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Very recently, P. Saha et al. [A global optimality result in probabilistic spaces using control function. Optimization. 2021;70:2387–2400] studied the existence of best proximity points for Banach type ϕ-proximal contractions in the framework of Menger probabilistic metric spaces. In this paper, we present a simple proof of their main existence result which is based on a fixed point theorem for ϕ-contractive self-mappings in complete Menger PM-spaces due to B.S. Choudhury and K. Das [A new contraction principle in Menger spaces. Acta Math Sin. 2008;24:13791386]. [ABSTRACT FROM AUTHOR]

Recently, Altun et al. [1] introduced the notion of p-proximal contractions and p-proximal contractive mappings and discussed about best proximity point results for this two classes of mappings. After that, Gabeleh and Markin [3] showed that the best proximity point theorem for p-proximal contractions proved in [1] follows from the same conclusion fixed point theory. In this short note, we show that the best proximity point theorem for p-proximal contractive mappings follows from the corresponding fixed point result for metric spaces. [ABSTRACT FROM AUTHOR]

In a recent paper [I. Altun and A. Tasdemir, On best proximity points of interpolative proximal contractions, Quaestiones Math. (2020), DOI: ] the authors proved two best proximity point theorems for a new class of non-self mappings, called interpolative Reich-Rus-Ćirić type proximal contractions of the first and second kinds. Our purpose is to show that their results follow from a fixed point theorem for interpolative Reich-Rus-Ćirić type contraction mappings [E. Karapinar, R. Agarwal and H. Aydi, Interpolative Reich-Rus-Ćirić contractions on partial metric spaces, Mathematics 6 (2018), 7 pages]. [ABSTRACT FROM AUTHOR]

Very recently Jain et al. (J. Inequal. Appl. 2022:73, 2022) introduced the concept of multivalued F-contraction with altering distance function and investigated the existence of best proximity points for this class of mappings. In this article we prove that the existence of best proximity points for multivalued F-contraction non-self mappings can be obtained from the corresponding fixed point result for multivalued F-contraction self mappings, and so the main conclusion due to Jain et al. is not a real generalization of fixed point theory. [ABSTRACT FROM AUTHOR]

Recently, Altun et al. [1] introduced the notion of p-proximal contractions and discussed about best proximity point results for this class of mappings. Then Gabeleh and Markin [4] showed that the best proximity point theorem proved by Altun et al. in [1] follows from the fixed point theory. In this short note, we show that if the p-proximal contraction constant k < 1 3 then the existence of best proximity point for p-proximal contractions follows from the celebrated Banach contraction principle. [ABSTRACT FROM AUTHOR]

Very recently, I. Altun, M. Aslantas and H. Sahin [1] introduced the notion of p -proximal contractions and surveyed the existence of best proximity points for such class of non-self mappings in metric spaces. In this note we show that this existence result is a straightforward consequence of the same conclusion in fixed point theory. [ABSTRACT FROM AUTHOR]

Collage Theorem provides a bound for the distance between an element of a given space and a fixed point of a self-map on that space, in terms of the distance between the point and its image. We give in this paper some results of Collage type for Reich mutual contractions in b-metric and strong b-metric spaces. We give upper and lower bounds for this distance, in terms of the constants of the inequality involved in the definition of the contractivity. Reich maps contain the classical Banach contractions as particular cases, as well as the maps of Kannan type, and the results obtained are very general. The middle part of the article is devoted to the invertibility of linear operators. In particular we provide criteria for invertibility of operators acting on quasi-normed spaces. Our aim is the extension of the Casazza-Christensen type conditions for the existence of inverse of a linear map defined on a quasi-Banach space, using different procedures. The results involve either a single map or two operators. The latter case provides a link between the properties of both mappings. The last part of the article is devoted to study the construction of fractal curves in Bochner spaces, initiated by the first author in a previous paper. The objective is the definition of fractal curves valued on Banach spaces and Banach algebras. We provide further results on the fractal convolution of operators, defined in the same reference, considering in this case the nonlinear operators. We prove that some properties of the initial maps are inherited by their convolutions, if some conditions on the elements of the associated iterated function system are satisfied. In the last section of the paper we use the invertibility criteria given before in order to obtain perturbed fractal spanning systems for quasi-normed Bochner spaces composed of Banach-valued integrable maps. These results can be applied to Lebesgue spaces of real valued functions as a particular case. [ABSTRACT FROM AUTHOR]

