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In this paper, we introduce a new iterative scheme to approximate the fixed point of generalized α-nonexpansive mappings. we first prove that the proposed iteration process is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas and Thakur processes for contractive mappings. We also obtain some weak and strong convergence theorems for generalized α-nonexpansive mappings. Using the example presented in [R. Pant and R. Shukla, Approximating fixed point of generalized α-nonexpansive mappings in Banach spaces, J. Numer. Funct. Anal. Optim. 38(2017) 248-266.], we compare the convergence behavior of the new iterative process with other iterative processes. [ABSTRACT FROM AUTHOR]

In this article, using only our recent concept of occasionally weakly biased mappings of type (A), in multiplicative metric spaces, we could find unique common fixed points. [ABSTRACT FROM AUTHOR]

The aim of this paper is to find out fixed point results with interpolative contractive conditions for pairs of generalized locally dominated mappings on closed balls in ordered dislocated metric spaces. We have explained our main result with an example. Our results generalize the result of Karapınar et al. (Symmetry 2018, 11, 8). [ABSTRACT FROM AUTHOR]

As a weaker form of fuzzy soft r-minimal continuity by Taha (2021), the notions of fuzzy soft almost (respectively (resp. for short) weakly) r-minimal continuous mappings are introduced, and some properties are given. Also, we show that every fuzzy soft r-minimal continuity is fuzzy soft almost (resp. weakly) r-minimal continuity, but the converse need not be true. After that, we introduce a concept of continuity in a very general setting called fuzzy soft r-minimal (A,B, C,D)-continuous mappings and investigate some properties of these mappings. [ABSTRACT FROM AUTHOR]

In the paper, the authors introduce a new notion "extended harmonically (s, m)-convex function" and establish some integral inequalities of the Hermite-Hadamard type for extended harmonically (s, m)-convex functions in terms of hypergeometric functions. [ABSTRACT FROM AUTHOR]

In this paper, the concept of Jordan triple higher (σ,τ)-homomorphisms on prime rings is introduced. A result of Herstein is extended on this concept from the ring into the prime ring . We prove that every Jordan triple higher (σ,τ)- homomorphism of ring into prime ring is either triple higher (σ,τ)- homomorphism or triple higher (σ,τ)-anti-homomorphism of into . [ABSTRACT FROM AUTHOR]

The objective of this paper is to determine a modified SP-iteration process for multi-valued mappings and to establish the convergence theorems for sequences generated by modified SP-iteration processes involving multi-valued Suzuki mappings converging to endpoints in uniformly convex hyperbolic spaces. The numerical example for supporting our main result is also presented. [ABSTRACT FROM AUTHOR]

We construct a new general Ostrowski type inequality for differentiable mappings whose first derivatives are bounded in terms of pre-assigned continuous functions. Applications to composite quadrature rules are also given. [ABSTRACT FROM AUTHOR]

This paper is concerned with the study of the fixed points of set-valued contractions on ordered g-metric spaces. The first part of the paper deals with the existence of fixed points for these mappings where the contraction condition is assumed for comparable variables. A coupled fixed point theorem is also established in the second part. [ABSTRACT FROM AUTHOR]

The goal of the research is to introduce new types of maps called semi totally Bccontinuous map and totally Bc-continuous map furthermore, study its properties. Additionally, we study the relationship of these functions and other known mappings are discussed. Keyw [ABSTRACT FROM AUTHOR]

In this work, we find the terms of the complex of characteristic zero in the case of the skew-shape (8,6, 3)/(u,1), where u = 1 and 2. We also study this complex as a diagram by using the mapping Cone and other concepts. [ABSTRACT FROM AUTHOR]

In this paper, we introduce weak and strong forms of ω-perfect mappings, namely the q-ω-perfect, weakly q-ω-perfect and stronglyq-ω-perfect mappings. Also, we investigate the fundamental properties of these mappings. Finally, we focused on studying the relationship between weakly q-ω-perfect and stronglyq -ω- perfect mappings. [ABSTRACT FROM AUTHOR]

