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In this paper, we introduce new types of contraction mappings named S-Pata-type contraction mapping and Generalized S-Pata-type contraction mapping in the framework of S-metric space. Then, we prove some new fixed-point results for S-Pata-type contraction mappings and Generalized S-Pata-type contraction mappings. To support our results, we provide examples to illustrate our findings and also apply these results to the ordinary differential equation to strengthen our conclusions. [ABSTRACT FROM AUTHOR]

We explore the intermixed method for finding a common element of the intersection of the solution set of a mixed variational inequality and the fixed point set of a nonexpansive mapping. We point out that Khuangsatung and Kangtunyakarn's statement [J. Inequal. Appl. 2023:1, 2023] regarding the resolvent utilized in their paper is not correct. To resolve this gap, we employ the epigraphical projection and the product space approach. In particular, we obtain a strong convergence theorem with a weaker assumption. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of graphical cone metric spaces over Banach algebra and prove some fixed point results for a particular type of contractive mappings defined on such spaces. These results extend and generalize several results from metric, graphical metric, and cone metric spaces. Some examples that demonstrate the results proved herein are provided. An application of our results to the existence of solution of a pair of initial value problems is provided. [ABSTRACT FROM AUTHOR]

In this paper, we define a new concept of left and right coordinate affine of a directed graph and then employ it to introduce a new accelerated common fixed point algorithm for a countable family of G-nonexpansive mappings in a real Hilbert space with a graph. We prove, under certain conditions, weak convergence theorems for the proposed algorithm. As applications, we also apply our results to solve convex minimization and image restoration problems. Moreover, we show that our algorithm provides better convergence behavior than other methods in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we define some new notions of gap functions for set-valued mixed quasi-variational inequalities under suitable conditions. Further, we obtain local/global bounds for the solution of set-valued mixed quasi-variational inequality problems in terms of the residual gap function, the regularized gap function, and the D-gap function. The results obtained in this paper are generalization and refinement of previously known results for some class of variational inequality problems. [ABSTRACT FROM AUTHOR]

In this paper, we combine a sequence of contractive mappings $\{h_{n}\}$ with the proximal operator and propose a generalized viscosity approximation method for solving the unconstrained convex optimization problems in a real Hilbert space H. We show that, under reasonable parameter conditions, our algorithm strongly converges to the unique solution of a variational inequality problem. Our result presented in the paper improves and extends the corresponding results reported by many authors recently. [ABSTRACT FROM AUTHOR]

In this paper, we prove that a three-step iteration process is stable for contractive-like mappings. It is also proved analytically and numerically that the considered process converges faster than some remarkable iterative processes for contractive-like mappings. Furthermore, some convergence results are proved for the mappings satisfying Suzuki's condition (C) in uniformly convex Banach spaces. A couple of nontrivial numerical examples are presented to support the main results and the visualization is showed by Matlab. Finally, by utilizing our main result the solution of a nonlinear fractional differential equation is approximated. [ABSTRACT FROM AUTHOR]

In this paper, we provide a more general regularization method for seeking a solution to a class of monotone variational inequalities in a real Hilbert space, where the regularizer is a hemicontinuous and strongly monotone operator. As a discretization of the regularization method, we propose an iterative method. We then prove that the proposed iterative method converges in norm to a solution of the class of monotone variational inequalities. We also apply our results to the constrained minimization problem and the minimum-norm fixed point problem for a generalized Lipschitz continuous and pseudocontractive mapping. The results presented in the paper improve and extend recent ones in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce new approximation methods for solutions of generalized non-accretive multi-valued mixed quasi-variational inclusion systems involving (A,η)-accretive mappings in q-uniformly smooth Banach spaces and, by using the new resolvent operator technique associated with (A,η)-accretive mappings, Nadler's fixed point theorem and Liu's inequality, we prove some existence theorems of solutions for our systems by constructing the new Mann iterative algorithm. Further, we study the stability of the iterative sequence generated by the perturbed iterative algorithms. The results presented in this paper improve and generalize the corresponding results of recent works given by some authors. [ABSTRACT FROM AUTHOR]

In this paper, some new generalization of Darbo's fixed point theorem is proved by using a $F(\psi,\varphi)$ -contraction in terms of a measure of noncompactness. Our result extends to obtaining a common fixed point for a pair of compatible mappings. The paper contains an application for nonlinear integral equations as well. [ABSTRACT FROM AUTHOR]

