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In this paper a new definition for the fuzzy inner product spaces of the type Kramosil-Michálek and the type George-Veeramani is presented. In the new setting a fuzzy inner product space can naturally become a fuzzy normed space, and a classical inner product space can be considered as a special case of fuzzy inner product spaces. Several examples are given to illustrate that, the new definition is a nontrivial generalization for classical inner product spaces, and so it has rich contents in fuzziness. By virtue of this definition, some elementary properties are described in terms of the families of semi-inner products and a fuzzy version of Pythagorean theorem is given. As applications, a fixed point theorem for nonlinear contractions is established and the existence of solution of global optimization problem is obtained. [ABSTRACT FROM AUTHOR]

In this paper a new definition for Menger probabilistic inner product spaces is presented. In the new setting a Menger probabilistic inner product space can naturally become a Menger probabilistic normed space, and a classical inner product space can be considered as a special case of Menger probabilistic inner product spaces. An example is given to illustrate that, the new definition is a nontrivial generalization for classical inner product spaces, and so it has rich contents in probability. By virtue of this definition, the topological structure is discussed and some elementary properties are described in terms of the families of semi-inner products. Also, some convergence theorems and probabilistic Pythagorean theorem are given. As applications, a new fixed point theorem for nonlinear contractions in Menger probabilistic inner product spaces is established. [ABSTRACT FROM AUTHOR]

In this paper, the extension of isometries is considered for some operators between the unit spheres of two real p-normed spaces ( 0 < p ≤ 1 ) under some nonexpansivity and expansivity assumptions. In the light of the characteristics of p-normed spaces, the notion of isometry is generalized to the case of r-isometries. By virtue of the technique of dual spaces, it is proved that such operators can be extended from the unit sphere to the whole space. [ABSTRACT FROM AUTHOR]

China's natural gas market is focusing on price reform and aims to reconstruct vertically integrated industrial chains in the future. Based on the mixed complementarity problem model of gas markets with nodes in Henan Province, China, as an example, this paper applies numerical modeling to simulate the effects of social welfare and equilibrium prices on nodes in two scenarios: pipeline integration and pipeline separation. The findings reveal the following: (1) Pipeline separation yields greater overall social welfare than pipeline integration, with the welfare shifting from gas producers to consumption markets. (2) Pipeline separation lowers the equilibrium consumption prices by driving competition among gas supply sources. (3) Pipeline separation will increase the contribution of natural gas to primary energy. [ABSTRACT FROM AUTHOR]

Recently, a modified definition of a fuzzy inner product space was introduced by Saheli and Gelousalar (2016) [1]. Here we provide some comments to this paper. It is pointed out that the additivity axiom (FI7) is a strong condition which leads their setting to be the null space in reality, so the orthogonality of the two vectors is not discussed in general. [ABSTRACT FROM AUTHOR]

Fractal attractors are considered as invariant sets for contraction mappings in hyperspaces of the KM fuzzy metric spaces. Using the properties of Hausdorff fuzzy metrics, several existence results of attractors are obtained for a finite family and a countable family of nonlinear contractions. In particular, unbounded invariant sets are also examined for the iterated function systems in KM fuzzy metric spaces. Our results are generalizations in some aspects and analogous to their counterparts in usual metric spaces. [ABSTRACT FROM AUTHOR]

A first-order semilinear fuzzy differential inclusion with fuzzy impulse characteristics and linear boundary conditions is considered in separable Banach spaces. By means of semigroup properties, stacking approach and the fixed point theorem for multivalued map due to Dhage, the existence results for fuzzy solution are established. Some general criteria are presented for a class of semilinear fuzzy differential inclusions including higher dimensional and infinite dimensional uncertain systems, and the conditions for existence of solutions in the results are concise and mild. Also, several examples are given to illustrate the utility and applicability. [ABSTRACT FROM AUTHOR]

Abstract: Probabilistic fractals are considered as self-similar sets for contraction mappings in hyperspaces of the Menger probabilistic metric spaces. The completeness of hyperspaces of all closed, or closed and bounded, or compact nonempty subsets with respect to the probabilistic Hausdorff metric is studied in some general conditions of triangular norm. Using the properties of hyperspaces and triangular norms of H-type, several existence results of attractors are obtained for a finite family and a countable family of probabilistic nonlinear contractions, respectively. Our results are generalizations in many aspects. [Copyright &y& Elsevier]

