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We define and study enriched Suzuki mappings in Hadamard spaces. The results obtained here are extending fundamental findings previously established in related research. The extension is realized with respect to at least two different aspects: the setting and the class of involved operators. More accurately, Hilbert spaces are particular Hadamard spaces, while enriched Suzuki nonexpansive mappings are natural generalizations of enriched nonexpansive mappings. Next, enriched Suzuki nonexpansive mappings naturally contain Suzuki nonexpansive mappings in Hadamard spaces. Besides technical lemmas, the results of this paper deal with (1) the existence of fixed points for enriched Suzuki nonexpansive mappings and (2) Δ and strong (metric) convergence of Picard iterates of the α -averaged mapping, which are exactly Krasnoselskij iterates for the original mapping. [ABSTRACT FROM AUTHOR]

Optical polymers are recognized for their high transparency, raised flexibility, low cost, and good film-forming ability; hence, they introduce a multitude of benefits in a wide range of devices, such as information storage, displays, optical communications, and filters. Among the optical properties, birefringence is an essential parameter in practical cases that demand the control of the state of polarization of light. This review is focused on describing some fundamental and applicative aspects concerning the optical birefringence of the polymer materials. First, elementary notions depicting the phenomenon of light double refraction in macromolecular media are provided. Furthermore, the most relevant optical techniques to determine birefringence are reviewed by highlighting the working principle and mathematical basis for computing this parameter. Then, a series of investigations of optically birefringent polymers are described, summarizing the most utilized approaches to induce light double refraction in such materials. The selected results are analyzed in relation to the pursued applications. In the end, the future of this scientific domain is briefly presented by establishing the research paths that need further exploration. Moreover, the novel directions that could be formulated and might contribute to certain considerable advancements in the materials employed in the modern optical technologies are mentioned. [ABSTRACT FROM AUTHOR]

In this paper, with the goal of investigating the problem of finding a common element of the set of fixed points of a nearly asymptotically nonexpansive mapping and the set of solutions of a system of generalized nonlinear variational-like inequalities, an iterative algorithm is proposed. The notions of graph convergence and P– η -proximal point mapping are used and a new equivalence relationship between graph convergence and proximal-point mappings convergence of a sequence of lower semicontinuous and η -subdifferentiable proper functionals is established. Finally, the strong convergence of the sequence generated by our suggested iterative algorithm to a common element of the two sets mentioned above are demonstrated. [ABSTRACT FROM AUTHOR]

Split variational inclusions are revealed as a large class of problems that includes several other pre-existing split-type issues: split feasibility, split zeroes problems, split variational inequalities and so on. This makes them not only a rich direction of theoretical study but also one with important and varied practical applications: large dimensional linear systems, optimization, signal reconstruction, boundary value problems and others. In this paper, the existing algorithmic tools are complemented by a new procedure based on a three-step iterative process. The resulting approximating sequence is proved to be weakly convergent toward a solution. The operation mode of the new algorithm is tracked in connection with mixed optimization–feasibility and mixed linear–feasibility systems. Standard polynomiographic techniques are applied for a comparative visual analysis of the convergence behavior. [ABSTRACT FROM AUTHOR]

Very recently, a new type of generalized nonexpansive mappings on Banach spaces was introduced as an extension for the nonexpansiveness condition of Suzuki. This paper adapts the new concept to modular spaces, successfully overcoming the problem of modulars having weaker properties than norms. The result consists in several fixed point-related outcomes. The modular nonexpansive mappings defined here also extends another recently developed concept, namely the modular Suzuki condition. An example is provided in order to prove the relevance of the concept defined in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we survey iterative algorithms for solving split variational inequalities and fixed point problems in Hilbert spaces. The investigated split problem is involved in two pseudomonotone operators and two pseudocontractive operators. We propose a self-adaptive Tseng-type algorithm for finding a solution of the split problem. Strong convergence of the suggested algorithm is shown under weaker conditions than sequential weak-to-weak continuity imposed on two pseudomonotone operators. [ABSTRACT FROM AUTHOR]

