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In this paper we introduce an argument property which gives an interesting relation between the classes of strongly convex and strongly starlike functions of order α and type β in the open unit disk. Also, the sufficient condition of starlikeness under cer-tain restrictions is obtained. [ABSTRACT FROM AUTHOR]

Based on the concepts of semigroup and Chang's fuzzy topological space, this paper gives the defines of the γ-fuzzy topological semigroups, γ-fuzzy topological left ideals (γ-fuzzy topological right ideals, γ-fuzzy topological intrinsic ideals and γ-fuzzy topological double ideals) and discusses the fuzzy continuous homomorphic image and the fuzzy continuous homomorphic inverse image of them. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new type of common fixed point for three mappings in Gb-complete Gb-metric space. On the other hand, we prove that the theory is also established in G-metric space and several corollaries and examples are listed. [ABSTRACT FROM AUTHOR]

In this paper, we prove several fixed point results for mappings of Caristi type in the setting of G-metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several extensions of Meir-Keeler contractive mappings in the structure of S-metric spaces. Then we investigate some existence, uniqueness, and generalized Ulam-Hyers stability results for the classes of MKC mappings via fixed point theory. Besides the the- oretical results, we also present some illustrative examples to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of continuous selection of a multivalued mapping in product space. Many authors provided existence of continuous map for lower semicontinuous. We provide continuous selection for weakly lower semicontinuous. Rhybinski [9] proved the existence for contraction type mapping. We prove the existence for some general type of mapping different from contraction mapping. [ABSTRACT FROM AUTHOR]

The Changhee polynomials and numbers are introduced in [3], and some interesting identities and properties of these polynomials are found by many researcher. In this paper, we consider the q-analogue of modified degen-erated Changhee polynomials and derive some new and interesting identities and properties of those polynomials. [ABSTRACT FROM AUTHOR]

This paper deals with the existence of continuous selection of a multivalued mapping in product space. Many authors provided existence of continuous map for lower semicontinuous. We provide continuous selection for weakly lower semicontinuous. Rhybinski [9] proved the existence for contraction type mapping. We prove the existence for some general type of mapping different from contraction mapping. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several extensions of Meir-Keeler contractive mappings in the structure of S-metric spaces. Then we investigate some existence, uniqueness, and generalized Ulam-Hyers stability results for the classes of MKC mappings via fixed point theory. Besides the the- oretical results, we also present some illustrative examples to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, a quadrature rule on an equidistant partition of the interval [a; b] for the finite Hilbert Transform of different classes of absolutely continuous functions via Simpson type inequalities is given, which may have the better error bounds than those obtained via trapezoid type inequalities. Some numerical experiments for different divisions of the interval [a; b] are also presented. [ABSTRACT FROM AUTHOR]

In this paper, we prove new common best proximity point theorems for proximally com- muting mappings in complete non-Archimedean PM-spaces. Our results generalized the recent results of S. Basha [Common best proximity points: global minimization of multi-objective functions, J. Global Optim. 49(2011), 15{21] and C. Mongkolkeha, P. Kumam [Some common best proximity points for proximity commuting mappings, Optim. Lett. 7 (2013), 1825{1836]. [ABSTRACT FROM AUTHOR]

In this paper, we study the superstability for the p-mixed trigonometric functional equation: ... where G is a locally compact group, f , g : G → C are continuous functions, μ is a complex bounded measure and σ is a continuous involution of G. We also give some applications. [ABSTRACT FROM AUTHOR]

In this paper, utilizing the concepts of weakly biased mappings and occasionally weakly biased mappings for a pair of self-mappings in Menger PM-spaces, some new common fixed point theorems under contractive conditions are obtained. Some examples are also given to exemplify our main results. [ABSTRACT FROM AUTHOR]

In this paper, we study the stability of solutions of a nonlinear functional integral equation of fractional order with control variable. The equation is considered in the Banach space of real functions defined, continuous and bounded on an unbounded interval. Existence of a control variable provides the extension of some previous results obtains in other studies. We will also include an example in order to indicate the validity of the assumptions. [ABSTRACT FROM AUTHOR]

In this paper we aim to study the separation problem for the second order elliptic differential expression of the form ... with the real-valued positive continuous functions bi, on a complete Riemannian manifold (M, g) with metric g, where ΔM is the scalar Laplacian on M and q ≥ 0 is a locally square integrable function on M. In the terminology of Everitt and Giertz, E is said to be separated in L² (M) if for u ∊ L² (M) such that Eu ∊ L² (M), we have ... and qu ∊ L² (M). We give sufficient conditions for E to be separated in L² (M). [ABSTRACT FROM AUTHOR]

This paper proposes a new weighted bivariate blending rational interpolator only based on function values. The interpolation function with some free parameters has simple and explicit mathematical representation, and it is C¹-continuous for any positive parameters and weighted coefficient. More important, the shape of the interpolating surfaces can be modified by selecting suitable parameters and weighted coefficient. In order to meet the needs of practical design, a local shape control method is employed to control the shape of interpolating surfaces. In the special case, the method of "Central Point Value Control" is discussed. [ABSTRACT FROM AUTHOR]

This paper addresses the approximation by feed-forward neural networks (FNNs) with sigmoidal active functions on the unit sphere. Firstly, some nice properties of typical logistic function are derived, and the function and its derivatives are taken as active functions to construct spherical FNNs approximation operators, where the spherical Cesáro mean is employed as a key link in constructing the operators. Subsequently, by using spherical quadrature formula and Marcinkiewicz-Zygmund type inequality, the error of the operators approximating continuous spherical function is estimated, and a Jackson type theorem is established by means of the best polynomial approximation. [ABSTRACT FROM AUTHOR]

In this paper, we explore two types of Hausdorff intuitionistic fuzzy metrics on compact sets, and prove that they are identical. Also, we prove that if two intuitionistic fuzzy metric spaces induce the same topology, then the corresponding Hausdorff intuitionistic fuzzy metric topological spaces coincide. [ABSTRACT FROM AUTHOR]

In this paper, we introduce general Jensen mappings of type I and II, and prove the Hyers-Ulam stability of these mappings. [ABSTRACT FROM AUTHOR]

Let I be a compact interval and (II, D) be the set of all nonempty connected closed subsets of I with the Hausdoff metric D. Suppose that f is a continuous map from I to II. In this paper, we show that if f has n-orbits and n⊳m (in the Sharkovskii ordering), then it also has m-orbits. [ABSTRACT FROM AUTHOR]