The concepts of generalized higher derivations, Jordan generalized higher derivations, and Jordan generalized triple higher derivations on Γ-ring M into ΓMmodules X are presented. We prove that every Jordan generalized higher derivation of Γ-ring M into 2-torsion free ΓM-module X, such that aαbβc=aβbαc, for all a, b, c ÎM and α,βÎΓ, is Jordan generalized triple higher derivation of M into X. [ABSTRACT FROM AUTHOR]

Catastrophe theory predicts that in certain limits universal relations should exist between barrier heights, curvatures and the positions of local maxima and minima on a potential or free energy surface. In the present work we investigate these relations for both first- and second-order phase transitions, revealing that the ideal ratios often hold quite well over a wide range of conditions. This elementary catastrophe theory is illustrated for the melting transition of an atomic cluster, the isotropic-to-nematic transition in a liquid crystal, and the ferromagnetic-to-paramagnetic phase transition in the two-dimensional Ising model. [ABSTRACT FROM AUTHOR]

A new class of contraction pairs in uniformly convex metric spaces is introduced. The coincidence and best proximity points of this class of mappings is studied, and finally, illustrative examples are given to support the new results. [ABSTRACT FROM AUTHOR]

Economic theory is a mathematically rich field in which there are opportunities for the formal analysis of singularities and catastrophes. This article looks at the historical context of singularities through the work of two eminent Frenchmen around the late 1960s and 1970s. Rene Thom (1923-2002) was an acclaimed mathematician having received the Fields Medal in 1958, whereas Gerard De-breu (1921-2004) would receive the Nobel Prize in economics in 1983. Both were highly influential within their fields and given the fundamental nature of their work, the potential for cross-fertilisation would seem to be quite promising. This was not to be the case: Debreu knew of Thom's work and cited it in the analysis of his own work, but despite this and other applied mathematicians taking catas-trophe theory to economics, the theory never achieved a lasting following and relatively few results were published. This article reviews Debreu's analysis of the so called regular and crtitical economies in order to draw some insights into the economic perspective of singularities before moving to how singularities arise naturally in the Nash equilibria of game theory. Finally, a modern treatment of stochastic game theory is covered through recent work on the quantal response equilibrium. In this view, the Nash equilibrium is to the quantal response equilib-rium what deterministic catastrophe theory is to stochastic catastrophe theory, with some caveats regarding when this analogy breaks down discussed at the end. [ABSTRACT FROM AUTHOR]

In the present paper we establish some theorems on the existence of common approximate fixed points for a pair of generalized contractive type mappings with the property that the diameter of the set of common e--fixed points is tending to zero as e tends to zero. [ABSTRACT FROM AUTHOR]

In this work, by using an integral identity together with both the Hölder and the Power-Mean integral inequality we establish several new inequalities for n-time differentiable r-convexand concave functions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study an Ishikawa-like iterative algorithm to approximate a common solution of a split common null point problem and a fixed point problem of asymptotically pseudo-contractive mappings in the intermediate sense on unbounded domains. We prove that the sequence generated by the iterative scheme strongly converges to a common solution of the above-said problems. The method in this paper is novel and different from those given in many other papers. The results are the extension and improvement of the recent results in the literature. [ABSTRACT FROM AUTHOR]

The main goal of this note is to formulate sequence-based necessary second-order optimality conditions for a semilinear elliptic optimal control problem, with a pointwise pure state constraint and a pointwise mixed state-control constraint, governed by nonsmooth functions. Using a modification of the Dubovitskii-Milyutin scheme, we develop necessary second-order conditions for optimality, which depend on given sequences, in terms of sequential tangent sets and sequential directional derivatives for not necessarily twice differentiable mappings. [ABSTRACT FROM AUTHOR]

