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This paper presents a straightforward statement for Khamsi's theorem without assuming continuity or nondecreasing restrictions on η. Additionally, a new proof provides an affirmative answer to Kirk's problem, supported by examples. Finally, Ekeland's variational principle (abbreviated EVP) is developed. [ABSTRACT FROM AUTHOR]

In this paper we solve a fixed point problem formulated through a combination of three different contemporary trends in fixed point theory, namely, φ-fixed point results, coupled fixed point results and the use of w-distances. We have cited examples to illustrate our main theorem and to demonstrate how our theorem generalizes some known theorems and augments the domain of applicability of our result to a larger family of functions compared to these previous results. Well-posedness property of the problem is established. In a separate section we discuss two different applications of our result to problems of integral equations and functional equations. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze two new results on the Mittag–Leffler–Ulam–Hyers stability for a class of nonlinear fractional reaction–diffusion equations with delay. We demonstrate that these equations exhibit Ulam–Hyers–Mittag–Leffler stability on a compact interval with respect to the Chebyshev and Bielecki norms, using fixed–point method. These results extend and encompass many previous findings while offering notable improvements. To illustrate the practical applications of our results, we provide three examples. Despite extensive literature on the Lyapunov, Ulam, and Mittag–Leffler stability of fractional equations with and without delays, there is limited research on the Mittag–Leffler–Ulam–Hyers stability of fractional equations with delay. Hence, a key aim of this work is to address this gap by exploring a class of nonlinear fractional reaction–diffusion equations with delay and establishing new results on their Mittag–Leffler–Ulam–Hyers stability. [ABSTRACT FROM AUTHOR]

In this paper, we establish sufficient conditions for the existence of solutions for a class of initial value problems for impulsive fractional differential equations involving the deformable fractional derivative. We achieve our results using classical fixed point theorems such as the Banach contraction principle, the Shaefer and the alternative Leray–Schauder theorems. We provide an example to illustrate our abstract results. [ABSTRACT FROM AUTHOR]

The objective of this study is to analyze a quasistatic frictional contact problem involving the interaction between a thermo-viscoelastic body and a thermally conductive foundation. The constitutive relation in our investigation is constructed using a fractional Kelvin–Voigt model to describe displacement behavior. Additionally, the heat conduction aspect is governed by a time-fractional derivative parameter that is associated with temperature. The contact is modeled using the Signorini condition, which is a version of Coulomb's law for dry friction. We develop a variational formulation for the problem and establish the existence of its weak solution using a combination of techniques, including the theory of monotone operators, Caputo derivative, Galerkin method, and the Banach fixed point theorem. To demonstrate the effectiveness of our approach, we include several numerical simulations that showcase the performance of the method. [ABSTRACT FROM AUTHOR]

This article proves the existence and uniqueness conditions of the solution of two-dimensional time-space tempered fractional diffusion-wave equation. We find analytical solution of the equation via the two-step Adomian decomposition method (TSADM). The existence result is obtained with the help of some fixed point theorems, while the uniqueness of the solution is a consequence of the Banach contraction principle. Additionally, we study the stability via the Ulam-Hyers stability for the considered problem. The existing techniques use numerical algorithms for solving the two-dimensional time-space tempered fractional diffusion-wave equation, and thus, the results obtained from them are the approximate solution of the problem with high computational and time complexity. In comparison, our proposed method eliminates all the difficulties arising from numerical methods and gives an analytical solution with a straightforward process in just one iteration. [ABSTRACT FROM AUTHOR]

In this article, some concepts of locally (δ , ϕ) -dominated mappings, locally (δ , ϕ) -continuous mappings and L R − (δ , ϕ) complete dislocated quasi-metric spaces have been introduced. Fixed point results for such mappings under new contractive conditions in these spaces have been established. As an application, fixed point results endowed with order and graph in such spaces have been examined. Furthermore, the results are substantiated with specific examples. Our empirically validated results represent a novel contribution to the existing body of literature. [ABSTRACT FROM AUTHOR]

