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The present paper is in two folds. In the first fold, we prove the Lipschitz continuity of the proximal mapping associated with a general strongly H-monotone mapping and compute an estimate of its Lipschitz constant under some mild assumptions imposed on the mapping H involved in the proximal mapping. We provide two examples to show that a maximal monotone mapping need not be a general H-monotone for a single-valued mapping H from a Banach space to its dual space. A class of multi-valued nonlinear variational inclusion problems is considered, and by using the notion of proximal mapping and Nadler's technique, an iterative algorithm with mixed errors is suggested to compute its solutions. Under some appropriate hypotheses imposed on the mappings and parameters involved in the multi-valued nonlinear variational inclusion problem, the strong convergence of the sequences generated by the proposed algorithm to a solution of the aforesaid problem is verified. The second fold of this paper investigates and analyzes the notion of Cn-monotone mappings defined and studied in [S.Z. Nazemi, A new class of monotone mappings and a new class of variational inclusions in Banach spaces, J. Optim. Theory Appl. 155(3)(2012) 785-795]. Several comments related to the results and algorithm appeared in the above mentioned paper are given. [ABSTRACT FROM AUTHOR]

In this note we point out some errors in the paper "On the set of solutions for the Darboux problem for fractional order partial hyperbolic functional differential inclusions" by S. Abbas and M. Benchohra published in Fixed Point Theory, vol. 14, no. 2, 2013, 253-262. [ABSTRACT FROM AUTHOR]

In the paper "AIMS Math. 5 (2020), no. 6, 6448-6456", Tian et al. [15, Theorem 1] considered a linear system of integro-time delay differential equations (IDDEs) with constant time retardation. In [15], firstly, a generalized double integral inequality was obtained and then less conservative asymptotically stability criteria were proposed by using that double integral inequality and choosing a new Lyapunov-Krasovskii functional (LKF). To the best of the information, we would like to note that the asymptotically stability criteria of Tian et al. [15, Theorem 1] consist of very interesting but strong conditions. However, in this paper, we define a more suitable LKF, then we obtain the result of Tian et al. [15, Theorem 1] for uniformly asymptotically stability under very weaker conditions using the LKF and also investigate the integrability of the norm and boundedness of solutions. To show the effectiveness of our results, two numerical examples are proposed for the uniformly asymptotically stability as well as integrability and boundedness of solutions. By this work, we do contributions to the work of Tian et al. [15, Theorem 1] under very weaker conditions and those in the previous relevant literature, and we obtain two more new results on the integrability of the norm of solutions and boundedness of solutions. The results of this paper are new and they may be useful for researchers working on the topics of this paper. [ABSTRACT FROM AUTHOR]

The paper contains a brief summary of the generalization of metrical structure regarding the fixed point theorem and corresponding operator equation problems. We observed that many researcher either tried to weaken the metrical structure, the contraction condition, or both. The idea behind this paper is to look for a minimal metrical structure to establish fixed point theorems. In this connection, we present new variants of the known fixed point theorem under non-triangular metric space (namely F-contraction, (A; S)-contraction, (A; S)-contraction). We also apply the obtain result in solving various types of operator equation problems. e.g., high-order fractional differential equation with non-local boundary conditions and non-linear integral equation problems. [ABSTRACT FROM AUTHOR]

A new iterative algorithm is proposed for finding a common solution of an equilibrium problem and a fixed point problem. Then, a strong convergence theorem is proved. As a consequence, they can be obtained some strong convergence theorems for an equilibrium problem and a split common fixed point problem. The obtained theorems can be applied to solve an equilibrium problem and a split common null point problem. The results presented in this paper extend and improve some corresponding ones in the literature. Finally, a numerical example is given to show the validity of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we study the following Schrödinger-Kirchhoff type equations involving the fractional p-Laplacian ... and H(x), we obtain the existence of positive ground state solutions and discuss their asymptotical behavior via the method used by Bartsch and Wang [Multiple positive solutions for a nonlinear Schrödinger equation. Z. Angew. Math. Phys. 51 (2000) 366-384]. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the nonemptiness and boundedness of the set of zeros of a monotone operator in Hadamard spaces. Two coercivity conditions R1 and R2 are proposed. The equivalence between the nonemptiness of the set of zeros of a monotone operator and coercivity condition R1 is established. Moreover, it is shown that coercivity condition R2 is a su_cient and necessary condition for the boundedness of the set of zeros of a monotone operator. Some applications in convex minimization and fixed point theory are also presented to support the main results. [ABSTRACT FROM AUTHOR]