This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature. [ABSTRACT FROM AUTHOR]

Our study in this paper is focused on the split equality fixed-point problem with firmly quasi-non-expansive operators in infinite-dimensional Hilbert spaces. A self-adaptive simultaneous scheme is introduced, and its weak convergence is established under mild and standard assumptions. The new proposed scheme generalizes and extends some related works in the literature, and its simple structure makes it easy for implementation and numerical testing. Primary experiments presented in this paper, in finite- and infinite-dimensional spaces, emphasize their practical advantages over existing results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is twofold. Firstly, certain common fixed point theorems are established via φ-contractive multivalued mappings involving point-dependent control functions as coefficients in the framework of complex valued metric spaces. Our results improve and extend several results in the existing literature. Moreover, this section is equipped by some illustrative examples in support of our results. Secondly, we point out some slip-ups in the examples of some recent papers based on multivalued contractive mappings in complex valued metric spaces. Our observations are also authenticated with the aid of some appropriate examples. Some rectifications to correct the erratic examples are also suggested. [ABSTRACT FROM AUTHOR]

In this paper, a (p , q) -fractional nonlinear difference equation of different orders is considered and discussed. With the help of (p , q) -calculus for integrals and derivatives properties, we convert the main integral boundary value problem (IBVP) to an equivalent solution in the form of an integral equation, we use the upper–lower solution technique to prove the existence of positive solutions. We present an example of the IBVP to apply and demonstrate the results of our method. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of variational inequality problems the constraint set of which is the set of common solutions of a finite family of operator equations, involving hemi-continuous accretive operators on a reflexive and strictly convex Banach space with a Gâteaux differentiable norm. We present a sequential regularization method of Lavrentiev type and an iterative regularization one in combination with an inertial term to speed up convergence. The strong convergence of the methods is proved without the co-coercivity imposed on any operator in the family. An application of our results to solving the split common fixed point problem with pseudocontractive and nonexpansive operators is given with computational experiments for illustration. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of unified interpolative contractions of the Reich–Rus–Ćirić type and give some results about the fixed points for these mappings in the framework of relational metric spaces. We present examples where the results of some previous research are not relevant. Also, we apply our results to solving problems related to nonlinear matrix equations, emphasizing their practical importance. [ABSTRACT FROM AUTHOR]

In this paper, we study split common fixed point problems with multiple output sets in Hilbert spaces. For solving this problem, we improve Reich and Tuyen's algorithms [10] and propose two new self-adaptive algorithms which do not need any priori information on the norms of the transfer operators. Then, we establish weak convergence theorems for them. It can be seen from our numerical experiments that the proposed methods depict a very significant improvement in terms of the number of iterations and execution time. [ABSTRACT FROM AUTHOR]

The notion of A -condensing operators via the measure of noncompactness is proposed, which retains the existing classes of condensing operators. Results concerning the existence of the best proximity point (pair) of cyclic (noncyclic) A -condensing operators along with the coupled best proximity-point theorem for cyclic A -condensing operators have been formulated. An application to a (k , ℷ) -Hilfer fractional differential equation of order 2 < p < 3 , type q ∈ [ 0 , 1 ] satistfying some boundary conditions is presented. The paper is the first to investigate the optimum solution of such a generalized fractional differential equation. The hypothesis involved in the investigation is independent of the incorporated measure of noncompactness, thereby making our result better in application than that present in the literature. Moreover, added numerical examples validate the theoretical conclusions. [ABSTRACT FROM AUTHOR]

In this paper, an inertial subgradient extragradient algorithm is proposed to solve the pseudomonotone variational inequality problems in Banach space. This iterative scheme employs a new line-search rule. Strong convergence theorems for the proposed algorithms are established under the assumptions that the operators are non-Lipschitz continuous. Furthermore, several numerical experiments are given to show that our method has better convergence performance than the known ones in the literatures. [ABSTRACT FROM AUTHOR]