In this paper, we define some new product types of rational contractions for single‐valued mappings in generalized metric spaces. We prove the uniqueness of fixed point (FP) and common fixed point (CFP) theorems under the new product types of rational contractions in generalized metric spaces with the application of boundary value problem. In support of our results, we present nontrivial illustrative examples for the uniqueness of FP and CFP in generalized metric spaces. Furthermore, we present an application of the first‐order periodic boundary value problem for the existence of unique solutions to unify our work. Using this approach, one can prove some more attractive unique FP and CFP results for different types of modified rational contractions in generalized metric spaces with the application of integral equations and boundary value problems. [ABSTRACT FROM AUTHOR]

In this paper, we present an existence result for ω-periodic solutions for an infinite system of third-order differential equations in a classical Banach sequence space c. This result is obtained using techniques related to measures of noncompactness together with the concept of Meir–Keeler condensing operators, considering the respective Green's function corresponding to the system. To illustrate the significance of our results, we provide some concrete examples. [ABSTRACT FROM AUTHOR]

This paper introduces a new class of contractions in JS-metric spaces and utilizes it to obtain fixed point results, which generalize several well-known results. Moreover, an example is given to illustrate the utility of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper we propose new averaged iterative algorithms designed for solving a split common fixed point problem in the class of demicontractive mappings. The algorithms are obtained by inserting an averaged term into the algorithms used in [Li, R. and He, Z., A new iterative algorithm for split solution problems of quasi-nonexpansive mappings J. Inequal. Appl.131 (2015), 1–12.] for solving the same problem but in the class of quasi-nonexpansive mappings, which is a subclass of demicontractive mappings. Basically, our investigation is based on the embedding of demicontractive operators in the class of quasi-nonexpansive operators by means of averaged mappings. For the considered algorithms we prove weak and strong convergence theorems in the setting of a real Hilbert space. A numerical example is given to illustrate the results. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to state nonexpansive Maia type fixed point theorems for Ćirić–Prešić operators in normed spaces endowed with a partial order. For this we do a thorough analysis in the hypotheses of our theorems, considering different properties of completeness, compactness, convexity and bounding. We state Maia type fixed point theorems for contraction and nonexpansive Ćirić–Prešić operators, including those defined by a multiply metric function. Fixed point theorems in spaces without a partial order, as well as, corollaries for monotone nonexpansive mappings are stated too. Our theorems generalize and improve results given by Ćirić and Prešić's (Acta Math Univ Comenian (NS) 76:143–147, 2007) and Balazs (Mathematica 10:18–31, 2018) and extend them to nonexpansive operators. [ABSTRACT FROM AUTHOR]

This work presents the concept of controlled dislocated metric spaces, and the Banach contraction principle in these spaces is examined. Next, we provide extensive examples of numerical convergence of fixed points to demonstrate the practical implications of such spaces. Along with specific instances, it presents the idea of a rational contraction of the $ \digamma - $ ϝ − type to determine common fixed points in such spaces. Moreover, numerical analysis and graphical comparisons are used to further assess the existence of common fixed points based on the provided notions. Lastly, using these ideas to solve a Volterra integral equation shows how useful they are for finding common solutions, improving our comprehension of fixed point theory in these spaces, and creating new avenues for applications. [ABSTRACT FROM AUTHOR]

The objective of this paper is to suggest and construct a general four step semi-implicit iterative scheme involving midpoint rule. We establish and analyse the convergence of the suggested scheme to reckon the fixed point of an almost contraction mapping. Also, we prove the stability of the suggested iterative scheme. Finally, suggested method and our main results are applied to examine a general variational inequality and a nonlinear integral equation. [ABSTRACT FROM AUTHOR]

In this paper, we study three fixed point problems. The first one is a fixed point problem with a set-valued mapping, while the second and third problems are convex feasibility problems with infinitely many constraints solved by the subgradient projection algorithm. We show that an approximate solution is reached after a finite number of iterations under the presence of computational errors. [ABSTRACT FROM AUTHOR]