This paper reports a facile microwave-assisted complex-gel auto-combustion method synthesis of La1.67Sr0.33NiO4 and YSZ composite powders and their utilization for the fabrication of high performance potentiometric NOx sensors. The synthesized composite powders with different YSZ concentrations (5wt%, 10wt% and 20wt%) were characterized using Fourier transformed infrared (FTIR) spectrum and X-ray diffraction (XRD). The gas sensing property of the composites to NO was tested at temperatures ranging from 400°C to 600°C. The sensor fabricated with 10wt% YSZ addition composite sensing electrode exhibited the biggest response (about 27mV for 700ppm NO) at 400°C. Moreover, the response time and recovery time were within 4–18s and 6–35s, respectively. The enhanced gas sensing performance of the sensor to NO may be attributed to the larger superficial area of triple phase boundary. This work demonstrated that the simply synthesized La1.67Sr0.33NiO4 and YSZ composite powders can be effectively used for the fabrication of potentiometric NOx sensors. [ABSTRACT FROM AUTHOR]

Abstract: The class of H-type triangular norms was introduced for the first time by Hadžić in 1978. In this paper a new characteristic property of the H-type triangular norm is presented. By virtue of this alternative characterization, the continuity of quasi-metrics and quasi-norms is studied and some properties of the probabilistic Menger spaces with this triangular norm are considered. As applications new fixed point and fixed degree theorems for probabilistic nonlinear contractions and fuzzy mappings are given. [Copyright &y& Elsevier]

Abstract: In this paper, a class of boundary problems for second order semilinear differential inclusions is studied. By applying techniques from multivalued analysis and fixed point theorems due to Covitz–Nadler, Bohnenblust–Karlin and Schaefer, some existence results of solutions are presented for the nonlinear term which is a Lipschitz continuous, upper or lower semicontinuous multivalued map, respectively. As consequences some existence conditions of solutions are given for a class of second order semilinear differential systems. [Copyright &y& Elsevier]

Abstract: In this paper the existence and unicity of fixed points for mappings in fuzzy metric spaces (in the sense of Kaleva and Seikkala) is discussed. Nonlinear contractions of the Boyd–Wong''s type, Alber–Guerre Delabriere''s type and Kannan–Reich''s type are considered, and several new fixed point theorems for these contractions in complete fuzzy metric spaces are presented, respectively. Also, some error estimates are given for iterations to approximate fixed point. Previous work with respect to fixed point in fuzzy metric spaces is based on the t-conorm max. The presented work does away with this restriction, by proposing weaker conditions defining a generic class of suitable binary operations. As applications the corresponding fixed point theorems for Menger probabilistic metric spaces are obtained. [Copyright &y& Elsevier]

Abstract: A second order semilinear differential inclusion with some boundary continuous and impulse characteristics in a separable Banach space is considered. Some existence theorems for mild solutions are given, when the multivalued nonlinearity of the inclusion is only a locally integrably bounded upper-Carathéodory map with convex and weakly compact values. Then the compactness of the set of all mild solutions for the problem is proved. The results are obtained by using the theory of continuous cosine families of bounded linear operators and a fixed point theorem for multivalued maps due to Agarwal, Meehan and O’Regan. A corresponding result for closed graph of composition is extended. [Copyright &y& Elsevier]

Abstract: In the paper “Coupled fixed point theorems for contractions in fuzzy metric spaces” by Sedghi et al. [S. Sedghi, I. Altun, N. Shobec, Coupled fixed point theorems for contractions in fuzzy metric spaces, Nonlinear Analysis 72 (2010) 1298–1304], a coupled common fixed point result was presented. However, our purpose is to show that this result and its proof are false. We give a counterexample and also explain how to correct this result. As a modification, we state and prove a coupled fixed point theorem under some hypotheses of fuzzy metric and -norm. [Copyright &y& Elsevier]

Abstract: Several hybrid probabilistic contractions with a gauge function are considered. Using the properties of the pseudo-metric and the triangular norm, some common coupled fixed point theorems are obtained in complete Menger probabilistic metric spaces. The main results are general because they do not assume any continuity or monotonicity conditions for . [Copyright &y& Elsevier]

Abstract: The existence of a continuous Chebyshev selection for a Hausdorff continuous set-valued mapping is studied in a Banach space with some uniform convexity. As applications, some existence results of Chebyshev fixed point for condensing set-valued mappings are given, and the existence of Chebyshev solutions for an integral inclusion is proved. [Copyright &y& Elsevier]

Abstract: The existence of fixed points of operators on -convex sets in -normed spaces is studied, where , . By means of homeomorphisms the fixed point theorems of the types of Brouwer, Schauder, Kakutani, Rothe, Petryshyn, Altman, and Krasnosel’skii are proved for -convex sets. As an application, the existence result of solutions for the game concerning -convex–concave operators is given in product -normed spaces. [ABSTRACT FROM AUTHOR]

Abstract: A new continuity theorem of minimum selection is presented for a continuous set-valued operator from a topological space into a Banach space with some uniform convexity. As applications, some problems concerning minimum right inverses for linear operators and minimum fixed points for condensing set-valued nonlinear operators are discussed. Also, the existence of minimum solutions for an integral inclusion is proved. [Copyright &y& Elsevier]