The mutual influence of two mesogenic components, namely a nematic liquid crystal N-(p-methoxy-bezylidene)-butylaniline (MBBA) and a lyotropic liquid crystal poly-(phenyl-methacrylic) ester of cetyloxybenzoic acid (PPMAECOBA) in tetra-chloromethane (TCM) is studied in this paper. The ordinary and extraordinary refractive indices of the mixtures, nematic liquid crystal and lyotropic liquid crystal were measured at 589.3 nm with a Rayleigh interferometer and some electro-optical parameters were computed. The main refractive indices, the birefringence, the main normalized polarizabilities and their difference are dependent on the mixture volumetric concentrations, proving the existence of the collective orientational interactions between the two types of liquid crystals. [ABSTRACT FROM AUTHOR]

In this paper, we construct a forward–backward splitting algorithm for approximating a zero of the sum of an α -inverse strongly monotone operator and a maximal monotone operator. The strong convergence theorem is then proved under mild conditions. Then, we add a nonexpansive mapping in the algorithm and prove that the generated sequence converges strongly to a common element of a fixed points set of a nonexpansive mapping and zero points set of the sum of monotone operators. We apply our main result both to equilibrium problems and convex programming. [ABSTRACT FROM AUTHOR]

In this paper, we present two new iterative algorithms for approximating a solution of the multiple-sets split feasibility problem. The suggested algorithms are based on the gradient method with selection technique. Weak and strong convergence theorems are demonstrated. [ABSTRACT FROM AUTHOR]

In this paper, a hybrid projection algorithm for a countable family of mappings is considered in Banach spaces. The sequence generated by algorithm converges strongly to the common fixed point of the mappings. We apply the result for the resolvent of a maximal monotone operator for finding a zero of it, which is a solution of the equilibrium problem. The results obtained extend the research in this context, such as the corresponding results of Aoyama et al. (Nonlinear Anal 71(12):1626-1632, 2009, nonlinear analysis and optimization, Yokohama Publishers, Yokohama, pp. 1-17, 2009), Solodov et al. (Math Program 87(1):189-202, 2000), Ohsawa et al. (Arch Math 81(4):439-445, 2003) and Kamimura et al. (SIAM J Optim 13(3):938-945, 2002). [ABSTRACT FROM AUTHOR]

In this paper, we state and prove common fixed point theorems for four mappings f; g; S and T satisfying a nonlinear contractive condition in ordered metric spaces, where the mappings f and g are dominating and weak annihilators of the mappings T and S respectively. In this regard, we will utilize the notion of C-class function, following the technique of Shatanawi and Postolache [Fixed Point Theory Appl. 2013:271 (2013)]. Also, we introduce an example to support the useability of our results. [ABSTRACT FROM AUTHOR]

By providing distinct results under different conditions, we investigate the existence of solutions for an uncontrolled multi-singular fractional differential equation with some boundary conditions. Also, we provide some examples to illustrate our main results. [ABSTRACT FROM AUTHOR]

Cosentino et al. introduced F-contractions in the setting of b-metric space and proved a fixed point theorem. In this paper, we generalize the result of Cosentino et al. by introducing Feng and Liu type F-contractions. Example and some applications to Fredholm integral equations are constructed to show the significance of our result. [ABSTRACT FROM AUTHOR]

The purpose of this survey is to prove that the fixed point results for various multiplicative contractions are in fact equivalent to the corresponding fixed point results in (standard) metric spaces. For example, such are recent results established by He et al. (Fixed Point Theory Appl. 2014:48, 2014), Mongkolkeha and Sintunavarat (J. Nonlinear Sci. Appl. 8:1134-1140, 2015) and Abdou (J. Nonlinear Sci. Appl. 9:2347-2363, 2016) and all others from the list of references. Our results here generalize, complement, and improve recent ones from existing literature. [ABSTRACT FROM AUTHOR]