Goebel's coincidence theorem, a remarkably simple extension of Banach's contraction principle widely applied in analysis, has found significant utility in the theory of differential and integral equations. Over the past fifty years, researchers have endeavored to generalize the definition of a metric space, thereby extending the scope of Goebel's coincidence theorem to diverse settings. This survey paper overviews valuable insights into Goebel's coincidence theorem's historical background, its relevance in the field of fixed point theory, and its practical implications in solving problems related to differential and integral equations. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the controllability in the α-norm for some impulsive partial functional integrodifferential equation with infinite delay in Banach space. To do this, we give sufficient conditions ensuring the controllability by assuming that the undelayed part admits a resolvent operator in the sense of Grimmer and that the delayed part is continuous with respect to the fractional power of the generator. The results are obtained by using the Schauder fixed-point theorem. [ABSTRACT FROM AUTHOR]

This paper study a class of time-space fractional reaction-diffusion equations with nonlocal initial conditions and construct an abstract theory in fractional power spaces to discuss the results related S-asymptotically ω -periodic mild solutions. When the coefficients are sufficiently small, under the condition that the nonlinear term can grow any number of orders, we discuss the existence and uniqueness of S-asymptotically ω -periodic solutions based on the theory of operator semigroups and fixed point theorem. In addition, we considered the Mittag-Leffler-Ulam-Hyers stability results using the singular type Gronwall inequality and appropriate fractional calculus. The results in the present paper extended the work of (Andrade et al. in Proc Edinb Math Soc 59:65–76, 2016) to the case of time-space fractional nonlocal reaction-diffusion equations. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence of p : q resonant orbit for the dissipative spin–orbit problem of the celestial mechanics. Our result is the generalization of the work (Biasco and Chierchia in J Differ Equ 246(11):4345–4370, 2009) from C ∞ topology to analytic and finitely differentiable topology. Moreover, our result gives the existence condition of p : q resonance solutions for concrete dissipative spin–orbit model under arbitrary potential frequency μ , which can reduce to result in work (Biasco and Chierchia in J Differ Equ 246(11):4345–4370, 2009) when μ = 2 . It is also a generalization from low-order resonance to arbitrary-order resonance. Our proof is based on Lyapunov–Schmidt decomposition, the contraction mapping principle on Sobolev space H s and H ρ , s and perturbation theory. [ABSTRACT FROM AUTHOR]

This article considers a Volterra-Fredholm integro-differential equation including multiple time-varying delays. The aim of this article is to study the uniqueness of solution, the Ulam–Hyers–Rassias stability and the Ulam–Hyers stability of the Volterra-Fredholm integro-differential equation including multiple time-varying delays. We prove four new results in connection with the uniqueness of solution, the Ulam–Hyers–Rassias stability and the Ulam–Hyers stability of the considered Volterra-Fredholm integro-differential equation, respectively. The new results of this article involve sufficient conditions. The techniques of the proofs depend on the fixed point method according to the definitions of a suitable metric, operators and the related calculations. In particular case of the considered Volterra-Fredholm integro-differential equation, two illustrative examples are presented to verify the applications of the results. This article also involves some new complementary outcomes in connection with qualitative theory of Volterra-Fredholm integro-differential equations with delays. [ABSTRACT FROM AUTHOR]