Abstract: In this paper level-cut measures of noncompactness are introduced in standard fuzzy normed spaces and condensing operators are studied. Using the extensions of nonlinear compact operators, topological degree theory with respect to condensing operators is given in standard fuzzy normed spaces. As an application of degree theory, a fixed point theorem for condensing operators is presented. [Copyright &y& Elsevier]

Abstract: In this paper a -step iterative scheme with error terms involving asymptotically quasi-nonexpansive mappings is studied. In usual Banach spaces, some sufficient and necessary conditions are given for the iterative scheme to approximate a common fixed point. In uniformly convex Banach spaces, power equicontinuity for a mapping is introduced and a series of new convergence theorems are established. Several known results in the current literature are extended and refined. [Copyright &y& Elsevier]

Abstract: In this paper, four gauge functionals on L-fuzzy real line are introduced and a pointwise pseudo-metric function on is given by means of them. It is pointed out that this metric function is identical with the Erceg metric function, and the metric topology is identical with the usual topology. Some relations between the families of neighborhood balls and remote-neighborhood balls are revealed. [Copyright &y& Elsevier]

Abstract: In this paper the pointwise pseudo-metric for molecular lattices introduced by Shi is studied. A series of expressions concerning neighborhood balls and remote-neighborhood balls are obtained. Some algebraic properties of the pointwise pseudo-metric function of molecular lattices are presented and their topological structure are discussed in terms of the conjugate families of mappings. These results show that there exist conjugate relations between neighborhoods and remote-neighborhoods. [Copyright &y& Elsevier]

In this paper, the Leray–Schauder topological degree theory is developed in a fuzzy normed space. Since the linear topology on this fuzzy normed space is not necessarily locally convex, and since each Menger probabilistic normed space can be considered as a special fuzzy normed space, the degree theory in this paper is different from the degree theory in locally convex linear topological space presented by Nagumo (Amer. J. Math. 73 (1951) 497–511), and it also is an extension of the degree theory in Menger probabilistic normed space studied by Zhang and Chen (Appl. Math. Mech. 10(6) (1989) 477–486). Applying this degree theory, some fixed point theorems for operators are given in fuzzy normed spaces, and some former corresponding results are extended and improved. [Copyright &y& Elsevier]

In this paper the new definition of the fuzzy norm of a linear operator from one fuzzy normed linear space into another is introduced; and the boundedness of such an operator is described. Furthermore, the space of all bounded linear operators endowed with this fuzzy norm is studied; consequently, its topological structure as well as completeness is given, and that it can itself be made into a fuzzy normed linear space is also shown. [Copyright &y& Elsevier]

Highlights: [•] We propose a reservoir operating rule extraction architecture inspired by self-adaptive learning of antibodies to antigens. [•] We establish a co-evolutionary artificial immune system model to extract the water-supply reservoir operating rules. [•] The model can self-adaptively track and adjust the population of the rules to be response to complex operation environment. [•] The obtained rules can gain the experience of reservoir operation and provide more sufficient decision-making information. [Copyright &y& Elsevier]

Space M&A based on industrial concentration and pursuing concentration rent and spillover effect in new normal has become an important method to realize industrial up-grading, and how to evaluate value effect of space M&A with two-stage production system becomes a new project that has yet to be studies in academia. The article builds a M&A value evaluation simulation model based on DEA non-cooperation game to evaluate value effect of space M&A in financial industry in China.it shows, Space M&A with hypotactic game relationship can bring about substantial potential cost saving, and there must be system M&A valid when all subsystems are M&A valid. Optimal input-output index and optimal value index of intermediate variables based on model calculation further helps to obtain the measure of space M&A value improvement, which provides commercial banks with immediate empirical evidences to select M&A under new normal, helps to facilitate optimization of financial resources space configuration, and promotes transformation and upgrading as well as innovative driving of financial industry in China. [ABSTRACT FROM PUBLISHER]

The key to deepening the reform of Chinese economic system is to speed up rural financial reform, strengthen the financial support for new agricultural business entities, and accelerate cultivation and development of new agricultural business entities. The paper, taking pilot area for rural financial reform in Lishui of Zhejiang as the subject of study, makes an in-depth research on an influence of Chinese rural financial reform on cultivation of new agricultural business entities. Empirical research shows, financial support is an important means of cultivating new agricultural business entities, special finances such as governmental universal finance and special finance from financing institutions and funds in the hands of family farms exert an outstanding influence on cultivation of new rural agricultural business entities. Finance supports with different sources play a certain alternative part in cultivation of new agricultural business entities. It is very important for cultivation of new agricultural business entities to strengthen the intensity of rural financial reform and optimize allocation of rural financial resources, which indicates the direction to deepen rural financial reform of China. [ABSTRACT FROM PUBLISHER]