In this note, we give affirmative answers to two open problems posed by Agarwal et al. in the paper (J Optim Theory Appl 163(2):482-490, ). [ABSTRACT FROM AUTHOR]

In this paper, we mainly introduce a new algorithm with a different line-search process for solving variational inequality problem of pseudomonotone and non-Lipschitz operators in real Hilbert spaces. Under some appropriate restrictions imposed on the parameters, we prove a strong convergence theorem for finding an element of solutions of variational inequality problem. At the same time, we give some numerical examples to illustrate the effectiveness of our proposed algorithm. The main results obtained in this paper extend and improve many recent ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we study the split common fixed point problem for a finite family of demimetric mappings and a finite family of Bregman relatively nonexpansive mappings in p-uniformly convex and uniformly smooth Banach spaces. We prove a strong convergence theorem of Halpern's type iteration for finding a solution of the split common fixed point problem. The iterative scheme does not require prior knowledge of operator norm. The obtained result of this paper complements many recent results in this direction. [ABSTRACT FROM AUTHOR]

The foremost target of the proposed work focuses on establishing fixed point theorems for the new concept named Intuitionistic fuzzy cone-b metric space (in short IFCbMS). Various definitions like compatible mappings, weakly-compatible maps (WC maps) and E.A. property are also used to prove new results for IFCbMS. The proofs of fixed points for FMS, IFMS, NFMS in the setting of E.A. property are taken as base for this research. Examples mentioned in the paper are increasing the importance of the research done. An application is also given to show the importance of the result proved. The application of this paper leads to the solution of an integral equation in context of implicit functions. [ABSTRACT FROM AUTHOR]

Let H be a Hilbert space and let C be a closed convex nonempty subset of H and $$T : C\rightarrow H$$ a non-self nonexpansive mapping. A map $$h : C\rightarrow R$$ defined by $$h(x) := \inf \{\lambda \ge 0 : \lambda x+(1-\lambda )Tx \in C \}$$ . Then, for a fixed $$x_0 \in C$$ and for $$\begin{aligned}{\alpha _0} = \max \left\{ {\frac{1}{2},h({x_0})} \right\}\end{aligned}$$ , Krasnoselskii-Mann algorithm is defined by $$x_{n+1}=\alpha _n+(1-\alpha _n)Tx_n,$$ where $$\alpha _{n+1}=\max \{\alpha _n, h(x_{x_{n+1}})\}$$ . Recently, Colao and Marino (Fixed Point Theory Appl 2015:39, 2015) have proved both weak and strong convergence theorems when C is a strictly convex set and T is an inward mapping. Meanwhile, they proposed a open question for a countable family of non-self nonexpansive mappings. In this article, authors will give an answer and will prove the further generalized results with the examples to support them. [ABSTRACT FROM AUTHOR]

We show that the result on cyclic weak contractions of Harjani et al. (J. Nonlinear Sci. Appl. 6:279-284, ) holds without the assumption of compactness of the underlying space, and also without the assumption of continuity of the given mapping. [ABSTRACT FROM AUTHOR]

The aim of this paper is to discuss some results concerning the demiclosedness principle of generalized, nonexpansive mappings in uniformly convex spaces. Further, we present some new fixed-point theorems for generalized nonexpansive mappings in different settings of Banach spaces. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative inertial simultaneous cyclic iterative algorithm designed to address a range of mathematical problems within the realm of split equality variational inequalities. Specifically, the algorithm accommodates finite families of split equality variational inequality problems, infinite families of split equality variational inclusion problems, and multiple-sets split equality fixed point problems involving demicontractive operators in infinite-dimensional Hilbert spaces. The algorithm integrates well-established methods, including the cyclic method, the inertial method, the viscosity approximation method, and the projection method. We establish the strong convergence of this proposed algorithm, demonstrating its applicability in various scenarios and unifying disparate findings from existing literature. Additionally, a numerical example is presented to validate the primary convergence theorem. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the solution of a class of monotone inclusion problems in reflexive Banach spaces. To reflect the geometry of the space and the operator, a more general proximal point iterative algorithm with Bregman divergence is proposed and some strong convergence results for the proposed scheme under standard assumptions are obtained. Meanwhile, the convex optimization problems and the critical point problems are studied in the applications, and the recovery of the sparse signal is simulated in the numerical experiments. [ABSTRACT FROM AUTHOR]