The primary goal of this paper is to study and examine an inertial modified S-iteration method that combines modified S-iteration with inertial extrapolation term to approximate a common solution of the Cayley inclusion problem and the fixed point problem in the framework of real Hilbert space. Under some modest circumstances, we prove weak and strong convergence theorems. A numerical example is also provided to demonstrate the effectiveness of the proposed iterative algorithm. Finally, a comparison has also been carried out of our algorithm with an existing method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel approach to approximate the solution of variational inequality problems without relying on the monotonicity assumption. We propose a two-step inertial modified projection and contraction method for solving quasi-monotone and without-monotone variational inequalities in real Hilbert spaces. We establish a weak convergence result for the proposed method under suitable conditions. Additionally, numerical examples and a network equilibrium flow problem are provided to illustrate the effectiveness of our method and compare it with recent related methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the concept of Wardowski's class of contraction is integrated with that of g-coupling to define some F-contractive type g-couplings. We establish existence results for a coupled coincidence point, a strong coupled coincidence point, and a coupled best proximity point for these couplings within the framework of complete metric space. Additionally, we establish the existence of a coupled coincidence point for multivalued F-contractive type g -coupling. Further, an application of our result with regard to the existence of a system of nonlinear integral equations is discussed. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the existence of solutions to a stationary neutron transport equation involving elastic and inelastic collision operators in $ L^p $ L p - espaces $ (1\leq p \lt \infty) $ (1 ≤ p < ∞). For $ 1 \lt p \lt \infty $ 1 < p < ∞ , we use the Krasnosel'slii fixed point theorem and the compactness which involved by the averaging result for neutron transport equation. For p = 1, our approach is different, it uses the measure of weak noncompactness of De Blasi, the concepts of Dunford–Pettis operators together with a recent version of Krasnosel'skii's fixed point theorem involving ws -compact and ww -compact operators and the weak compactness. [ABSTRACT FROM AUTHOR]

This paper aims to investigate new coincidence point theorems for self‐maps under an extended rational contraction. Our approach uses the p‐adic distance in partially ordered ultrametric spaces. Furthermore, to illustrate our major discoveries, we give a comprehensive numerical analysis. This study expands on prior research in partially ordered ultrametric spaces to provide a more comprehensive understanding of such spaces using rational contraction. [ABSTRACT FROM AUTHOR]

This paper presents a systematic approach to investigating the existence of solutions for fractional integro-differential equation systems incorporating delay and relaxation impulsive terms. By employing suitable definitions of fractional derivatives, we establish physically interpretable boundary conditions. To account for abrupt state changes, impulsive conditions are integrated into the model. The system is transformed into an equivalent integral equation, facilitating the application of Banach and Schaefer fixed-point theorems to prove the existence and uniqueness of solutions. The practical applicability of our findings is demonstrated through an illustrative example. [ABSTRACT FROM AUTHOR]

The primary focus of this study is how to expedite the convergence rate of the extragradient method by tactfully choosing inertial parameters and building up the step-size rule. To achieve this goal, we introduce three improvements to Korpelevich's extragradient method. These improvements include the use of dual inertial steps as well as a self-adaptive step-size rule. The proposed iterative techniques are employed for solving equilibrium problems in real Hilbert spaces. Initially, we establish the results for weak convergence of the proposed methods, assuming the involved bifunction to be both pseudomonotone and Lipschitz-type continuous. Subsequently, we demonstrate linear convergence in scenarios where the bifunction is strongly pseudomonotone and Lipschitz-type continuous. Finally, we present multiple numerical experiments to illustrate the practical effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The aim of this article is to present, in a specific metric space, a density theorem. Then, as an application, we give a relaxation theorem for a first-order set-differential inclusion, through an abstract convexity notion. [ABSTRACT FROM AUTHOR]

In this work, we investigate a contraction-type method for solving monotone variational inclusion problems in real Hilbert spaces. We obtain strong convergence theorems for two algorithms with a self-adaptive step size for solving monotone variational inclusions. The advantage of our algorithms is that we do not require a cocoercivity assumption nor do we need to know the Lipschitz-type constant of the single-valued operator. Moreover, a convergence rate is derived in the case where one of the operators is maximally and strongly monotone, and the other is monotone and Lipschitz continuous. The performance of our proposed methods is illustrated by numerical experiments regarding signal recovery. Our results improve and extend some known results, and our experiments show that our proposed algorithms are efficient and outperform other algorithms which are available in the literature. [ABSTRACT FROM AUTHOR]

We show that if X is a complete metric space with uniform relative normal structure and G is a subgroup of the isometry group of X with bounded orbits, then there is a point in X fixed by every isometry in G. As a corollary, we obtain a theorem of U. Lang (2013) concerning injective metric spaces. A few applications of this theorem are given to the problems of inner derivations. In particular, we show that if L 1 ⁢ (μ) is an essential Banach L 1 ⁢ (G) -bimodule, then any continuous derivation δ : L 1 ⁢ (G) → L ∞ ⁢ (μ) is inner. This extends a theorem of B. E. Johnson (1991) asserting that the convolution algebra L 1 ⁢ (G) is weakly amenable if G is a locally compact group. [ABSTRACT FROM AUTHOR]