In this paper, we present a family of conjugate gradient projection methods for solving large-scale nonlinear equations. At each iteration, it needs low storage and the subproblem can be easily solved. Compared with the existing solution methods for solving the problem, its global convergence is established without the restriction of the Lipschitz continuity on the underlying mapping. Preliminary numerical results are reported to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper we study the hyperbolic and Euclidean area distortion of measurable sets under some classes of K-quasiconformal mappings from the upper half-plane and the unit disk onto themselves, respectively. [ABSTRACT FROM AUTHOR]

This paper is concerned with upper Hölder continuity and Hölder calmness of a perturbed vector optimization problem. We establish some new sufficient conditions for upper Hölder continuity and Hölder calmness of the perturbed solution mappings and the perturbed optimal value mappings of a vector optimization problem under the case that the objective function and the feasible set are, respectively, perturbed by parameters. Our results generalize and extend the corresponding ones of Li and Li (Appl. Math. Comput. 232:908-918, 2014). [ABSTRACT FROM AUTHOR]

Due to its simplicity and numerical efficiency for unconstrained optimization problems, the spectral gradient method has received more and more attention in recent years. In this paper, two spectral gradient projection methods for constrained equations are proposed, which are combinations of the well-known spectral gradient method and the hyperplane projection method. The new methods are not only derivative-free, but also completely matrix-free, and consequently they can be applied to solve large-scale constrained equations. Under the condition that the underlying mapping of the constrained equations is Lipschitz continuous or strongly monotone, we establish the global convergence of the new methods. Compared with the existing gradient methods for solving such problems, the new methods possess a linear convergence rate under some error bound conditions. Furthermore, a relax factor γ is attached in the update step to accelerate convergence. Preliminary numerical results show that they are efficient and promising in practice. [ABSTRACT FROM AUTHOR]

In the present paper we investigate a class of harmonic mappings for which the second dilatation is a close-to-convex function of complex order b, $b\in\mathbb{C} / \{ 0 \}$ (Lashin in Indian J. Pure Appl. Math. 34(7):1101-1108, 2003). [ABSTRACT FROM AUTHOR]

In this paper, we prove that the fixed point results in the context of complex-valued metric spaces can be obtained as a consequence of corresponding existing results in the literature in the setting of associative metric spaces. In particular, we deduce that any complex metric space is a special case of cone metric spaces with a normal cone. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of soft Meir-Keeler contractive mappings and weaker ϕ-Meir-Keeler contractive mappings, and the purpose of this paper is to prove two theorems which assures the existence of fixed points for these two soft Meir-Keeler type contractive mappings on a soft metric space. Our results generalize and improve many recent fixed point results in the literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to propose an algorithm to solve the split common fixed point problems for total asymptotically strict pseudocontraction mappings in Hilbert spaces. Without the assumption of semi-compactness on the mappings, the iterative scheme is shown to converge strongly to a split common fixed point of such mappings. The results presented in the paper improve and extend some recent corresponding results. [ABSTRACT FROM AUTHOR]