The paper presents an abstract theory regarding the problems with semilinear operator equations involving iterates of a strongly monotone symmetric linear operator. We obtain existence and localization results of positive solutions for such problems using Krasnosel'skiĭ's technique and abstract Harnack inequality. In particular, we obtain results for problems with semilinear poly-Laplace operators. [ABSTRACT FROM AUTHOR]

Let A and B be two nonempty subsets of a normed space X, and let T : A ∪ B → A ∪ B be a cyclic (resp., noncyclic) mapping. The objective of this paper is to establish weak conditions on T that ensure its relative nonexpansiveness. The idea is to recover the results mentioned in two papers by Matkowski (Banach J. Math. Anal. 2:237–244, 2007; J. Fixed Point Theory Appl. 24:70, 2022), by replacing the nonexpansive mapping f : C → C with a cyclic (resp., noncyclic) relatively nonexpansive mapping to obtain the best proximity pair. Additionally, we provide an application to a functional equation. [ABSTRACT FROM AUTHOR]

In this paper, motivated by Reich contraction and tool of measure of noncompactness, some generalizations of Reich, Kannan, Darbo, Sadovskii, and Krasnoselskii type fixed point results are presented by considering a pair of maps A, B on a nonempty closed subset M of a Banach space X into X. The existence of a solution to the equation A x + B x = x , where A is k-set contractive and B is a generalized Reich contraction, is established. As applications, it is established that the main result of this paper can be applied to learn conditions under which a solution of a nonlinear integral equation exists. Further we explain this phenomenon with the help of a practical example to approximate such solutions by using fixed point techniques. The graphs of exact and approximate solutions are also given to attract readers for further research activities. [ABSTRACT FROM AUTHOR]

The aim of this paper is to broaden the applicability of convex orbital (α , β) -contraction mappings to geodesic spaces. This class of mappings is a natural extension of iterated contraction mappings. The paper derives fixed-point theorems both with and without assuming continuity. Furthermore, the paper investigates monotone convex orbital (α , β) -contraction mappings and establishes a fixed-point theorem for this class of mappings. [ABSTRACT FROM AUTHOR]

This paper explores the concept of normal structure by introducing a generalized form known as P-proximal normal structure. Focusing on the framework of Hausdorff locally convex spaces, the study establishes optimal proximity outcomes for both cyclic and noncyclic relatively P-nonexpansive mappings. Furthermore, the paper presents in the realm of probabilistic normed spaces, considered as instances of Hausdorff locally convex spaces, some theorems that address the existence of best proximity points within this context. [ABSTRACT FROM AUTHOR]

The present paper is concerned with the Ekeland Variational Principle (EkVP) and its equivalents (Caristi–Kirk fixed point theorem, Takahashi minimization principle, Oettli-Théra equilibrium version of EkVP) in quasi-uniform spaces. These extend some results proved by Hamel and Löhne [A minimal point theorem in uniform spaces. In: Nonlinear analysis and applications: to V. Lakshmikantham on his 80th birthday. Vols 1, 2. Dordrecht: Kluwer Academic Publishers; 2003. p. 577–593] and Hamel [Equivalents to Ekeland's variational principle in uniform spaces. Nonlinear Anal. 2005;62:913–924] in uniform spaces, as well as those proved in quasi-metric spaces by various authors. The case of F-quasi-gauge spaces, a non-symmetric version of F-gauge spaces introduced by Fang [The variational principle and fixed point theorems in certain topological spaces. J Math Anal Appl. 1996;202:398–412], is also considered. The paper ends with the quasi-uniform versions of some minimization principles proved by Arutyunov and Gel'man [The minimum of a functional in a metric space, and fixed points. Zh Vychisl Mat Mat Fiz. 2009;49:1167–1174] and Arutyunov [Caristi's condition and existence of a minimum of a lower bounded function in a metric space. Applications to the theory of coincidence points. Proc Steklov Inst Math. 2015;291(1):24–37] in complete metric spaces. [ABSTRACT FROM AUTHOR]