We focus on two alternating inertial projection iterative algorithms to a class of split common null point problem, specifically, the common solution of the pseudomonotone variational inequality problem and the fixed-point problem of demi-contractive mapping. We construct the relation between the inertial parameters and Mann's iteration coefficients to obtain the convergence, which in turn allows some interesting results, that is, the traditional constraints on inertia parameters can be removed. Meanwhile, we give two numerical examples to verify the superiority and effectiveness of the schemes. [ABSTRACT FROM AUTHOR]

This study concerns a Krasnoselskii-type fixed point theorem for the sum of two operators A,BA,B in a Banach space EE, where BB is a Reich-type contractive mapping and AA is a k-set contractive mapping. We introduce a class of operators θ:X×X→[1,+∞)\theta :X\times X\to \left[1,+\infty ) satisfying some axioms and use it as a new metric to prove a fixed point theorem in the spirit of Azam et al. [Reich-Krasnoselskii-type fixed point results with applications in integral equations, J. Inequal. Appl. 2023 (2023), 131].

This article aims to provide a modified Noor iterative scheme to approximate the fixed points of generalized nonexpansive mappings with property (EE) called MN-iteration. We establish the strong and weak convergence results in a uniformly convex Banach space. Additionally, numerical experiments of the iterative technique are demonstrated using a signal recovery application in a compressed sensing situation. Ultimately, an illustrative analysis regarding Noor, SP-, and MN-iteration procedures is obtained via polysomnographic techniques. The images obtained are called polynomiographs. Polynomiographs have importance for both the art and science aspects. The obtained graphs describe the pattern of complex polynomials and also the convergence properties of the iterative method. They can also be used to increase the functionality of the existing polynomiography software.

The problem of common solutions for nonlinear equations has significant theoretical and practical value. In this article, we first introduce a new concept of a pair of (α,Θ)\left(\alpha ,\Theta )-type contractions, and then, we present some common fixed point results for the contractions in complete metric spaces. Finally, our results are applied to consider the existence, uniqueness and approximation of common solutions for two classes of nonlinear fractional differential equations.

Krasnoselskii’s iteration is a classical and important method for approximating the fixed point of an operator that satisfies certain conditions. Many authors have used this approach to obtain several famous fixed point theorems for different types of operators. It is well known that Kirk’s iteration can be seen as a generalization of Krasnoselskii’s iteration, in which the iterates are generated by a certain generalized averaged mapping. This approximation method is of great practical significance because the iterative formula contains more information related to the operator in question. The purpose of this study is to define weak (αn,βi)\left({\alpha }_{n},{\beta }_{i})-convex orbital Lipschitz operators. These concepts not only extend the previously introduced Popescu-type convex orbital (λ,β)\left(\lambda ,\beta )-Lipschitz operators in Fixed-point results for convex orbital operators, (Demonstr. Math. 56 (2023), 20220184), but also encompass many classical contractive operators. Popescu also proved a fixed point result for his proposed operator using the graphic contraction principle and obtained an approximation of the fixed point with Krasnoselskii’s iterates. To extend Popescu’s main results from Krasnoselskii’s iterative scheme to Kirk’s iterative scheme, several fixed point theorems are established, in which an appropriate Kirk’s iterative algorithm can be used to approximate the fixed point of a kk-fold averaged mapping associated with our presented convex orbital Lipschitz operators. These results not only generalize, but also complement the existing results documented in the previous literature.