In this paper, a self-adaptive algorithm involving inertial technique will be introduced to solve bilevel pseudo-monotone variational inequality problems in Hilbert spaces. The main advantages of our algorithm is that the strong convergence theorem of the stated iterative method is proved without Lipschitz continuity condition of the associated mapping. Finally, the effectiveness and superiority of the proposed algorithm are proposed by numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, two generalized algorithms for solving the variational inequality problem in Banach spaces are proposed. Then the strong convergence of the sequences generated by these algorithms will be proved under suitable conditions. Finally, using MATLAB software, we provide some numerical examples to illustrate our results. [ABSTRACT FROM AUTHOR]

A generalized method of alternating resolvents was introduced by Boikanyo and Moro{\c s}anu as a way to approximate common zeros of two maximal monotone operators. In this paper we analyse the strong convergence of this algorithm under two different sets of conditions. As a consequence we obtain effective rates of metastability (in the sense of Terence Tao) and quasi-rates of asymptotic regularity. Furthermore, we bypass the need for sequential weak compactness in the original proofs. Our quantitative results are obtained using proof-theoretical techniques in the context of the proof mining program. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new notion of generalized α-φ-Geraghty proximal contraction mappings and investigate the existence of the best proximity point for such mappings in complete metric spaces. The obtained results extend, generalize, and complement some known fixed and best proximity point results from the literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider the notion of generalized multi-valued F contraction mappings and prove fixed point theorems for this type mappings. Finally, we construct non-trivial example to validate the potential of our result. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish a general fixed point theorem for mean nonexpansive multivalued mappings defined on weakly compact and convex subsets of Banach spaces with property (D). The main result obtained in this paper significantly extends and improves many of the well-known results in the existing literature. [ABSTRACT FROM AUTHOR]

In the book, Fixed Point Structure Theory (I.A. Rus, Fixed Point Structure Theory, Cluj Univ. Press, Cluj-Napoca, 2006) there are studied fixed point structures on a set with structure. In this paper we introduce the notion of the set-mapping pair (U;M) (i.e., U:= a class of sets with the same type structure and for X; Y 2 U a set of mappings, M(X; Y), from X to Y is given) and the notion of fixed point structure (f.p.s.) on a such pair. After some examples of f.p.s. we study the preserving of the fixed point property by, (U;M)-bijections, retractions, cartesian product and exponential. We give some fixed point results in terms of a f.p.s. and we consider some special f.p.s.: f.p.s. with common fixed point property, with coincidence point property and with coincidence producing mappings. Some open problems are also formulated. [ABSTRACT FROM AUTHOR]

In their recent papers, A.V. Arutyunov and A.V. Greshnov introduced (q1; q2)-quasimetric spaces and studied their properties: investigated covering mappings between (q1; q2)- quasimetric spaces, established sufficient conditions for the existence of a coincidence point for two mappings acting between (q1; q2)-quasimetric spaces such that one is a covering mapping and the other is Lipschitz continuous, proved Banach's fixed point theorem, obtained generalizations for multivalued mappings. The class of (q1; q2)-quasimetric spaces is sufficiently wide; it includes quasimetric spaces, b-metric spaces, Carnot-Caratheodory spaces with Box-quasimetics, Lp-spaces with p 2 (0; 1), etc. The development of the theory of coincidence points of mappings on (q1; q2)- quasimetric spaces initiated interest in the study of more general f-quasimetric spaces and in generalizing Banach's fixed point theorem to such spaces. The present paper is a review of these results. [ABSTRACT FROM AUTHOR]

In this paper we give some fixed point theorems for nonself operators on a large Kasahara space, which generalize some results given by I.A. Rus and M.-A. Sérban (I.A. Rus, M.-A. Serban, Some fixed point theorems for nonself generalized contractions, Miskolc Math. Notes, 17(2016), no.2, 1021-1031) and by S. Reich and A.J. Zaslavski (S. Reich, A.J. Zaslavski, A note on Rakotch contractions, Fixed Point Theory, 9(2008), no.1, 267-273). [ABSTRACT FROM AUTHOR]

In this paper, we prove a general fixed point theorem for ultrametric n-Banach spaces. We also show its applications in proving the hyperstability, in the sense of Gavruta, of the following monomial functional equation ...? [ABSTRACT FROM AUTHOR]