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

In this paper, we solve the system of functional equations { f (x + y) + g (y − x) = 2 f (x) , g (x + y) − f (y − x) = 2 g (y) and we investigate the stability of g-derivations in Banach algebras. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two types of weak enriched contractions, namely weak enriched F -contraction, weak enriched F ′ -contraction, and k-fold averaged mapping based on Kirk's iterative algorithm of order k. The types of contractions introduced herein unify, extend, and generalize several existing classes of enriched and weak enriched contraction mappings. Moreover, K-fold averaged mappings can be viewed as a generalization of the averaged mappings and double averaged mappings. We then prove the existence of a unique fixed point of the k-fold averaged mapping associated with weak enriched contractions introduced herein. We study necessary conditions that guarantee the equality of the sets of fixed points of the k-fold averaged mapping and weak enriched contractions. We show that an appropriate Kirk's iterative algorithm can be used to approximate a fixed point of a k-fold averaged mapping and of the two weak enriched contractions. We also study the well-posedness, limit shadowing property, and Ulam–Hyers stability of the k-fold averaged mapping. We provide necessary conditions that ensure the periodic point property of each illustrated weak enriched contraction. Some examples are presented to show that our results are a potential generalization of the comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

The contraction condition in the Banach contraction principle forces a function to be continuous. Many authors overcome this obligation and weaken the hypotheses via metric spaces endowed with a partial order. In this paper, we present some coupled fixed point theorems for the functions having mixed monotone properties on ordered vector metric spaces, which are more general spaces than partially ordered metric spaces. We also define the double monotone property and investigate the previous results with this property. In the last section, we prove the uniqueness of a coupled fixed point for non-monotone functions. In addition, we present some illustrative examples to emphasize that our results are more general than the ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of Hadamard 픇-hom-der on Banach algebras. Further, we apply the fixed point method to prove the stability of the Hadamard 픇-hom-der on Banach algebras. [ABSTRACT FROM AUTHOR]

In this paper, we first investigate the existence and uniqueness of solution for the Darboux problem with modified argument on both bounded and unbounded domains. Then, we derive different types of the Ulam stability for the proposed problem on these domains. Finally, we present some illustrative examples to support our results. [ABSTRACT FROM AUTHOR]

In this paper, we initiate the fixed point theorems for an orthogonal hybrid interpolative Riech Istrastescus type contractions map on orthogonal b-metric spaces to modify this class proficiently. Also, we provide some examples supporting our main results. Finally, we provide an application to solve the existence and uniqueness of an integral equation with numeric results, which is powerful in a greater way. [ABSTRACT FROM AUTHOR]

In this paper, we propose the notion of extended neutrosophic rectangular metric space and prove some fixed point results under contraction mapping. Finally, as an application of the obtained results, we prove the existence and uniqueness of the Caputo fractional differential equation. [ABSTRACT FROM AUTHOR]

Cyclic mappings describe fixed paths for which each point is sequentially transmitted from one set to another. Cyclic mappings satisfying certain cyclic contraction conditions have been used to obtain the best proximity points, which constitute a suitable framework for the mirror reflection model. Alternative contraction mappings introduced by Chen (Symmetry 11:750, 2019) built a new model containing several mirrors in which the light reflected from a mirror does not go to the next mirror sequentially, and its path may diverge to any other mirror. The aim of this paper is to present a new variant of alternative contraction called alternative p-contraction and study its properties. The best proximity point result for such contractions under the alternative UC property is proved. An example to support the result proved herein is provided. [ABSTRACT FROM AUTHOR]