In this study, we introduce the following additive functional equation:g(λu+v+2y)=λg(u)+g(v)+2g(y)g\left(\lambda u+v+2y)=\lambda g\left(u)+g\left(v)+2g(y) for all λ∈C\lambda \in {\mathbb{C}}, all unitary elements u,vu,v in a unital Poisson C*{C}^{* }-algebra PP, and all y∈Py\in P. Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of the aforementioned additive functional equation in unital Poisson C*{C}^{* }-algebras. Furthermore, we apply to study Poisson C*{C}^{* }-algebra homomorphisms and Poisson C*{C}^{* }-algebra derivations in unital Poisson C*{C}^{* }-algebras.

In this paper, based on Mann-type and Halpern-type algorithms, we introduce two modified extragradient algorithms with novel stepsize rules and inertial technique for solving pseudo-monotone variational inequality problems in Hilbert and reflexive Banach spaces. Under some reasonable assumptions on the parameters, strong convergence and R-linear convergence results for our methods are established without prior knowledge of the Lipschitz constant of the bounded operator. Moreover, we provide some numerical experiments to demonstrate the efficiency of our proposed algorithm, and numerical results reveal that our algorithm outruns other algorithms in the literature. [ABSTRACT FROM AUTHOR]

We propose a new concept of stability, called here as “aggregated multi-stability”, which is based on multiple aggregation functions and also uses Mittag-Leffler and hypergeometric functions. This is inspired by the general framework of the Ulam, Hyers and Rassias types of stability, but differs in essence both in the multi-dependency of various aggregation functions and in choosing special functions to play the role of controllers. This notion is applied here to a class of J -Hilfer fractional differential equations for which we identify sufficient conditions to guarantee its aggregated multi-stability. [ABSTRACT FROM AUTHOR]

The objective of this article is to obtain coincidence points and common fixed point theorem in complete partial metric space. We provide some examples to support the usability of our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate two types of Levitin–Polyak well-posedness for split equilibrium problems. We establish the binary gap function of split equilibrium problems and present sufficient and necessary conditions to characterize two types of Levitin–Polyak well-posedness of split equilibrium problems. Further, based on the upper semicontinuity of the approximate solution sets, we propose equivalent characterizations of the type I Levitin–Polyak well-posedness. Under certain conditions, we prove that split equilibrium problems are type I Levitin–Polyak well-posed if and only if the solution sets are nonempty and compact in finite-dimensional spaces. Numerical examples are provided to illustrate the proposed findings. [ABSTRACT FROM AUTHOR]

This paper focuses on the approximate controllability of Sobolev-type fuzzy Hilfer fractional neutral integro-differential inclusions involving the Clarke subdifferential. We establish the approximate controllability of this inclusion problem using fuzzy set theory, Sobolev-type methods, Fractional calculus, and Clarke subdifferentials. These techniques help to derive the necessary conditions for approximate controllability of the system. Dhage’s fixed point theorem is applied to prove the results related to approximate controllability. Finally, an example is provided to illustrate the discussion. [ABSTRACT FROM AUTHOR]

In this paper, we study the concept of bilevel variational inequality featuring strongly monotone variational inequality over the solution set of the split variational inequality problem with multiple output sets in real Hilbert spaces. We propose two new two-step inertial iterative methods with self-adaptive step sizes for approximating the problem’s solution in the framework of Hilbert spaces. Our proposed algorithms eliminate the dependence on the norm of the transformation operators and the strongly monotone and Lipschitz continuous constants of the involved operators. Furthermore, strong convergence results are obtained without the co-coerciveness of the associated single-valued operators. Finally, we apply our result to study certain classes of split inverse problems and we present several numerical experiments to demonstrate the implementability of the proposed method. [ABSTRACT FROM AUTHOR]

The split common fixed point problem is an optimization challenge that involves finding an element within one fixed point set such that when transformed by a bounded linear operator, it belongs to another fixed point set. This problem falls under the category of inverse problems in mathematics. We present a novel self-adaptive algorithm based on double inertial steps for solving the split common fixed point problem for demicontractive mappings. We also establish a weak convergence theorem for our method. Furthermore, we also present some numerical experiments illustrating the convergence behavior and the efficiency of our proposed algorithm. [ABSTRACT FROM AUTHOR]