We introduce the notion of a $C^{*}$-algebra-valued b-metric space. We generalize the Banach contraction principle in this new setting. As an application of our result, we establish an existence result for an integral equation in a $C^{*}$-algebra-valued b-metric space. [ABSTRACT FROM AUTHOR]

In this paper, we study strong and △-convergence for a newly defined two-step iteration process involving two asymptotically nonexpansive mappings in the intermediate sense which is wider than the class of asymptotically nonexpansive mappings in the setting of $\operatorname{CAT}(0)$ spaces. Our results generalize, unify and extend many known results from the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we study strong and △-convergence of a newly defined three-step iteration process for nearly asymptotically nonexpansive mappings in the setting of $\operatorname{CAT}(k)$ spaces. Our results generalize, unify and extend many known results from the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we study some tripled fixed and coincidence point theorems for two mappings F : X × X × X → X and ɡ : X → X satisfying a nonlinear contraction based on ϕ-maps. Our results extend and improve many existing results in the literature. Also, we introduce an example to support the validity of our results. [ABSTRACT FROM AUTHOR]

A simple method for determining the linear birefringence of the thin layers based on the determination of the orientation of the polarization ellipse of totally polarized light is proposed and it is applied to PVA thin foils. Theoretical notions and the experimental procedure are described. The linear birefringence of polymer thin foils with different degrees of stretching is determined and the applicability of the method is discussed. [ABSTRACT FROM AUTHOR]

It is well-known that Mann’s algorithm fails to converge for Lipschitzian pseudocontractions and strong convergence of Ishikawa’s algorithm for Lipschitzian pseudocontractions have not been achieved without compactness assumption on pseudocontractive mapping T or underlying space C. A new algorithm, which couples Ishikawa algorithms with hybrid techniques for finding the fixed points of a Lipschitzian pseudocontractive mapping, is constructed in this paper. Strong convergence of the presented algorithm is shown without any compactness assumption. MSC: 47H05, 47H10, 47H17. [ABSTRACT FROM AUTHOR]

In this article, we introduce the notion of a Chatterjea-type cyclic weakly contraction and derive the existence of a fixed point for such mappings in the setup of complete metric spaces. Our result extends and improves some fixed point theorems in the literature. Example is given to support the usability of the result. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an iterative scheme for finding a common element of the set of solution of a pseudomonotone, Lipschitz-continuous variational inequality problem and the set of common fixed points of an infinite family of nonexpansive mappings. The proposed iterative method combines two well-known schemes: extragradient and approximate proximal methods. We derive some necessary and sufficient conditions for strong convergence of the sequences generated by the proposed scheme. [ABSTRACT FROM AUTHOR]

In our very recent published work [Int. J. Geom. Meth. Mod. Phys.8(4) (2011) 783-796], we considered the Riemannian manifold M = ℝ2 endowed with the warped metric ḡ(x, y) = diag(g(y), 1), where g is a positive function, of C∞-class, depending on the variable y only. Within this framework, we found a wide class of 2D gradient Ricci solitons and specialized our results to discuss some case studies. This research is a natural continuation, providing classification results for the subclass of steady gradient Ricci solitons. [ABSTRACT FROM AUTHOR]

This paper aims to be a natural continuation of our very recent research, published in [Int. J. Geom. Meth. Mod. Phys.8(4) (2011) 783-796]. Using as geometric background a generalized Poincaré manifold, this work presents models of new explicit classes of manifolds within the class of gradient Ricci solitons. In Sec. 1 we shortly introduce a history of this topic to motivate its relevance both for theoretical and applied sciences, and in Sec. 2 our work contains its notations and assumptions. In Sec. 3 we give our framework and introduce the basic result, and in Sec. 4 we develop our theory. Finally, in Sec. 5, we conclude this paper and suggest possible further development. While the background in the first two sections is introductory, the theory in Secs. 3 and 4 is new as a whole, containing original results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we obtain some stability results in complete convex metric spaces for nonselfmappings satisfying certain general contractivity condition. We prove our results for Jungck–Mann and Jungck–Ishikawa iterations. Our results extend several stability results in the literature. [Copyright &y& Elsevier]