This paper provides convergence analysis of some variants of the hybrid extragradient algorithm (HEA) in Hilbert spaces. We employ the HEA to compute the common solution of the equilibrium problem and split fixed-point problem associated with the finite families of k -demicontractive mappings. We also incorporate appropriate numerical results concerning the viability of the proposed variants with respect to various real-world applications. [ABSTRACT FROM AUTHOR]

This paper studies the existence of radial solutions of the boundary value problem of p-Laplace equation with gradient term { − Δ p u = K (| x |) f (| x | , u , | ∇ u |) , x ∈ Ω , ∂ u ∂ n = 0 , x ∈ ∂ Ω , lim | x | → ∞ u (x) = 0 , where Ω = { x ∈ R N : | x | > r 0 } , N ≥ 3 , 1 < p ≤ 2 , K : [ r 0 , ∞) → R + , and f : [ r 0 , ∞) × R × R + → R are continuous. Under certain inequality conditions of f, the existence results of radial solutions are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we apply the Cădariu–Radu method derived from the Diaz–Margolis theorem to investigate existence, uniqueness approximation of Ξ-Hilfer fractional differential equations, and Hypergeometric stability for both finite and infinite domains. An example is given to illustrate the main result for a fractional system. [ABSTRACT FROM AUTHOR]

In this paper, by combining the inertial technique and the gradient descent method with Polyak's stepsizes, we propose a novel inertial self-adaptive gradient algorithm to solve the split feasibility problem in Hilbert spaces and prove some strong and weak convergence theorems of our method under standard assumptions. We examine the performance of our method on the sparse recovery problem beside an example in an infinite dimensional Hilbert space with synthetic data and give some numerical results to show the potential applicability of the proposed method and comparisons with related methods emphasize it further. [ABSTRACT FROM AUTHOR]

A modular string averaging procedure (MSA, for short) for a finite number of operators was first introduced by Reich and Zalas in 2016. The MSA concept provides a flexible algorithmic framework for solving various feasibility problems such as common fixed point and convex feasibility problems. In 2001 Bauschke and Combettes introduced the notion of coherence and applied it to proving weak and strong convergence of many iterative methods. In 2019 Barshad, Reich and Zalas proposed a stronger variant of coherence which provides a more convenient sufficient convergence condition for such methods. In this paper we combine the ideas of both modular string averaging and coherence. Focusing on extending the above MSA procedure to an infinite sequence of operators with admissible controls, we establish strong coherence of its output operators. Various applications of these concepts are presented with respect to weak and strong convergence. They also provide important generalizations of known results, where the weak convergence of sequences of operators generated by the MSA procedure with intermittent controls was considered. [ABSTRACT FROM AUTHOR]

In this paper, we study a nonlinear fractional p-Laplacian boundary value problem containing both left Riemann–Liouville and right Caputo fractional derivatives with initial and integral conditions. Some new results on the existence and uniqueness of a solution for the model are obtained as well as the Ulam stability of the solutions. Two examples are provided to show the applicability of our results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of a class of impulsive nonlinear evolution partial differential equations. We give new results about existence and multiplicity of global classical solutions. The method used is based on the use of fixed points for the sum of two operators. Our main results will be illustrated by an application to an impulsive Burgers equation. [ABSTRACT FROM AUTHOR]

This paper concerns the existence, uniqueness and stability of solutions of stochastic Volterra integral equations perturbed by some random processes. The obtained results extend, generalize and enrich the theory of stochastic Volterra integral equations in literature. Lastly, for illustration, we give an example that agrees with the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, using the method of Hicks, we prove some new related fixed point theorems for pair of mappings on two d-complete topological spaces under the suitable conditions. We also derive some related fixed point theorems from our main results. Finally, by using w-continuity, we establish a related fixed point theorem in d-complete Hausdorff topological spaces. [ABSTRACT FROM AUTHOR]

In this paper, in the first part, we will improve and extend the main results 1 and 2 of Mishra et al. [6] in a b-metric space, and in the second and last part, we will improve and extend Theorem 5 and Theorem 6 of Shah [7] in a b-metric-like space, in both sections, we will use our new notion of occasionally weakly biased maps of type (풜). Some illustrative examples are given in order to clarify and support our findings. [ABSTRACT FROM AUTHOR]