We introduce the notion of (α , ν) -relaxed polygonal metric spaces, where α > 0 and ν : [ 0 , ∞) → [ 0 , ∞) is a function satisfying certain conditions. This notion generalizes the concept of s-relaxed p metric spaces proposed by Fagin et al. (SIAM J Discrete Math 17(1): 134–160, 2003). The originality of the introduced notion is justified by examples of (α , ν) -relaxed polygonal metric spaces that are not s-relaxed p metric spaces. We establish several properties of (α , ν) -relaxed polygonal metric spaces. In particular, we introduce the concept of (α , ν) -metric bounded distance, and show that, if δ : Z × Z → [ 0 , ∞) is symmetric, then δ is a (α , ν) -relaxed polygonal metric, if and only if δ is a (α , ν) -metric bounded distance. We next define the convergence of sequences, Cauchy sequences, and completeness. We also establish some fixed point results in (α , ν) -relaxed polygonal metric spaces. Namely, we extend the Banach contraction principle and the Kannan fixed point theorem from metric spaces to (α , ν) -relaxed polygonal metric spaces. The novelty of our fixed point results are supported by examples in which the standard Banach and Kannan fixed point theorems are not applicable. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the existence of solution of a generalized Hadamard proportional fractional integral equations involving non-singular kernels. First, we introduce Hadamard fractional integral equations. Then, we demonstrate the existence of the solution of Hadamard proportional fractional integral equations based on the concept of a measure of noncompactness and Petryshyn's fixed point theorem. After that, we provide suitable examples which evidence the existing result. [ABSTRACT FROM AUTHOR]

In this work we are interested in proving a general common fixed point theorem for a pair of multi-valued mappings satisfying a new type of implicit relation in complex-valued b-metric spaces. The results in this paper generalize the results obtained in Ahmad et al. (in: Abstract and Applied Analysis, vol 2013, p 12, 2013; J Linear Topol Algebra 9(1):75–94, 2020). An example and an application to a complex linear system are given to support our results. [ABSTRACT FROM AUTHOR]

In this paper, we propose an alternated multi-step inertial iterative algorithm for solving the split feasibility problem involving two bounded linear operators in Hilbert spaces. The proposed algorithm adopts self-adaptive step size and the step size is bounded away from zero. Under some mild conditions, the strong convergence of the sequence generated by the proposed algorithm is established. Finally, the numerical experiments are presented to verify the effectiveness and superiority of our proposed algorithm. Our results are innovative and can be an enrichment to the recently published results in the literature. [ABSTRACT FROM AUTHOR]

Developing a model of fractional differential systems and studying the existence and stability of a solution is considebly one of the most important topics in the field of analysis. Therefore, this manuscript was dedicated to deriving a new type of fractional system that arises from the combination of three sequential fractional derivatives with fractional pantograph equations. Also, the fixed-point technique was used to evaluate the existence and uniqueness of solutions to the supposed hybrid model. Furthermore, stability results for the intended system in the sense of the Mittag-Leffler-Ulam have been investigated. Ultimately, an illustrative example has been highlighted in order to reinforce the theoretical results and suggest applications for this article.

The objective of this study is to determine the criteria under which the infinite system of integral equations in three variables has a solution in the Banach tempering sequence space c0β{c}_{0}^{\beta } and ℓ1β{\ell }_{1}^{\beta }, utilizing the Meir-Keeler condensing operators. Our research builds upon the findings of Malik and Jalal. Furthermore, we provide illustrative examples to demonstrate the implications of our established conditions.

In this study, we generalize fuzzy metric-like, non-Archimedean fuzzy metric-like, and all the variants of fuzzy metric spaces. We propose the idea of fuzzy metric-unlike and non-Archimedean fuzzy metric-unlike, respectively. We also propose the idea of (α,F)\left(\alpha ,F)-Geraghty-type generalized FF-contraction mappings utilizing fuzzy metric-unlike and non-Archimedean fuzzy metric-unlike spaces. We investigate the presence of unique fixed points using the recently introduced contraction mappings. In order to complement our study, we consider an application to dynamic market equilibrium.