The asymptotic behavior of lower Q-homeomorphisms relative to a p-modulus in ℝn, n ≥ 2, at a point is studied. A number of logarithmic estimates for the lower limits under various conditions imposed on the function Q are obtained. Some applications of these results to the Orlicz-Sobolev classes Wloc1,φ in ℝn, n ≥ 3 under the Calderon-type condition imposed on the function φ and, in particular, to the Sobolev classes Wloc1,p for p > n - 1 are given. The example of a homeomorphism with finite distortion which shows the exactness of the found order of growth is constructed. [ABSTRACT FROM AUTHOR]

In this paper, to introduce approximate efficiency notions in variable ordering structures, some coradiant-valued maps are dealt with. Approximate nondominated and minimal elements are defined and some of their properties are studied. Corresponding to these concepts, necessary and sufficient conditions are provided. To obtain such conditions, some scalarization methods are investigated. The paper also investigates possible relationships between the Pascoletti-Serafini radial scalarization, approximate efficiency, approximate nondominance, and minimality utilizing some coradiant-valued maps. [ABSTRACT FROM AUTHOR]

In this paper, we prove some theorems and a common fixed point theorem in vector metric spaces for generalized contraction mappings and give an example. [ABSTRACT FROM AUTHOR]

In this paper, the concept of generalized difference for fuzzy n-cell numbers is presented, and we use the generalized difference to introduce and study the differentiability for fuzzy n-cell mappings. Next, the convexity for fuzzy n-cell mappings is studied, which is based on the concept of the partial ordering of fuzzy n-cell numbers proposed in this study. Finally, using the differentiability and the convexity for fuzzy n-cell mappings, we obtain the KKT optimality conditions for a class of fuzzy constrained minimization problem. [ABSTRACT FROM AUTHOR]

This methodological study provides a step-by-step introduction to a computational implementation of word and paradigm morphology using linear mappings between vector spaces for form and meaning. Taking as starting point the linear regression model, the main concepts underlying linear mappings are introduced and illustrated with R code. It is then shown how vector spaces can be set up for Latin verb conjugations, using 672 inflected variants of two verbs each from the four main conjugation classes. It turns out that mappings from form to meaning (comprehension), and from meaning to form (production) can be carried out loss-free. This study concludes with a demonstration that when the graph of triphones, the units that underlie the form space, is mapped onto a 2-dimensional space with a self-organising algorithm from physics (graphopt), morphological functions show topological clustering, even though morphemic units do not play any role whatsoever in the model. It follows, first, that evidence for morphemes emerging from experimental studies using, for instance, fMRI, to localize morphemes in the brain, does not guarantee the existence of morphemes in the brain, and second, that potential topological organization of morphological form in the cortex may depend to a high degree on the morphological system of a language. [ABSTRACT FROM AUTHOR]

It is shown that every knot or link is the set of complex tangents of a 3-sphere smoothly embedded in the 3-dimensional complex space. We show in fact that a 1-dimensional submanifold of a closed orientable 3-manifold can be realised as the set of complex tangents of a smooth embedding of the 3- manifold into the 3-dimensional complex space if and only if it represents the trivial integral homology class in the 3-manifold. The proof involves a new application of singularity theory of differentiable maps. [ABSTRACT FROM AUTHOR]

We consider an M / M/ c queue with catastrophes and state-dependent control at idle time. Properties of the queues which terminate when the servers become idle are first studied. Recurrence, equilibrium distribution, and equilibrium queue-size structure are studied for the case of resurrection and no catastrophes. All of these properties and the first effective catastrophe occurrence time are then investigated for the case of resurrection and catastrophes. In particular, we obtain the Laplace transform of the transition probability for the absorbing M / M/ c queue. [ABSTRACT FROM AUTHOR]

In this paper, new efficient quadrature rules are established using a newly developed special type of kernel for n-times differentiable mappings, having five steps. Some previous inequalities are also recaptured as special cases of our main inequalities. At the end, efficiency of the newly developed quadrature rules are discussed. [ABSTRACT FROM AUTHOR]