Abstract: In this paper, we establish coupled coincidence and common coupled fixed point theorems for -weakly contractive mappings in ordered -metric spaces. Presented theorems extend, generalize and improve many existing results in the literature. An example is given. [Copyright &y& Elsevier]

We introduce the concepts of a G-weak contraction mapping of types A and B and we establish some fixed point theorems for a G-weak contraction mapping of types A and B in complete Gmetric spaces. Our results generalize several well-known comparable results in the literature. [ABSTRACT FROM AUTHOR]

We consider a new class of multitime multiobjective variational problems of minimizing a vector of quotients of functionals of curvilinear integral type. Based on the efficiency conditions for multitime multiobjective ratio variational problems, we introduce a ratio dual of generalized Mond-Weir-Zalmai type, and under some assumptions of generalized convexity, duality theorems are stated. We prove our weak duality theorem for efficient solutions, showing that the value of the objective function of the primal cannot exceed the value of the dual. Direct and converse duality theorems are stated, underlying the connections between the values of the objective functions of the primal and dual programs. As special cases, duality results of Mond-Weir-Zalmai type for a multitimemultiobjective variational problem are obtained. This work further develops our studies in (Pitea and Postolache (2011)). [ABSTRACT FROM AUTHOR]

A previous paper (2011), Pitea and Postolache, considered the problem of minimization of vectors of curvilinear functionals (well known as mechanical work), thought as multitime multiobjective variational problem, subject to PDE and/or PDI constraints. They have chosen the suitable framework offered by the second-order jet bundle, and initiated an optimization theory for this class of problems by introducing necessary conditions. As natural continuation of these results, the present work introduces a dual program theory, the general setting, and the theory which is new as a whole, containing our results. [ABSTRACT FROM AUTHOR]

We consider a multitime scalar variational problem (SVP), a multitime multiobjective variational problem (VVP) and a multitime vector fractional variational problem (VFP). For (SVP) we establish necessary optimality conditions. For the two vector variational problems (VVP) and (VFP), we define the notions of efficient solution and of normal efficient solution and using these notions we establish necessary efficiency conditions. Using the notion of (ρ b)-quasiinvexity adapted for variational problems, we introduce a duality of Mond-Weir-Zalmai type for the fractional problem (VFP) through weak, direct and converse duality theorems. [ABSTRACT FROM AUTHOR]

We introduce a study of Riemannian manifold M = ℝ2 endowed with a metric of diagonal type of the form $\bar g(x^1, x^2) = {\rm diag}(g(x^2), 1)$, where g is a positive function, of C∞-class, depending on the variable x2 only. We emphasize the role of metric $\bar g$ in determining manifolds having negative, null or positive sectional curvature. Within this framework, we find a wide class of gradient Ricci solitons (see, Theorems 4 and 7) and specialize these results to discuss some 2D and 4D case studies. The present study can be thought as a natural continuation of those included in monograph [22] by Constantin Udrişte, and to those in the research article [12] by Richard S. Hamilton (the result in Proposition 8 is precisely the famous "Hamilton cigar" in polar coordinates). [ABSTRACT FROM AUTHOR]

The notion of invexity is introduced by Hanson [6] in 1981, for real differentiable functions, see also [2] by Craven. After the works of Hanson and Craven, other types of differentiable functions have appeared with the intent of generalizing invex functions from different viewpoints. see [7] by Jeyakumar, [8] by Maul and Maul and [15], [16], [22] by Mititelu. Stipulating possible applications of these functions for programming problems, see [11] by Mishra and [24] by Nahak and Mohapatra to quote some examples, some scientists payed attention to possible extensions of this concept to nonsmooth functions. A direction is those of Craven [3] followed by Reiland [26], which extended the concept of invexity to nonsmooth functions by using the generalized directional derivative of Clarke for Lipschitz functions. Another direction is those of Mititelu, which extended the concept of invexity to nonsmooth functions by using essentially the upper directional derivative of Dini [5], [13], [16], [17], [18], [19], [22]. The goal of this work is to describe the state of the art on the question of invex functions for this case. We recall the main results on this theory with proofs when necessary, we supply up to date references, a description of some further developments and a few new results as well. For additional background material on this topic, we address the reader to the following research works: [10], [12], [14], [21], [23]. [ABSTRACT FROM AUTHOR]