In this paper we present some suggestions for unifying the terminology of the mappings appearing in fixed point iterative methods for the case when the setting is a metric space. We consider the following concepts: contraction type mapping, contractive type mapping and nonexpansive type mapping, for which some problems are formulated. [ABSTRACT FROM AUTHOR]

In this paper we study the existence of multiple nontrivial positive weak solutions to the following system of problems. We will guarantee the existence of a solution in the Nehari manifold. Further by using the Lusternik-Schnirelman category we will prove the existence of at least cat(?) + 1 number of solutions. [ABSTRACT FROM AUTHOR]

In this paper, we propose the viscosity method for solving variational inequality problems defined over a set of fixed points of a nonexpansive mapping and involving a Τ-contraction mapping and another nonexpansive mapping in the setting of Hadamard manifolds. Several special cases of such a variational inequality problem are also considered. The convergence analysis of the proposed method is studied. We illustrate proposed algorithm and convergence result by a numerical example. The algorithms and convergence results of this paper extend and improve several known algorithms and results from linear structure to Hadamard manifolds. [ABSTRACT FROM AUTHOR]

In this paper we present a variety of Leray-Schauder type continuation theorems for general classes of weakly Mönch type maps. [ABSTRACT FROM AUTHOR]

In this paper, by using the Guo-Krasnoselskii theorem, we investigate the existence and nonexistence of positive solutions of a class of boundary value problem of third-order nonlinear differential equation involving Stieltjes integral conditions. Under some growth conditions imposed on the nonlinear term, we obtain explicit ranges of values of parameters with which the problem has a positive solution and has no positive solution respectively. An example is given to illustrate the main results of the paper. [ABSTRACT FROM AUTHOR]

In this paper we prove a new version of Kransoselskii's fixed-point theorem under a (ψ, θ, ϕ)-weak contraction condition. The theoretical result is applied to prove the existence of a solution of the following fractional hybrid differential equation involving the Riemann-Liouville differential and integral operators orders of 0<α<1 and β>0: ... where Dα is the Riemann-Liouville fractional derivative order of α, Iβ is Riemann-Liouville fractional integral operator order of β>0, J=[t0, t0+a], for some fixed t0∈ ℝ, a>0 and the functions f: J × ℝ → ℝ and g: J × ℝ × ℝ → ℝ satisfy certain conditions. An example is also furnished to illustrate the hypotheses and the abstract result of this paper. [ABSTRACT FROM AUTHOR]

In this paper, under some new appropriate conditions imposed on the parameter and mappings involved in the resolvent operator associated with an (H; η)-monotone operator, its Lipschitz continuity is proved and an estimate of its Lipschitz constant is computed. This paper is also concerned with the establishment of a new equivalence relationship between the graph convergence of a sequence of (H; η)-monotone operators and their associated resolvent operators, respectively, to a given (H; η)-monotone operator and its associated resolvent operator. A new iterative scheme for approximating a common element of the set of solutions of a variational inclusion problem and the set of fixed points of a given total asymptotically nonexpansive mapping is constructed. As an application of the obtained equivalence conclusion concerning graph convergence, under some suitable conditions, the strong convergence of the sequence generated by our suggested iterative algorithm to a common element of the above-mentioned two sets is proved. Our results improve and generalize the corresponding results of recent works. [ABSTRACT FROM AUTHOR]

In this paper, we present some results concerning the existence and attractivity of solutions for generalized Cauchy problem involving Hilfer fractional derivative using the well-known Krasnoselskii fixed point theorem and the measure of noncompactness. Finally, some examples are provided to illustrate the efficiency of the results. [ABSTRACT FROM AUTHOR]

In this paper, we study a viscosity approximation method for finding a nearest fixed point of a continuous pseudo-contraction mapping in a Hadamard space. We applied our result to solve some convex minimization problems. We also present an example to validate our new findings. This work substantially improves and generalizes some well-known results in the literature. [ABSTRACT FROM AUTHOR]

This paper addresses the numerical solution of the matrix square root problem. Two fixed point iterations are proposed by rearranging the nonlinear matrix equation A - X² = 0 and incorporating a positive scaling parameter. The proposals only need to compute one matrix inverse and at most two matrix multiplications per iteration. A global convergence result is established. The numerical comparisons versus some existing methods from the literature, on several test problems, demonstrate the efficiency and effectiveness of our proposals. [ABSTRACT FROM AUTHOR]

