then, we will prove, the global existence and uniqueness result in [math] .

In this paper, we introduce a new algorithm for solving pseudomonotone variational inequalities with a Lipschitz-type condition in a real Hilbert space. The algorithm is constructed around two algorithms: the subgradient extragradient algorithm and the inertial algorithm. The proposed algorithm uses a new step size rule based on local operator information rather than its Lipschitz constant or any other line search scheme and functions without any knowledge of the Lipschitz constant of an operator. The strong convergence of the algorithm is provided. To determine the computational performance of our algorithm, some numerical results are presented.

In this paper, we study the solution of fractal energy integral equation for one-dimensional compressible flows without body force using measure of noncompactness. We also discuss the solution of the local fractal equation of losing energy system using the notion of local fractal differential idea. For this, a new notion of χ - Δ -set contraction condition under simulation function is defined and two main fixed point and coupled fixed point results are obtained.

In 1968, M. G. Maia [16] generalized Banach’s fixed point theorem for a set X endowed with two metrics. In 2014, Ansari [2]introduced the concept of C-class functions and generalized many fixed point theorems in the literature. In this paper, we prove some Maia’s type fixed point results via C-class function in the setting of two metrics space endowed with a binary relation. Our results, generalized and extended many existing fixed point theorems, for generalized contractive and quasi-contractive mappings, in a metric space endowed with binary relation.

In this paper, a general form of the Suzuki type function is considered on S- metric space, to get a fixed point. Then we show that our results generalize some old results.

In this paper, we study the Hyers-Ulam stability of a nonautonomous semilinear reaction-diffusion equation. More precisely, we consider a nonautonomous parabolic equation with a diffusion given by the fractional Laplacian. We see that such a stability is a consequence of a Gronwall-type inequality.

In this work, the existence of Hilfer fractional integro-differential equations with nonlocal conditions are discussed. To obtain such result, we use M o ¨ nch fixed point theorem and the techniques of noncompactness. An application is presented to validate the theoretical results.

Y. Xu (2016) investigated existence results of Caputo fractional differential equations with integral and anti-periodic boundary conditions of fractional order α ∈ ( 1 , 2 ) . In this paper, we investigate the existence of solutions for fractional differential equation with integral and anti-periodic boundary conditions due to Y. Xu for infinite systems in the multivalued case (inclusions). Our results are based on a suitable fixed point theorem for condensing maps due to Martelli (1975). Finally, we present an illustrative example to verify the effectiveness and applicability of the main results.

The aim of this paper is to establish some fixed point results for surrounding quasi-contractions in non-triangular metric spaces. Also, we prove the Banach principle of contraction in non-triangular metric spaces. As applications of our theorems, we deduce certain well-known results in b-metric spaces as corollaries.