Very recently, in a series of subsequent papers, Nan and Charoensawan introduced the notion of g-coincidence point of two mappings in different settings (metric spaces and G-metric spaces) and proved some theorems in order to guarantee the existence and uniqueness of such kind of points. Although their notion seems to be attractive, in this paper, we show how this concept can be reduced to the unidimensional notion of coincidence point, and how their main theorems can be seen as particular cases of existing results. Moreover, we prove that the proofs of their main statements have some gaps. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a proximal point iterative algorithm with general errors for monotone mappings in Banach spaces. We prove that the proposed algorithm converges strongly to a proximal point for monotone mappings. Our theorems in this paper improve and unify most of the results that have been proposed for this important class of nonlinear mappings. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a general iterative algorithm for finding a common solution of a finite family of mixed equilibrium problems, a general system of generalized equilibria and a fixed point problem of nonexpansive mappings in a real Hilbert space. Under some appropriate conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution, which also solves some optimization problem. The result presented in this paper improves and extends some corresponding ones in the earlier and recent literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and analyze a multistep Mann-type extragradient iterative algorithm by combining Korpelevich's extragradient method, viscosity approximation method, hybrid steepest-descent method, Mann's iteration method, and the projection method. It is proven that under appropriate assumptions, the proposed algorithm converges strongly to a common element of the fixed point set of infinitely many nonexpansive mappings and a strict pseudocontraction, the solution set of finitely many generalized mixed equilibrium problems (GMEPs), the solution set of finitely many variational inclusions and the solution set of a variational inequality problem (VIP), which is just a unique solution of a system of hierarchical variational inequalities (SHVI) in a real Hilbert space. The results obtained in this paper improve and extend the corresponding results announced by many others. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence of solutions for a variational-like inequality and a generalized variational-like inequality in the relaxed η-α pseudomonotone and strictly η-quasimonotone cases in Banach spaces by using the KKM technique. The results presented in this paper improve and extend some corresponding results of several authors. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the concepts of total asymptotically demicontractive mappings and total asymptotically hemicontractive mappings. Under suitable conditions some strong convergence theorems for these two kinds of mappings to converge to their fixed points in CAT(0) space are proved. The results presented in the paper extend and improve some recent results announced in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, by using a nonlinear scalarization technique, we obtain sufficient conditions for Hölder continuity of the solution mapping for a parametric generalized vector quasi-equilibrium problem with set-valued mappings. The results are different from the recent ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a two-steps modifying Halpern iteration for Bregman strongly nonexpansive multi-valued mappings in the framework of reflexive Banach spaces is established. Under suitable limit conditions, some strong convergence theorems for this iteration are proved. We apply our main results to solve classical equilibrium problems in the framework of reflexive Banach spaces. The main results presented in the paper improve and extend the corresponding results in the work by Suthep et al. (Comput. Math. Appl. 64:489-499, 2012), Li et al. (Fixed Point Theory Appl. 2013:197, 2013) and Chang and Wang (Appl. Math. Comput. 228:38-48, 2014). [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a second-order composed contingent epiderivative for set-valued maps and discuss some of its properties. Then, by virtue of the second-order composed contingent epiderivative, we establish second-order sufficient optimality conditions and necessary optimality conditions for the weakly efficient solution of set-valued vector equilibrium problems with unconstraints and set-valued vector equilibrium problems with constraints, respectively [ABSTRACT FROM AUTHOR]

In this paper, we consider two families Ψ1 and Ψ2 of mappings defined on [0,+∞) satisfy some certain properties. Using the mentioned properties for Ψ1 and Ψ2, we prove the analogous PPF dependent fixed point theorems for mappings as in Drici et al. (Nonlinear Anal. 67:641-647, 2007) in partially ordered Banach spaces where mappings satisfy the weaker contractive conditions without assuming the topological closedness with respect to the norm topology for the Razumikhin class Rc. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new hybrid iteration for a finite family of asymptotically strictly pseudocontractive mappings. We also prove that such a sequence converges strongly to a common fixed point of a finite family of asymptotically strictly pseudocontractive mappings. Results in the paper extend and improve recent results in the literature. [ABSTRACT FROM AUTHOR]

The concept of a four-dimensional generalized difference matrix and its domain on some double sequence spaces was recently introduced and studied by Tuğ and Başar (AIP Conference Proceedings, vol. 1759, 2016) and Tuğ (J. Inequal. Appl. 2017(1):149, 2017). In this present paper, as a natural continuation of (J. Inequal. Appl. 2017(1):149, 2017), we introduce new almost null and almost convergent double sequence spaces $B(\mathcal{C}_{f})$ and $B(\mathcal{C}_{f_{0}})$ as the four-dimensional generalized difference matrix $B(r,s,t,u)$ domain in the spaces $\mathcal{C}_{f}$ and $\mathcal{C}_{f_{0}}$ , respectively. Firstly, we prove that the spaces $B(\mathcal{C}_{f})$ and $B(\mathcal{C}_{f_{0}})$ of double sequences are Banach spaces under some certain conditions. Then we give an inclusion relation of these new almost convergent double sequence spaces. Moreover, we identify the α-dual, $\beta(bp)$ -dual and γ-dual of the space $B(\mathcal{C}_{f})$ . Finally, we characterize some new matrix classes $(B(\mathcal{M}_{u}):\mathcal{C}_{f})$ , $(\mathcal{M}_{u}:B(\mathcal {C}_{f}))$ , and we complete this work with some significant results. [ABSTRACT FROM AUTHOR]

In this paper, a new general identity for differentiable mappings via k-fractional integrals is derived. By using the concept of $(h,m)$ -convexity, $(\alpha,m)$ -convexity and the obtained equation, some new trapezium-like integral inequalities are established. The results presented provide extensions of those given in earlier works. [ABSTRACT FROM AUTHOR]