In this paper we investigate the existence of mild solutions for a class of first-order nonlinear impulsive functional differential inclusions with nonlocal condition in Banach spaces. Sufficient condition for the existence is obtained with the help of Martelli's fixed point theorem. We generalize some relevant results and give an example to illustrate the main result. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce a viscosity-type proximal point algorithm for approximating a common solution of a finite family of equilibrium problems and fixed point problem for a certain class of nonspreading-type mappings recently introduced by Phuengrattana [Applied General Topology 18(2017), 117-129]. We further establish a strong convergence of our proposed algorithm to a common solution of a finite family of equilibrium problems which is also a fixed point of this class of mappings and a unique solution of some variational inequality problems in an Hadamard space. We also analyse the asymptotic behaviour of the sequence generated by a viscosity-type algorithm and extend the analysis to approximate a common solution of a finite family of equilibrium problems in an Hadamard space. Furthermore, we applied our results to solve some optimization problems in Hadamard spaces. [ABSTRACT FROM AUTHOR]

In this paper we obtain nonlinear alternatives of Leray-Schauder and Mönch type for nonself vector-valued operators, under hybrid conditions of Perov contraction and compactness. Thus, we give vector versions of the theorems of Krasnosel'skii, Avramescu, Burton-Kirk and Gao-Li-Zhang. An application is given to a boundary value problem for a system of second order differential equations in which some of the equations are implicit. [ABSTRACT FROM AUTHOR]

In this paper, we study some new fixed point results in the context of w-distance as well as on wt-distance by using α-admissible mappings. Our results enhance and generalize several well known results available in the literature. We present examples to support our new findings. As an application, we utilize our results to obtain a solution of a nonlinear integral equation. [ABSTRACT FROM AUTHOR]

In this paper, an implicit viscosity iterative algorithm for nonexpansive mappings is proposed and investigated on Hadamard manifolds. A convergence theorem of a fixed point of a nonexpansive mapping is established on Hadamard manifolds. It is proved that the fixed point also solves a variational inequality. [ABSTRACT FROM AUTHOR]

In a real Hilbert space, let the GSVI and CFPP represent a general system of variational inclusions and a common fixed point problem of countable nonexpansive mappings and an asymptotically nonexpansive mapping, respectively. In this paper, via a new inertial subgradient extragradient rule we introduce and analyze two iterative algorithms for solving the monotone bilevel equilibrium problem (MBEP) with the GSVI and CFPP as constraints. Some strong convergence theorems for the proposed algorithms are established under some mild assumptions. Our results improve and extend some corresponding results in the earlier and very recent literature. [ABSTRACT FROM AUTHOR]

In this paper, we consider a hierarchical variational inequality problem defined over the set of zeros of a set-valued monotone vector field in the setting of Hadamard manifolds. We also consider bilevel variational inequality problems and bilevel optimization problems as special cases of our variational inequality problem. We develop implicit and explicit viscosity methods for solving our problem for weak contraction mappings. An inexact version of the explicit viscosity method is also studied. At the end, we provide two examples and computational experiments to illustrate implicit and explicit viscosity methods. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notions of φ-contractive parent-child possibly infinite iterated function system (pcIIFS) and orbital φ-contractive possibly infinite iterated function system (oIIFS) and we prove that the corresponding fractal operator is weakly Picard. The corresponding notions of shift space, canonical projection and their properties are also treated. [ABSTRACT FROM AUTHOR]

The purpose of this paper is concerned with the approximate solution of split equality problems. Two types of CQ algorithms with a new self-adaptive stepsize criterion are presented without prior knowledge of operator norms. The corresponding strong convergence theorems are obtained under mild conditions. Moreover, some numerical examples including an application in signal recovery problems, are provided to show the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

The ultimate goal of this paper is to investigate the approximation of involution in fuzzy C*-algebra. If A is fuzzy Banach algebra and f is function which defined on it, we prove that under conditions A has unique involution. In this case, fuzzy Banach algebra A can be evolute to Fuzzy C*-algebra. For this purpose, we use the Hyers-Ulam-Rassias stability method and the fixed point technique. [ABSTRACT FROM AUTHOR]

In this paper, four extragradient-type algorithms are presented for solving bilevel variational inequalities of pseudomonotone and non-Lipschitz continuous operators in real Hilbert spaces. The proposed iterative schemes employ two Armijo-type linesearch methods making them work adaptively. Strong convergence theorems of the suggested algorithms are established under some mild conditions. Finally, some numerical experiments and applications are given to verify the advantages and efficiency of the proposed algorithms over some previously known ones. [ABSTRACT FROM AUTHOR]