In this paper we focused our study on derived from Anosov diffeomorphisms (DA diffeomorphisms ) of the torus $$\mathbb {T}^3,$$ it is, an absolute partially hyperbolic diffeomorphism on $$\mathbb {T}^3$$ homotopic to a linear Anosov automorphism of the $$\mathbb {T}^3.$$ We can prove that if $$f: \mathbb {T}^3 \rightarrow \mathbb {T}^3 $$ is a volume preserving DA diffeomorphism homotopic to a linear Anosov A, such that the center Lyapunov exponent satisfies $$\lambda ^c_f(x) > \lambda ^c_A > 0,$$ with x belongs to a positive volume set, then the center foliation of f is non absolutely continuous. We construct a new open class U of non Anosov and volume preserving DA diffeomorphisms, satisfying the property $$\lambda ^c_f(x) > \lambda ^c_A > 0$$ for $$m-$$ almost everywhere $$x \in \mathbb {T}^3.$$ Particularly for every $$f \in U,$$ the center foliation of f is non absolutely continuous. [ABSTRACT FROM AUTHOR]

In this work, we establish some fixed point theorems for admissible weak contractions in b-metric-like spaces and b-metric-like spaces endowed with a partial order. Also, we give some fixed point theorems for cyclic contractive mapping in such spaces. The new results in this paper generalize and extend many theorems that we can find in the literature. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present some coincidence and common fixed point results for generalized contractive mappings with some special type auxiliary functions using the concept of partially weakly G-α-admissibility in the framework of G-metric space. Also we obtain certain new coincidence and common fixed point theorems in partially ordered G-metric spaces. Moreover, some examples are also provided to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

The purpose of this article is to resolve the non-linear programming problem of globally minimizing the real valued function x - d(x; Tx) where T is an R-contraction mapping. In fact, under appropriate conditions, we study the existence theorem of best proximity points for a cyclic R-contraction, which is a nice extension of the cyclic Meir-Keeler contraction. [ABSTRACT FROM AUTHOR]

We consider a generalized type of integral operator and study the mapping properties of the starlike functions under this operator. We indicate the relevant special cases of our results with some known ones. [ABSTRACT FROM AUTHOR]

Some new Ostrowski's inequalities for functions whose nth derivatives are quasi-convex are established. [ABSTRACT FROM AUTHOR]

In this paper, we derive five new versions of Landau-type theorems for biharmonic mappings of unit disk. Moreover, we prove that all five results are sharp when the bounds are equal to 1. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We study the local behavior of closed-open discrete mappings of the Orlicz-Sobolev classes in ℝ ; n ≥ 3 : It is proved that the indicated mappings have continuous extensions to an isolated boundary point x of a domain D/{ x}, whenever its inner dilatation of order p ∈ ( n − 1 ; n] has FMO (finite mean oscillation) at this point, and, in addition, the limit sets of f at x and on ∂ D are disjoint. Another sufficient condition for the possibility of a continuous extension can be formulated as a condition of divergence of a certain integral. [ABSTRACT FROM AUTHOR]

Some new inequalities of Fejér type for twice differentiable mappings are established via quantum calculus on finite intervals. The results presented are extensions of those given earlier. [ABSTRACT FROM AUTHOR]

A generalized Ostrowski inequality is given for differentiable functions, i.e. bounded below functions and bounded above functions. Some applications are discussed for solving error bounds of midpoint, trapezoidal, 1 3 Simpson's and 3 8 Simpson's quadrature rules. Error bounds for some nonstandard quadratures rules are also given. We also retrieve many established results. [ABSTRACT FROM AUTHOR]

The authors deduce a differentiable mapping integral identity with two parameters. Using this integral identity, this paper establishes new inequalities of Simpson type for extended ( s, m )-convex functions under certain conditions. This contributes to new better estimates than the earlier results. Finally, these inequalities are applied to special means. [ABSTRACT FROM AUTHOR]

Some new Ostrowski's inequalities for n-times differentiable mappings which are ϕ-convex are established. [ABSTRACT FROM AUTHOR]