A copula is a function which joins (or 'couples') a bivariate distribution function to its marginal (one-dimensional) distribution functions. In this paper, we obtain Chebyshev type inequalities by utilising copulas. [ABSTRACT FROM AUTHOR]

In this paper, a new form of the symmetric vector equilibrium problem is introduced and, by mixing properties of the nonlinear scalarization mapping and the maximal element lemma, an existence theorem for it is established. We show that Ky Fan's lemma, as a usual technique for proving the existence results for equilibrium problems, implies the maximal element lemma, while it is useless for proving the main theorem of this paper. Our results can be viewed as an extension and improvement of the main results obtained by Farajzadeh (Filomat 29(9):2097-2105, 2015) and some corresponding results that appeared in this area by relaxing the lower semicontinuity, quasiconvexity on the mappings and being nontrivial of the dual cones. Finally, some examples are given to support the main results. [ABSTRACT FROM AUTHOR]

The objective of this research is to present new fixed point theorems for two separate families of fuzzy-dominated mappings. These mappings must satisfy a unique locally contraction in a complete b-multiplicative metric space. Also, we have obtained novel results for families of fuzzy-dominated mappings on a closed ball that meet the requirements of a generalized locally contraction. This research introduces new and challenging fixed-point problems for families of ordered fuzzy-dominated mappings in ordered complete b-multiplicative metric spaces. Moreover, we demonstrate a new concept for families of fuzzy graph-dominated mappings on a closed ball in these spaces. Additionally, we present novel findings for graphic contraction endowed with graphic structure. These findings are groundbreaking and provide a strong foundation for future research in this field. To demonstrate the uniqueness of our novel findings, we provide evidence of their applicability in obtaining the common solution of integral and fractional differential equations. Our findings have resulted in modifications to several contemporary and classical results in the research literature. This provides further evidence of the originality and impact of our work. [ABSTRACT FROM AUTHOR]

This paper provides a normal form for a class of lower dimensional hyperbolic invariant tori of nearly integrable symplectic mappings with generating functions. We prove the persistence and the Gevrey-smoothness of the invariant tori under some conditions. [ABSTRACT FROM AUTHOR]

In this paper, we present the $L^{p}$ mapping properties of multiple singular integrals related to homogeneous mappings with rough kernels given by the radial function $h\in\Delta_{\gamma}$ (or $h\in U_{\gamma}$ ) for some $\gamma>1$ (or $\gamma\geq1$ ) and the sphere function $\Omega\in L(\log^{+}L)^{2} (S^{m-1}\times S^{n-1})$ (or $\Omega\in L(\log^{+}L)^{2/\gamma'} (S^{m-1}\times S^{n-1})$ ). In addition, the $L^{p}$ bounds for the related maximal operators are also given. Our main results extend and improve some known ones. [ABSTRACT FROM AUTHOR]

In this paper, our aim is to address the existence and uniqueness of solutions for a class of integral equations in IFMT-space. Therefore, we introduce the concept of IFMT-spaces and prove a common fixed point theorem in a complete IFMT-space; next we study an application. [ABSTRACT FROM AUTHOR]

In this paper, inspired by Hussain et al. (Fixed Point Theory Appl. 2015:17, ), we study a modified Mann method to approximate strongly fixed points of strict pseudo-contractive mappings. In (Hussain et al. in Fixed Point Theory Appl. 2015:17, ) it is shown that the same algorithm converges strongly to a fixed point of a nonexpansive mapping under suitable hypotheses on the coefficients. Here the assumptions on the coefficients are different, as well as the techniques of the proof. [ABSTRACT FROM AUTHOR]

In this paper, we present a generalization of a combinatorial lemma we stated and proved in a recent work. Then we apply the generalized lemma to prove: (1) a theorem on the existence of a zero for an excess demand mapping, (2) the existence of a continuum of zeros for a parameterized excess demand mapping, (3) Sperner's lemma on labelings of triangulations. Proofs of these results are constructive: they contain algorithms (based on the combinatorial lemma) for the computation of objects of interest or, at least, of their approximations. [ABSTRACT FROM AUTHOR]

In this paper, we discuss generalized hierarchical minimax theorems with four set-valued mappings and we propose some scalar hierarchical minimax theorems and generalized hierarchical minimax theorems in topological spaces. Some examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