Let X be an arbitrary topological space and g : X x X → R be a real valued continuous function defined on X x X. In this article, we introduce two notions like topologically Berinde weak proximal contraction and topologically proximal weakly contractive mapping with respect to g. We explore sufficient conditions for the existence and uniqueness of best proximity points for these classes of mappings. Moreover, in the last part of the paper, we show that the best proximity point theorem for topologically proximal weakly contractive mapping can be deduced from some fixed point theorems in topological spaces. [ABSTRACT FROM AUTHOR]

This paper is devoted to determining the eigenvalue intervals of the parameters λ1, λ2,..., λn for which there exist positive solutions of the iterative systems of second-order with m-point impulsive boundary value problem. We use the Guo-Krasnosel'skii fixed point theorem on the cones in order to achieve our results. An example is also presented to demonstrate the applicability of the main results obtained. [ABSTRACT FROM AUTHOR]

In this paper, we establish strong convergence of the Halpern's type iteration for a semigroup of α-nonexpansive mappings in Banach spaces. Using the concept of quasilinearization, we extend this result to CAT(0) spaces, an important subclass of metric spaces. Our work generalizes and complements several comparable results existing in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new algorithm for solving split feasibility problems in Hilbert spaces. The algorithm stems from the relaxed CQ method and the alternated inertial step method. The proposed algorithm uses variable step-sizes which are updated at each iteration by a cheap computation without linesearch. This step-size rule allows the resulting algorithm to work more easily without the prior knowledge of the operator norm. Numerical experiments are implemented to illustrate the theoretical results and also to compare with existing algorithms. [ABSTRACT FROM AUTHOR]

Let C be a nonempty closed bounded (not necessary convex) subset of a Banach space X and let T : C → C be an (αβ)-nonexpansive mapping with α > 0, β > 0 and α + β < 1. In this paper, we show that T has a unique fixed point. Moreover, T is a Picard operator if and only if T is asymptotically regular. [ABSTRACT FROM AUTHOR]

In this paper, we first revise some results and proofs on θ-metric spaces. Next, we construct an explicit metric to metrize a given θ-metric that gives an affirmative answer to an open question on the metrization of θ-metric spaces. After that, we use the obtained result to calculate such metric of known θ-metrics, and reprove a fixed point theorem in θ-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we give some further comments to the counterexample and the results of Bisht in [R.K. Bisht, Comment on: A new fixed point theorem in the fractal space, Indagationes Mathematicae, 29(2018), no.2, 819-823.]. [ABSTRACT FROM AUTHOR]

In this paper we study the initial value problem of first order nonlinear differential equations with maxima and discuss the existence and approximation of the solutions. The main result relies on the Dhage iteration method embodied in a recent hybrid fixed point theorem of Dhage (2014) in a partially ordered normed linear space. At the end, we give an example to illustrate the hypotheses and applicability of the abstract results of this paper. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a hybrid inertial algorithm for approximating fixed points of noncommutative generic 2-generalized Bregman nonspreading mappings with equilibrium in reflexive Banach space. Also, we proved that the sequence generated by such algorithm converges strongly to the common fixed points of such mappings and solved some equilibrium problems in the space. The result established improved and generalized some recently announced results in the literature. A numerical example is given at end of the paper to ascertain some least level of improvement. [ABSTRACT FROM AUTHOR]

This paper is devoted to a class of semilinear Riemann-Liouville fractional evolution equations in Banach spaces. Using the Banach fixed point theorem and semigroup theory, we first establish an existence and uniqueness theorem of the mild solution, which improves the existing results in literature. Then, we consider an optimal control problem governed by semilinear fractional diffusion equations. The existence of optimal pairs and the compactness of the states are obtained. Moreover, the necessary optimality conditions of first order are derived. [ABSTRACT FROM AUTHOR]

In this paper, by applying the fixed point theorem of Krasnosel'skii, we prove the existence and compactness of the set of solutions for a 2-order nonlinear integrodifferential equation in N variables in an arbitrary Banach space E. Here, an appropriate Banach space X1 for the above equation is defined and a sufficient condition for relatively compact subsets in X1 is proved. An example is given to verify the efficiency of the used method. [ABSTRACT FROM AUTHOR]

This paper is devoted to study a class of semilinear elliptic equations with critical or supercritical variable exponents. By means of the mountain pass lemma, the existence of a nontrivial radial solution to this problem is obtained. [ABSTRACT FROM AUTHOR]