The aim of this article is to revisit some problems of constrained extrema and discuss their peculiarities as they appear in our works [1]-[17], as well as to indicate possible up to date state of investigations in this field. As basic tool of this work is the idea of considering the values of a function along all curves from a given family, which allows an unitary approach of various types of extrema problems (either holonomic or nonholonomic). Some open problems with comments will be stated. The research on this topic has started with the distinguished collaboration of C. Udrişte and has been continued in the last years with the coauthors I. Ţevy, M. Ferrara, V. Dogaru and al. [ABSTRACT FROM AUTHOR]

Based on a generalization of the classical notion of differential, the subdifferential is a relatively new notion in Functional Analysis. It results in a natural way from the need for finding appropriate treatments of some classes of problems in Optimization Theory. The aim of this work is to survey the concept of subdifferential emphasizing the contribution of Professor Ştefan Mititelu to the development of this field. [ABSTRACT FROM AUTHOR]

We bring into the attention of mathematical world some classes of open problems risen by Professor Constantin Udrişte and his research collaborators, as they appear in the works [4]÷[11]. This work pay attention to the following research directions: extrema theory; vector fields theory; dynamical systems; optimal control. [ABSTRACT FROM AUTHOR]

Based on the normal efficiency conditions for a multiobjective non-fractional variational problem, we consider fractional duals of generalized Mond- Weir type and fractional Mond-Weir-Zalmai type. Under some assumptions of (ρ, b)-quasiinvexity, weak, direct and converse duality theorems are stated in various variants. [ABSTRACT FROM AUTHOR]

he notion of self-concordant function on Euclidean spaces was introduced and studied by Nesterov and Nemirovsky [6]. They have used these functions to design numerical optimization algorithms based on interior-point methods ([7]). In [12], Constantin Udrişte makes an ex- tension of this study to the Riemannian context of optimization methods. In this paper, we use a decomposable function to introduce a new class of self-concordant functions, defined on Riemannian manifolds endowed with metrics of diagonal type. While §1 is introductory in nature, §2 contains our results. We state and prove sufficient conditions for a function to be self-concordant and make two case studies. Examples we found could be used as self-concordant functions to design Newton-type algorithms on smooth manifolds in the sense of Jiang, Moore and Ji [5]. We also solve a very important problem in Riemannian geometry, rised by Professor Constantin Udrişste during the preparation of this paper, regarding the existence of the metric generated by a function which is self self-concordant. [ABSTRACT FROM AUTHOR]

Consider a pseudo-Riemannian manifold (M; g) with the connection ∇ and a smooth function f : M → R whose Hessian with respect to g is non-degenerate. Then we can define on M the associated pseudo-Riemannian Hessian metric h = ∇2 gf, having the connection ∇. The goal of this paper is twofold. On the one hand we establish a link between the two connections ∇ and ∇ respectively. In this respect, we use invariant calculus. The proof of Theorem 2.1 is original. On the other hand we give the PDEs determined by the associativity of the deformation algebra when g has a particular form. Of course, our theoretical presentation is not exhaustive, so the reader is encouraged to consult another recent works. The standard reference for Hessian structures is the monograph by Shima [10]. For additional background material on the subject of this paper, the authors recommend this treatise and the following research works ([1], [4], [7], [8] and [9]). [ABSTRACT FROM AUTHOR]

The values of the birefringence Δ n in the visible range were determined for the poly (phenyl methacrylic) ester of cetyloxybenzoic acid (PPMAECOBA) of 107 molecular weight in tetrachloromethane (TCM). The dependence of the birefringence values on the nature of an external alternating electric field, applied perpendicular to the light propagation direction, emphasizes the dipolar nature of the side chains ordering. [ABSTRACT FROM AUTHOR]