By using the improved Hübner inequalities, in this paper we obtain an asymptotically sharp lower bound estimate for the coefficients of harmonic K-quasiconformal self-mappings of the unit disk ${\mathbb{D}}$ which keep the origin fixed. The result partly improves the former results given by (Partyka and Sakan in Ann. Acad. Sci. Fenn., Math. 30:167-182, ) and (Zhu and Zeng in J. Comput. Anal. Appl. 13:1081-1087, ). Furthermore, using some estimate for the derivative of the boundary function of a harmonic K-quasiconformal self-mapping w of ${\mathbb{D}}$ which keeps the origin fixed, we obtain an upper bound estimate for the coefficients of w. [ABSTRACT FROM AUTHOR]

This paper is devoted to the study of gap functions of random generalized variational inequality problems in a fuzzy environment. Further by using the residual vector we compute error bounds for random generalized variational inequality problems and we generalize the regularized gap functions proposed by Fukushima. Furthermore we study various properties of the generalized regularized gap functions in random fuzzy mappings and derive the global error bounds for random generalized variational inequality problems. Our results are new and generalize a number of known results to generalized variational inequality problems with fuzzy mappings. [ABSTRACT FROM AUTHOR]

Two new ergodic convergence theorems for approximating the common element of the set of zero points of an m-accretive mapping and the set of fixed points of an infinite family of non-expansive mappings in a real smooth and uniformly convex Banach space are obtained, which improves some of the previous work. The computational experiments to demonstrate the effectiveness of the proposed iterative algorithms in this paper are conducted. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a notion of Levitin-Polyak well-posedness for generalized semi-infinite multiobjective programming problems in terms of weakly efficient solutions. We obtain some metric characterizations of Levitin-Polyak well-posedness for this problem. We derive the relations between the Levitin-Polyak well-posedness and the upper semi-continuity of approximate solution maps for generalized semi-infinite multiobjective programming problems. Examples are given to illustrate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and uniqueness of a fixed point of certain operators in the setting of complete quasi- b-metric-like spaces via admissible mappings. Our results improve, extend, and unify several well-known existence results. [ABSTRACT FROM AUTHOR]

In this paper, we consider the generic stability of the weakly efficient solution mapping for set-valued optimization problems. Firstly, we obtain the upper semicontinuity of the weakly efficient solution mapping for set-valued optimization problems. Secondly, we show that, in the sense of Baire category, most set-valued optimization problems are stable. Finally, we give sufficient conditions ensuring the existence of essential. Our results extend and improve the corresponding results of Song et al. (J. Optim. Theory Appl. 156:591-599, 2013). [ABSTRACT FROM AUTHOR]

In this paper, we introduce the class of $SKC$-mappings, which is a generalization of the class of Suzuki-generalized nonexpansive mappings, and we prove the strong and Δ-convergence theorems of the S-iteration process which is generated by $SKC$-mappings (Karapinar and Tas in Comput. Math. Appl. 61:3370-3380, 2011) in uniformly convex hyperbolic spaces. As uniformly convex hyperbolic spaces contain Banach spaces as well as $\operatorname {CAT}(0)$ spaces, our results can be viewed as an extension and generalization of several well-known results in Banach spaces as well as $\operatorname {CAT}(0)$ spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove a weak convergence theorem and a strong convergence theorem for split common fixed point problem involving a quasi-strict pseudo contractive mapping and an asymptotical nonexpansive mapping in the setting of two Banach spaces. Our results are new and seem to be the first outside Hilbert spaces. [ABSTRACT FROM AUTHOR]

Recently, Ma et al. introduced the notion of $C^{*}$-valued metric spaces and extended the Banach contraction principle for self-mappings on $C^{*}$-valued metric spaces. Motivated by the work of Jachymski, in this paper we extend and improve the result of Ma et al. by proving a fixed point theorem for self-mappings on $C^{*}$-valued metric spaces satisfying the contractive condition for those pairs of elements from the metric space which form edges of a graph in the metric space. Our result generalizes and extends the main result of Jachymski and Ma et al. We also establish some examples to elaborate our new notions and to substantiate our result. [ABSTRACT FROM AUTHOR]

In this paper, we establish some fixed point theorems on some extensions of Geragthy contractive type mappings in the context of b-metric-like spaces. [ABSTRACT FROM AUTHOR]