In this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a q-uniformly smooth Banach space. The proposed algorithm is based on descent, splitting and inertial ideas. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to the unique solution of the abovementioned problems. Numerical examples are also given to demonstrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the split equilibrium problems and fixed point problems in Hilbert spaces. We provide a unified framework for solving such problem in which the involved equilibrium bifunctions f and g are pseudomonotone and monotone, respectively, and the operators S and T are pseudocontractive. We suggest an iterative algorithm for solving the split problem and demonstrate its weak convergence. [ABSTRACT FROM AUTHOR]

The aim of this paper is to formulate and analyze a cyclic iterative algorithm in real Hilbert spaces which converges strongly to a common solution of fixed point problem and multiple-sets split common fixed point problem involving demicontractive operators without prior knowledge of operator norm. Significance and range of applicability of our algorithm has been shown by solving the problem of multiple-sets split common null point, multiple-sets split feasibility, multiple-sets split variational inequality, multiple-sets split equilibrium and multiple-sets split monotone variational inclusion. [ABSTRACT FROM AUTHOR]

This manuscript is concerned with the oscillatory properties of 4th-order differential equations with variable coefficients. The main aim of this paper is the combination of the following three techniques used: the comparison method, Riccati technique and integral averaging technique. Two examples are given for applying the criteria. [ABSTRACT FROM AUTHOR]

This paper introduces a new three-step algorithm to solve the split feasibility problem. The main advantage is that one of the projective operators interferes only in the final step, resulting in less computations at each iteration. An example is provided to support the theoretical approach. The numerical simulation reveals that the newly introduced procedure has increased performance compared to other existing methods, including the classic CQ algorithm. An interesting outcome of the numerical modeling is an approximate visual image of the solution set. [ABSTRACT FROM AUTHOR]

The aim of this work is to study oscillatory properties of a class of fourth-order delay differential equations. New oscillation criteria are obtained by using generalized Riccati transformations. This new theorem complements and improves a number of results reported in the literature. Some examples are provided to illustrate the main results. [ABSTRACT FROM AUTHOR]

In this paper, the original C Q algorithm, the relaxed C Q algorithm, the gradient projection method ( G P M ) algorithm, and the subgradient projection method ( S P M ) algorithm for the convex split feasibility problem are reviewed, and a renewed S P M algorithm with S-subdifferential functions to solve nonconvex split feasibility problems in finite dimensional spaces is suggested. The weak convergence theorem is established. [ABSTRACT FROM AUTHOR]

The class of Suzuki mappings is reanalyzed in connection with a three-steps Thakur procedure. The setting is provided by a uniformly convex Banach space, that is normed space endowed with some symmetric geometric properties and some topological properties. Once more, the fact that property (C) holds on as a generalized nonexpansiveness condition is emphasized throughout some examples. One example uses the setting of R 2 with the Taxicab norm. It is further included in a numerical experiment in connection with seven iteration procedures, resulting a visual analysis of convergence. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the pseudomonotone variational inequalities and fixed point problem of pseudocontractive operators in Hilbert spaces. An iterative algorithm has been constructed for finding a common solution of the pseudomonotone variational inequalities and fixed point of pseudocontractive operators. Strong convergence analysis of the proposed procedure is given. Several related corollaries are included. [ABSTRACT FROM AUTHOR]

A convex combined expectations regularized gap function with uncertain variable is presented to deal with uncertain nonlinear variational inequality problems (UNVIP). The UNVIP is transformed into a minimization problem through an uncertain weighted expected residual function. Moreover, the convergence of the global optimal solutions of the uncertain weighted expected residual minimization model is given through the integration by parts method under the compact space of the uncertain event. The limiting behaviors of the transformed model are analyzed. Furthermore, a compact approximation method is proposed in the unbounded uncertain event space. Through analysis of the convergence of UWERM model and reasonable hypothesis, the compact approximation method is verified under the circumstance of Holder continuity. [ABSTRACT FROM AUTHOR]